Math in Focus

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 15 Practice 6 Volume of a Rectangular Prism and Liquid provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 15 Practice 6 Answer Key Volume of a Rectangular Prism and Liquid

Write each measure in milliliters.

Question 1.
690 cm³ = ____________
Answer:
690 cm³ = 690 milliliters,

Explanation:
Given 690 cm³ to measure in milliliters,
as 1 cubic centimeter is equal to 1 milliliters
so 690 cm³ = 690 X 1 milliliters = 690 milliliters.

Question 2.
207 cm³ = ____________
Answer:
207 cm³ = 207 milliliters,

Explanation:
Given 207 cm³ to measure in milliliters,
as 1 cubic centimeter is equal to 1 milliliters
so 207 cm³ = 207 X 1 milliliters = 207 milliliters.

Question 3.
2,000 cm³ = ____________
Answer:
2,000 cm³ = 2,000 milliliters,

Explanation:
Given 2,000 cm³ to measure in milliliters,
as 1 cubic centimeter is equal to 1 milliliters
so 2,000 cm³ = 2,000 X 1 milliliters = 2,000 milliliters.

Question 4.
4,600 cm³ = ____________
Answer:
4,600 cm³ = 4,600 milliliters,

Explanation:
Given 4,600 cm³ to measure in milliliters,
as 1 cubic centimeter is equal to 1 milliliter
so 4,600 cm³ = 4,600 X 1 milliliters = 4,600 milliliters.

Write each measure in cubic centimeters.

Question 5.
420 mL = ________cm³,
Answer:
420 ml = 420 cm³,

Explanation:
Given 420 ml to measure in cubic centimeters,
as 1 milliliters is equal to 1 cubic centimeters,
so 420 ml = 420 X 1 cubic centimeters = 420 cm³ .

Question 6.
568 mL = ____________cm³,
Answer:
568 ml = 568 cm³,

Explanation:
Given 568 mL to measure in cubic centimeters,
as 1 milliliters is equal to 1 cubic centimeters,
so 568 ml = 568 X 1 cubic centimeters = 568 cm³ .

Question 7.
3 L = ____________cm³,
Answer:
3 L = 3,000 X 1 ml = 3,000 cm³,

Explanation:
Given 3 L = 3,000 ml to measure in cubic centimeters,
as 1 milliliters is equal to 1 cubic centimeters,
so 3,000 ml = 3,000 X 1 cubic centimeters = 3,000 cm³ .

Question 8.
15 L = ___cm³,
Answer:
15 L = 15,000 X 1 ml = 15,000 cm³,

Explanation:
Given 15 L = 15,000 ml to measure in cubic centimeters,
as 1 milliliters is equal to 1 cubic centimeters,
so 15,000 ml = 15,000 X 1 cubic centimeters = 15,000 cm³ .

Question 9.
2 L 125 mL = ___________cm³,
Answer:
2 L 125 mL = 2,125 X 1 cubic centimeters = 2,125 cm³,

Explanation:
Given 2 L 125 mL = 2 ,125 mL to measure in cubic centimeters,
as 1 milliliters is equal to 1 cubic centimeters,
so 2L 125 mL = 2,125 X 1 cubic centimeters = 2,125 cm³ .

Question 10.
5 L 60 mL = ____________cm³,
Answer:
5 L 60 mL = 5,060 X 1 cm = 5,060 cm³,

Explanation:
Given 5 L 60 mL = 5,060 mL to measure in cubic centimeters,
as 1 milliliters is equal to 1 cubic centimeters,
so 5 L 60 mL = 5,060 X 1 cubic centimeters = 5,060 cm³.

Question 11.
10 L 50mL = _______cm³,

Explanation:
Given 10 L 50 mL = 10,050 mL to measure in cubic centimeters,
as 1 milliliters is equal to 1 cubic centimeters,
so 10 L 50 mL = 10,050 X 1 cubic centimeters = 10,050 cm³ .

Question 12.
7 L 2mL = ____________cm³,
Answer:
7 L 2 mL = 7,002 cm³,

Explanation:
Given 7 L 2 mL = 7 ,002 mL to measure in cubic centimeters,
as 1 milliliters is equal to 1 cubic centimeters,
so 7 L 2 mL = 7,002 X  1 cubic centimeters = 7,002 cm³.

Do you know which national park is the oldest in the United States?
Match the letters to the answers to find out.

Answer:
YELLOW STONE  is the oldest national park in the United States,

Explanation:
Yes, After matching the letters the answer is YELLOW STONE,
the oldest national park in the United States.

Write each measure in liters and milliliters.

Question 13.
720 cm³ = ____________milliliters³,
Answer:
720 cm³ = 720 milliliters³,

Explanation:
Given 720 cm³ to measure in cubic centimeters,
as 1 cubic centimeter is equal to 1 milliliters
so 720 cm³ = 720 X 1 cubic centimeters = 720 milliliters.

Question 14.
7,000 cm³ = _________,
Answer:
7,000 cm³ = 7 L ,

Explanation:
Given 7,000 cm³ to measure in cubic centimeters,
as 1 cubic centimeter is equal to 1 milliliters and
1 liter is equal to 1000 milliliters
so 7,000 cm³ = 7,000 X 1 milliliters = 7 X 1,000 milliliters =  1 L.

Question 15.
2,050 cm³ = ___________
Answer:
2,050 cm³ = 2 L 50 mL ,

Explanation:
Given 2,050 cm³ to measure in cubic centimeters,
as 1 cubic centimeter is equal to 1 milliliters and
1 liter is equal to 1000 milliliters
so 2,050 cm³ = 2,050 X 1 milliliters = 2  X 1,050 milliliters =  2 L, 50 mL.

Question 16.
1,470 cm³ = ____________
Answer:
1,470 cm³ = 1 L 470 mL ,

Explanation:
Given 1,470 cm³ to measure in cubic centimeters,
as 1 cubic centimeter is equal to 1 milliliters and
1 liter is equal to 1000 milliliters
so 1,470 cm³ = 1,470 X 1 milliliters = 1  X 1,470 milliliters =  1 L, 470 mL.

Question 17.
9,801 cm³ = ____________
Answer:
9,801 cm³ = 9 L 801 mL ,

Explanation:
Given 9,801 cm³ to measure in cubic centimeters,
as 1 cubic centimeter is equal to 1 milliliters and
1 liter is equal to 1000 milliliters
so 9,801 cm³ = 9,801 X 1 milliliters = 9 L X 801 milliliters =  9 L, 801 mL.

Question 18.
4,003 cm³ = ____________
Answer:
4,003 cm³ = 4 L 3 mL ,

Explanation:
Given 4,003 cm³ to measure in cubic centimeters,
as 1 cubic centimeter is equal to 1 milliliters and
1 liter is equal to 1000 milliliters
so 4,003 cm³ = 4,003 X 1 milliliters = 4 L X 3 milliliters =  4 L, 3 mL.

Question 19.
10,600 cm³ = ____________
Answer:
10,600 cm³ = 10,600 mL ,

Explanation:
Given 10,600 cm³ to measure in cubic centimeters,
as 1 cubic centimeter is equal to 1 milliliters and
1 liter is equal to 1000 milliliters
so 10,600 cm³ = 10,600 X 1 milliliters = 10 L X 600 milliliters =  10 L, 600 mL.

Question 20.
1,075 cm³ = _____1 L 075 mL_______
Answer:
1,075 cm³ = 1 L 075 mL ,

Explanation:
Given 1,075 cm³ to measure in cubic centimeters,
as 1 cubic centimeter is equal to 1 milliliters and
1 liter is equal to 1000 milliliters
so 1,075 cm³ = 1 L X  75 milliliters = 1 L X 75 milliliters =  1 L, 75 mL.

Find the volume of water in each rectangular tank in milliliters.
(Hint: 1 cm³ = 1 mL)

Question 21.

Volume = ____288 mL_______
Answer:
Volume = 288 mL,

Explanation:
Given rectangular tank has volume 12 cm X 4 cm X 6 cm = 288 cm³
as 1 cubic centimeter is equal to 1 milliliters,
so, 288 cm³ = 288 mL.

Question 22.

Volume = ___________
Answer:
Volume = 315 mL,

Explanation:
Given rectangular tank has volume as 7 cm X 5 cm X 9 cm = 315 cm³
as 1 cubic centimeter is equal to 1 milliliters,
so 315 cm³ = 315 mL.

Find the volume of water in each rectangular tank in liters and milliliters.
(Hint: 1,000 cm³ = 1 L)

Question 23.

Volume = ___________
Answer:
Volume = 1 L,

Explanation:
Given rectangular tank has volume as 25 cm X 8 cm X 5 cm = 1000 cm³ ,
1,000 cm³ to measure in cubic centimeters,
as 1 cubic centimeter is equal to 1 milliliters and
1 liter is equal to 1000 milliliters
so 1,005 cm³ = 1,000 milliliters = 1 L.

Question 24.

Volume = ___________
Answer:
Volume = 1 L 8 mL,

Explanation:
Given rectangular tank has volume as 28 cm X 6 cm X 6 cm = 1,008 cm³ ,
1,008 cm³ to measure in cubic centimeters,
as 1 cubic centimeter is equal to 1 milliliters and
1 liter is equal to 1000 milliliters
so 1,008 cm³ = 1,008 milliliters = 1 L 8 mL.

Question 25.

Volume = ____ _______
Answer:
Volume = 1 L 458 mL,

Explanation:
Given rectangular tank has volume as 18 cm X 9 cm X 9 cm = 1,458 cm³ ,
1,458 cm³ to measure in cubic centimeters,
as 1 cubic centimeter is equal to 1 milliliters and
1 liter is equal to 1000 milliliters
so 1,458 cm³ = 1,458 milliliters = 1 L 458 mL.

Question 26.

Volume = ___________
Answer:
Volume = 1 L 456 mL,

Explanation:
Given rectangular tank has volume as 26 cm X 8 cm X 7 cm = 1,456 cm³ ,
1,456 cm³ to measure in cubic centimeters,
as 1 cubic centimeter is equal to 1 milliliters and
1 liter is equal to 1000 milliliters
so 1,456 cm³ = 1,456 milliliters = 1 L 456 mL.

Solve. Show your work.

Question 27.
How much water is in this tank when it is \(\frac{1}{3}\) full?

Answer:
The tank is filled with volume 218 cm³,

Explanation:
Given rectangular tank has volume with dimensions 12 cm X 6 cm X 9 cm = 648 cm³,
water in the tank is \(\frac{1}{3}\),
So \(\frac{1}{3}\) X 648 cm³ = 218 cm³.

Question 28.
This rectangular tank is filled with water to a height of 4 centimeters.
How much more water is needed to fill the tank completely?

Answer:
Water needed to fill the tank completely is 432 cm³,

Explanation:
Given rectangular tank has volume with dimensions 18 cm X 12 cm X 6 cm = 1,296 cm³ and
tank is filled with water to a height of 4 centimeters,
so volume of tank with water filled is 18 cm X 12 cm X 4 cm = 864 cm³,
Therefore more water is needed to fill the tank completely is 1,296 cm³– 864 cm³  = 432 cm³.

Solve. Show your work.

Question 29.
A cubical tank with an edge length of 20 centimeters is filled with 3.75 liters of water.
How much more water is needed to fill the tank completely? Give your answer in liters.

Answer:
More water needed to fill the tank completely is 4.25 liters,

Explanation:
Given rectangular tank has volume with dimensions 20 cm X 20 cm X 20 cm = 8,000 cm³,
So the volume of the tank in liters is 8 X 1000 mL= 8 L,
and tank cubical tank with an edge length of 20 centimeters is filled with 3.75 liters of water.
Therefore more water is needed to fill the tank completely is 8 L – 3.75 L = 4.25 liters.

Question 30.
The rectangular tank shown is \(\frac{1}{4}\)-filled with water.
Then another 1 liter 400 milliliters of water is added.
Find the volume of water in the tank in the end. Give your answer in liters and milliliters.

Answer:
The volume of water in the tank in the end is 2L 520 mL,

Explanation:
Given rectangular tank has volume with dimensions 28 cm X 20 cm X 8 cm = 4,480 cm³,
and the rectangular tank shown is \(\frac{1}{4}\)-filled with water.
So volume of tank in liters is \(\frac{1}{4}\) X 4,480 cm³ = 1,120 cm³,
1 L 120 mL to this another 1 liter 400 milliliters of water is added and tank has
1 L 120 mL + 1L 400 mL =  2L 520  mL.

Solve. Show your work.

Question 31.
This container is half-filled with oil. What is the volume of oil in the container?
Give your answer in liters and milliliters.

Answer:
The container is filled with volume 1 L 862 mL,

Explanation:
Given rectangular tank has volume with dimensions 14 cm X 14 cm X 19 cm = 3,724 cm³,
Container is half-filled with oil so volume of oil in the container is
\(\frac{1}{2}\) X 3,724 cm³ = 1,862 cm³ = 1 L 862 mL.

Question 32.
A cubical tank whose edges each measure 1 2 centimeters is half-filled with water.
The water is poured into an empty rectangular tank measuring
10 centimeters by 8 centimeters by 7 centimeters until it is full.
How much water is left in the cubical tank? Give your answer in milliliters.

Answer:
Water left in the cubical tank is  1,168 cm³,

Explanation:
Given a cubical tank whose edges each measure 1 2 centimeters is half-filled with water.
So volume with dimensions 12 cm X 12 cm X 12 cm = 1,728 cm³ and
the water is poured into an empty rectangular tank measuring
10 centimeters by 8 centimeters by 7 centimeters until it is full.
So water poured is 10 cm X 8 cm X 7 cm = 560 cm³ ,
therefore, water left in the cubical tank is 1,728 cm³ – 560 cm³ = 1,168 cm³.

Solve. Show your work.

Question 33.
The rectangular swimming pool shown contains 600 cubic meters of water.
How much more water has to be added so that the water level is 1 meter from the top?

Answer:
Volume left in swimming pool is 4,900 cubic meters,

Explanation:
Given swimming pool contains volume of 50 m X 30 m X 3 m = 4,500 cubic meters
and the rectangular swimming pool shown contains 600 cubic meters of water.
and that the water level is 1 meter from the top is
4,500 cubic meters + 1 L = 5,500 cubic meters,
therefore, volume left in swimming pool is
5,500 cubic meters – 600 cubic meters = 4,900 cubic meters.

Question 34.
The rectangular tank shown is filled completely with water.
How much water must be taken out so the height of the water
level in the tank is 10 centimeters? Give your answer in milliliters.

Answer:
Water to be taken out, so the height of the water
level in the tank is 10 centimeters is 240 cubic meters,

Explanation:
Given the rectangular tank shown is filled completely with water,
so, volume of 6 cm X 8 cm X 15 cm = 720 cubic meters,
The height of the water level in the tank is 10 centimeters,
so, volume of 6 cm X 8 cm X 10 cm = 480 cubic meters,
Water to be taken out is 720 cubic meters – 480 cubic meters = 240 cubic meters.

Solve. Show your work.

Question 35.
The large rectangular tank shown is \(\frac{4}{5}\)-filled with water.
The water is then poured into the smaller rectangular container until it is full.
How much water is left in the tank? Give your answer in liters and milliliters.

Answer:
Water left in the tank is 1,920 cm³,

Explanation:
Given large rectangular tank has volume with dimensions 15 cm X 15 cm X 12 cm = 2,700 cm³,
The large rectangular tank shown is \(\frac{4}{5}\) filled with water
therefore tank has \(\frac{4}{5}\) X 2,700 cm³ =
\(\frac{4 X 2,700}{5}\) cm³ = 2,160 cm³.
The water is then poured into the smaller rectangular container until it is full.
Volume of smaller rectangular container with dimensions 6 cm X 5 cm X 8 cm = 2,40 cm³,
Water left in the tank is 2,160 cm³– 2,40 cm³= 1,920 cm³.

Question 36.
Water flows into this tank at 8 liters per minute. How long will it take to fill the tank?

Answer:
long it will take to fill the tank is 7.5 minutes,

Explanation:
Given rectangular tank has volume with dimensions
60 cm X 50 cm X 20 cm = 60,000 cm³ = 60 liters,
and Water flows into this tank at 8 liters per minute.
So long will it take to fill the tank is 60 liters ÷ 8 liters per minute = 7.5 minutes.

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 15 Practice 5 Volume of a Rectangular Prism and Liquid provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 15 Practice 5 Answer Key Volume of a Rectangular Prism and Liquid

Write the length, width, and height of each rectangular prism or cube.

Example

Answer:
Volume of given rectangular prism is 240 cm³,

Explanation:
Given Length = 5 cm, Width = 8 cm and Height = 6 cm,
Volume of the rectangular prism is lwh = 5 cm X 8 cm X 6 cm = 240 cm³.

Question 1.

Length = _____12_______ ft
Width = _______12_____ ft
Height = _______20_____ ft
Answer:
Volume of the recangular prism is cube is 2,880 ft³,

Explanation:
Given rectangular prism has length 12 ft, width 12 ft and height 20 ft,
so volume of the rectangular prism is 12 ft X 12 ft X 20 ft = 2,880 ft³.

Question 2.

Length = ____12________ in.
Width = ______25______ in.
Height = _______16_____ in.
Answer:
Volume of the recangular prism is 4,800 in³,

Explanation:
Given rectangular prism has length 12 in, width 25 in and height 16 in,
so volume of the rectangular prism is 12 in X 25 in X 16 in = 4,800 in³.

Question 3.

Length = _____18_______ m
Width = ______18______ m
Height = ______18______ m
Answer:
Volume of the cube is 5832 m³,

Explanation:
Given cube has length 18 m, width 18 m and height 18 m,
so volume of the cube is 18 m X 18 m X 18 m = 5832  m³.

Find the volume of each rectangular prism.

Question 4.

The length of the rectangular prism is _______12_____ centimeters.
The width of the rectangular prism is _______5_____ centimeters.
The height of the rectangular prism is _______9_____ centimeters.
Volume of the rectangular prism = length × width × height
= _____12_______ × _____5_______ ×______9______
= ______540______ cm³
Answer:
Volume of the recangular prism is cube is 540 cm³,

Explanation:
Given rectangular prism has length 12 cm, width 5 cm and height 9 cm,
so volume of the rectangular prism is 12 cm X 5 cm X 9 cm = 540 cm³.

Question 5.

Volume = _____24_______in³
Answer:
Volume of the recangular prism is 24 in³,

Explanation:
Given rectangular prism has length 3 in, width 4 in and height 2 in,
so volume of the rectangular prism is 3 in X 4 in X 2 in = 24 in³.

Question 6.

Volume = _____120_______ yd³,
Answer:
Volume of the recangular prism is 120 yd³,

Explanation:
Given rectangular prism has length 5 yd, width 8 yd and height 3 yd,
so volume of the rectangular prism is 5 yd X 8 yd X 3 yd = 120 yd³.

Find the volume of each rectangular prism or cube.

Question 7.

Volume = _____120_______ft³,
Answer:
Volume of the recangular prism is cube is 120 ft³,

Explanation:
Given rectangular prism has length 4 ft, width 6 ft and height 5 ft,
so volume of the rectangular prism is 4 ft X 6 ft X 5 ft = 2,880 ft³.

Question 8.

Volume = ______4,096______m³,
Answer:
Volume of the cube is 4,096 m³,

Explanation:
Given cube has length 18 m, width 18 m and height 18 m,
so volume of the cube is 16 m X 16 m X 16 m = 4,096 m³.

Question 9.

Volume = _____384_______cm³,

Answer:
Volume of the recangular prism is cube is 384 cm³,

Explanation:
Given rectangular prism has length 4 cm, width 24 cm and height 4 cm,
so volume of the rectangular prism is 4 cm X 24 cm X 4 cm = 384 cm³.

Question 10.

Volume = _____189_______ in³,
Answer:
Volume of the recangular prism is 189 in³,

Explanation:
Given rectangular prism has length 7 in, width 9 in and height 3 in,
so volume of the rectangular prism is 7 in X 9 in X 3 in = 189 in³.

Question 11.

Volume = ______448______ in³,
Answer:
Volume of the recangular prism is 448 in³,

Explanation:
Given rectangular prism has length 8 in, width 8 in and height 7 in,
so volume of the rectangular prism is 8 in X 8 in X 7 in = 448 in³.

Question 12.

Volume = _____120_______ m³,
Answer:
Volume of the recangular prism is 120 m³,

Explanation:
Given rectangular prism has length 8 m, width 3 m and height 5 m,
so volume of the rectangular prism is 8 m X 3 m X 5 m = 120 m³.

Find the volume of each rectangular prism.

Question 13.
Length = 5 cm
Width = 12 cm
Height = 9 cm
Volume = ______540_______ cm³,
Answer:
Volume of the recangular prism is 540 cm³,

Explanation:
Given rectangular prism has length 5 cm, width 12 cm and height 9 cm,
so volume of the rectangular prism is 5 cm X 12 cm X 9 cm = 540 cm³.

Question 14.
Length = 10 in.
Width = 25 in.
Height = 14 in.
Volume = ______3,500_______ in³,
Answer:
Volume of the recangular prism is 3,500 in³,

Explanation:
Given rectangular prism has length 10 in, width 25 in and height 14 in,
so volume of the rectangular prism is 10 in X 25 in X 14 in = 3,500 in ³.

Question 15.
Length = 7 m
Width = 12 m
Height = 8 m
Volume = _____672________ m³,
Answer:
Volume of the recangular prism is 672 m³,

Explanation:
Given rectangular prism has length 7 m, width 12 m and height 8 m,
so volume of the rectangular prism is 7 m X 12 m X 8 m = 672 m³.

Question 16.
Length = 24 ft
Width = 10 ft
Height = 15 ft
Volume = ______3,600_______ ft³,
Answer:
Volume of the recangular prism is 3,600 ft³,

Explanation:
Given rectangular prism has length 24 ft, width 10 ft and height 15 ft,
so volume of the rectangular prism is 24 ft X 10 ft X 15 ft = 3,600 ft³.

Solve. Show your work.

Question 17.
Find the volume of a cube with edges measuring 9 centimeters.
Answer:
Volume of the cube is 729 cm³,

Explanation:
Given cube has edges measuring 9 centimeters each
means length 9 cm, width 9 cm and height 9 cm,
so volume of the cube is 9 cm X 9 cm X 9 cm = 729 cm³.

Question 18.
A rectangular prism has a width of 8 feet and a height of 5 feet.
Its length is twice its width.
Find the volume of the rectangular prism.
Answer:
Volume of the recangular prism is 640 ft³,

Explanation:
Given rectangular prism has width 8 feet and height 5 feet,
its length is twice its width so length is 2 X 8 feet = 16 feet,
so volume of the rectangular prism is 16 ft X 8 ft X 5 ft =640 ft³.

Question 19.
The base of a rectangular prism is a square whose sides each measure 9 inches.
The height of the rectangular prism is 11 inches. Find its volume.
Answer:
Volume of the recangular prism is 891 in³,

Explanation:
Given the base of a rectangular prism is a square whose sides are each measure 9 inches.
The height of the rectangular prism is 11 inches.
So the rectangular prism has length 9 inches, width 9 inches and height 11 inches,
therefore, volume of the rectangular prism is 9 inches X 9 inches X 11 inches = 891 in³.

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 15 Practice 3 Nets and Surface Area provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 15 Practice 3 Answer Key Nets and Surface Area

Find the surface area of each cube.

Example

3 × 3 = 9
6 × 9 = 54
Surface area of cube = 54 cm²

Question 1.

Answer:
S.A = 150 in.²,

Explanation:
As we know surface area (S.A) of cube is 6 X (side X side),
Given cube has 5 in side therefore S.A = 6 X (5 in X 5 in) =
6 X (25 in.²) = 150 in.².

Question 2.

Answer:
S.A = 864 in.²,

Explanation:
As we know surface area (S.A) of cube is 6 X (side X side),
Given cube has 12 in side therefore S.A = 6 X (12 in X 12 in) =
6 X (144 in.²) = 864 in.².

Question 3.

Answer:
S.A = 1924 cm²,

Explanation:
As we know surface area (S.A) of cube is 6 X (side X side),
Given cube has 18 in side therefore S.A = 6 X (18 cm X 18 cm) =
6 X (324 cm²) = 1924 cm².

Find the surface area of each rectangular prism.

Example

2 × 8 × 4 = 64
2 × 22 × 4 = 176
2 × 22 × 8= 352
64 + 176 + 352 = 592
Surface area of rectangular prism = 592 in.²

Question 4.

Answer:
The surface area of rectangular prism is 684 in.²,

Explanation:
As the surface area of rectangular prism is
2 X [(width X length) + (height X length) + (height X width)],
= 2 X [(12 in X 15 in) + (6 in X 15 in) + (6 in X 12 in)],
= 2 X [(180 in.²) + (90 in.²) + (72 in.²)]
= 2 X [ 342 in.²],
= 684 in.².

Question 5.

Answer:
The surface area of rectangular prism is 952 m.²,

Explanation:
As the surface area of rectangular prism is
2 X [(width X length) + (height X length) + (height X width)],
= 2 X [(8 m X 19 m) + (12 m X 19 m) + ( 12 m X  8 m)],
= 2 X [(152 m.²) + (228 m.²) + (96 m.²)]
= 2 X [ 476 m.²],
= 952 m.².

Find the surface area of each triangular prism.

Example

Answer:
Surface area of triangular prism = 228 in.²

Explanation:
2 × \(\frac{1}{2}\) × 3 in × 4 in = 12 in.²
4 in × 18 in = 72 in.²
3 in × 18 in = 54 in.²
5 in × 18 in = 90 in.²
12 in.²+ 72  in.² + 54 in.² + 90 in.² = 228 in.²
Surface area of triangular prism = 228 in.²

Question 6.

Answer:

Explanation:
The formula for the surface area of triangular prism is:
Surface area = bh + (l X w + w X h + l X h),
= (5 cm X 35 cm) + (13 cm X 24 cm + 24 cm X 5 cm + 13 cm X 35 cm),
= 175  cm²+ ( 312 cm²+ 120 cm²+ 455 cm²)
= 1,062 cm².

Solve. Show your work.

Question 7.

Jeffrey cuts out the net of a box he wants to make.
Find the surface area of the box.

Answer:
The surface area of Jeffrey box is 684 in.²,

Explanation:
Jeffrey box contains 1 square of 8 in side,
2 rectangles of length 15 in and 8 in width,
2 rectangles of length 15 in and 10 in width,
1 rectangle of length 10 in and 8 in width,
So the surface area of Jeffrey box is
8 in X 8 in = 64 in.²
2 X (15 in X 8 in) = 2 X 120 in.²= 240 in.²
2 X (15 in X 10 in) = 2 X 150 in.²= 300 in.²
1 X (10 in X 8 in) = 80 in.²
surface area = 64 in.²+ 240 in.² + 300 in.²+ 80 in.²,
surface area = 684 in.².

Solve. Show your work.

Question 8.
This glass fish tank does not have a cover. Find the total area of the
glass panels used to make the tank.

Answer:
The total area of the glass panels used to make the tank is = 288 cm²,

Explanation:
Given glass fish tank that does not have a cover. The total area of the
glass panels used is in the shape of cuboid,
therefore to make the tank we need
2(lw + lh + hw) = 2 X [(24 cm + 21 cm) + (24 cm + 27 cm) + (27 cm + 21 cm)],
= 2 X (45 cm² + 51 cm² + 48 cm²),
= 2 X (144 cm²),
= 288 cm².

Question 9.
The tank shown is made of steel. It does not have a cover.
Find the area of steel sheet used to make the tank.

Answer:
The total area of the steel sheet is 190 ft²,

Explanation:
Given tank shown is made of steel,
The total area of the steel sheet used is in the shape of rectangular prism,
therefore to make the tank we need
2(lw + lh + hw) = 2 X [(6 1/2 ft + 28 ft) + (6 1/2 ft + 13 ft) + (13 ft + 28 ft)],
= 2 X (34 1/2 ft² + 19 1/2 ft² + 41 ft²),
= 2 X (95 ft²),
= 190 ft².

Question 10.
A rectangular piece of poster board measures 60 centimeters by 80 centimeters.
Linn draws the net of a box on the poster board and cuts it out.
If the box measures 10 centimeters by 16 centimeters by 27 centimeters,
what is the area of the poster board left?
Answer:
The area of the poster board left 3076 cm²,

Explanation:
Given a rectangular piece of poster board measures 60 centimeters by 80 centimeters.
Area of poster board is 60 cm X 80  cm = 4800 cm².
Linn draws the net of a box on the poster board and cuts it out.
If the box measures 10 centimeters by 16 centimeters by 27 centimeters,
the surface area of the box is
2(lw + lh + hw) = 2 X [(10 cm + 16 cm) + (16 cm + 27 cm) + (27 cm + 10 cm)],
= 2 X (160 cm² + 432 cm² + 270 cm²),
= 2 X (862 cm²),
= 1724 cm²,
therefore 4800 cm²– 1724 cm² = 3076 cm².

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 15 Practice 2 Drawing Cubes and Rectangular Prisms provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 15 Practice 2 Answer Key Drawing Cubes and Rectangular Prisms

Draw on dot paper.

Question 1.
Draw a unit cube.

Answer:

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
Shown the volume of a unit cube = Side × Side × Side,
= 1 unit × 1 unit × 1 unit,
= 1 unit cubes.

Question 2.
Draw two different views of a rectangular prism made up of 2 unit cubes.

Answer:

Explanation:
Drawn two different views of a rectangular prism made up of 2 unit cubes,
A unit cube has all its sides of length 1 unit
and 2 unit cubes shows the volume of a 2 unit cubes = 2 X (Sides × Side × Side),
= 2 X (1 unit × 1 unit × 1 unit),
= 2 unit cubes.

Question 3.
Draw two different solids made up of 3 unit cubes each.

Answer:

Explanation:
Drawn two different views of a rectangular prism made up of 3 unit cubes,
A unit cube has all its sides of length 1 unit
and 3 unit cubes shows the volume of a 3 unit cubes = 3 X (Sides × Side × Side),
= 3 X (1 unit × 1 unit × 1 unit),
= 3 unit cubes.

Draw each cube or rectangular prism on the dot paper.

Example

Question 4.

Answer:

Explanation:
Drawn one cube on the dot paper,
As given cube has 4 units shown the volume of cube =
side X side X side = 4 units X 4 units X 4 units = 64 unit cubes.

Question 5.

Answer:

Explanation:
Drawn one rectangular prism on the dot paper,
As given rectangular prism has 4 units X 4 units  X 1 unit =
16 unit cubes rectangular prism.

Question 6.

Answer:

Explanation:
Drawn one rectangular prism on the dot paper,
As given rectangular prism has 4 units X 2 units  X 2 units =
16 unit cubes rectangular prism.

Draw each cube or rectangular prism on the dot paper.

Question 7.

Answer:

Explanation:
Drawn one rectangular prism on the dot paper,
As given rectangular prism has 2 units X 2 units  X 2 units =
8 unit cubes rectangular prism.

Question 8.

Answer:

Explanation:
Drawn one rectangular prism on the dot paper,
As given rectangular prism has 3 units X 1 unit  X 1 unit =
3 unit cubes rectangular prism.

Draw a cube with edges 4 times as long as the edges of this unit cube.

Question 9.

Answer:

Explanation:
Given 1 unit cube with volume 1 unit X 1 unit X 1 unit = 1 cubic unit and
Drawn a cube with edges 4 times as long as the given edge so the volume is
4 units X 4 units X 4 units = 64 cubic units.

Complete the drawing of each cube or rectangular prism.

Question 10.

Answer:

Explanation:
Completed the drawing of given cube as shown above
which has 2 units.

Question 11.

Answer:

Explanation:
Completed the drawing of given cube as shown above
which has 3 units.

Question 12.

Answer:

Explanation:
Completed the drawing of given rectangular prism as shown above
which has 2 units.

Question 13.

Answer:

Explanation:
Completed the drawing of given cube as shown above
which has 3 units.

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 1 Practice 5 Rounding and Estimating to finish your assignments.

Math in Focus Grade 5 Chapter 1 Practice 5 Answer Key Rounding and Estimating

Mark an ✗ to show where each number is located on the number line. Then round each number.

Example

656 rounded to the nearest ten is 660

Question 1.

9,709 rounded to the nearest hundred is ____
Answer: 9,700
Rounding is a way of simplifying numbers to make them easier to understand or work with. Rounding can be used when an exact number isn’t needed, and an approximate answer will do.
When rounding a number such as 9709 to the nearest hundred, we use the following rules:
A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.
B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.
C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.
In this case, Rule B applies and 9709 rounded to the nearest hundred is: 9,700

9,709 rounded to the nearest hundred is 9,700.

Question 2.

31,600 rounded to the nearest thousand is ___
Answer: 32,000
Rounding off the numbers means shortening the length of the number from long digits by replacing it with the nearest value. Round of to the nearest 1000 means minimizing the given decimal number to its nearest 1000 value.
How to round off the numbers to the nearest 1000:
Based on the below steps, we can easily round the numbers to the nearest 1000.
1. First, Find out the thousand’s digit in the number.
2. Next, choose the next smallest number (that is the hundredth digit of the number).
3. Now, check the hundred’s digit is either <5 (That means 0, 1, 2, 3, 4) or > = 5 (That is 5, 6, 7, 8, 9).
(i) If the digit is < 5, then the hundreds place is replaced with the digit ‘0’.
(ii) If the digit is > = 5, then the hundred’s digit is replaced with the digit ‘0’, and the thousand’s place digit is increased by 1 digit.
Number 31,600 Round to the Nearest 1000
Step 1: Thousand’s digit of the number is 1.
Step 2: Hundred’s digit of the number is 0.
Step 3: The hundred’s digit ‘0’ is <5, then we have to apply 3(i) conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
31,600 rounding of the nearest 1000 is equal to 32,000.

Round each number to the nearest thousand.

Question 3.
5,637 ____
Answer: 6000
Explanation:
Rounding off the numbers means shortening the length of the number from long digits by replacing it with the nearest value. Round of to the nearest 1000 means minimizing the given decimal number to its nearest 1000 value.
How to round off the numbers to the nearest 1000:
Based on the below steps, we can easily round the numbers to the nearest 1000.
1. First, Find out the thousand’s digit in the number.
2. Next, choose the next smallest number (that is the hundredth digit of the number).
3. Now, check the hundred’s digit is either <5 (That means 0, 1, 2, 3, 4) or > = 5 (That is 5, 6, 7, 8, 9).
(i) If the digit is < 5, then the hundreds place is replaced with the digit ‘0’.
(ii) If the digit is > = 5, then the hundred’s digit is replaced with the digit ‘0’, and the thousand’s place digit is increased by 1 digit.
Number 5,637 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 5.
Step 2: Hundred’s digit of the number is 6.
Step 3: The hundred’s digit ‘6’ is >5, then we have to apply 3(ii) conditions. That is, the hundred’s placed is replaced with the digit ‘0’and the thousand’s place digit is increased by 1 digit.
5,637 rounding of the nearest 1000 is equal to 6000.

Question 4.
9,541 ____
Answer: 10,000
Explanation:
Number 9,541 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 9.
Step 2: Hundred’s digit of the number is 5.
Step 3: The hundred’s digit ‘5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’and the thousand’s place digit is increased by 1 digit.
9,541 rounding of the nearest 1000 is equal to 10,000.

Question 5.
1,399 ___
Answer: 1000
Explanation:
Number 1,399 Round to the Nearest 1000
Step 1: Thousand’s digit of the number is 1.
Step 2: Hundred’s digit of the number is 3.
Step 3: The hundred’s digit ‘3’ is <5, then we have to apply conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
1,399 rounding of the nearest 1000 is equal to 1000.

Question 6.
72,245 ____
Answer:  72000
Explanation:
Number 72,245 Round to the Nearest 1000
Step 1: Thousand’s digit of the number is 2.
Step 2: Hundred’s digit of the number is 2.
Step 3: The hundred’s digit ‘2’ is <5, then we have to apply conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
72,245 rounding of the nearest 1000 is equal to 72,000.

Question 7.
473,075 _________
Answer: 473,000
Explanation:
Number 473,075 Round to the Nearest 1000
Step 1: Thousand’s digit of the number is 3.
Step 2: Hundred’s digit of the number is 0.
Step 3: The hundred’s digit ‘0’ is <5, then we have to apply conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
473,075 rounding of the nearest 1000 is equal to 473,000.

Question 8.

69,547 ___
Answer: 70,000
Explanation:
Number 69,547 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 9.
Step 2: Hundred’s digit of the number is 5.
Step 3: The hundred’s digit ‘5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’and the thousand’s place digit is increased by 1 digit.
69,547 rounding of the nearest 1000 is equal to 70,000.

Question 9.
20,100 ____
Answer: 20,000
Explanation:
Number 20,100 Round to the Nearest 1000
Step 1: Thousand’s digit of the number is 0.
Step 2: Hundred’s digit of the number is 1.
Step 3: The hundred’s digit ‘1’ is <5, then we have to apply conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
20,100 rounding of the nearest 1000 is equal to 20,000.

Question 10.
756,715 ____
Answer: 757000
Explanation:
Number 756,715 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6.
Step 2: Hundred’s digit of the number is 7.
Step 3: The hundred’s digit ‘7’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’and the thousand’s place digit is increased by 1 digit.
756,715 rounding of the nearest 1000 is equal to 757,000.

Answer each question. Use the number line to help you.

Example
Rounding to the nearest thousand, what is the least and the greatest number that rounds to 3,000?

Least number: 2,500
Greatest number: 3,499

Question 11.
Rounding to the nearest thousand, what is
a. the least number that rounds to 5,000?

_______
Answer: The least number of 5000 is 4,500.
Explanation:
Number 4,500 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 4.
Step 2: Hundred’s digit of the number is 5.
Step 3: The hundred’s digit ‘5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’and the thousand’s place digit is increased by 1 digit.
4,500 rounding of the nearest 1000 is equal to 5,000.
So, the least number to round up 5000 is 4,500.

b. the greatest number that rounds to 90,000?

Answer:90,499
Explanation:
Number 90,000 Round to the Nearest 1000
Step 1: Thousand’s digit of the number is 0.
Step 2: Hundred’s digit of the number is 0.
Step 3: The hundred’s digit ‘0’ is <5, then we have to apply conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
But here the greatest number is asked to round up the 90,000 that means the number we need to find out to get the 90,000 if we calculate the nearest values to that number.
If I take 90,499.
Step 1: The thousand’s place is 0.
Step 2: Hundred’s place is 4.
Step 3: The hundred’s digit ‘4’ is <5 then we have to apply conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Finally, if we calculate 90,499 with the nearest 1000 with the above rules then the number will be 90,000.

Round each number to the nearest thousand. Then estimate the sum.

Example
9,286 + 5.703
9,286 rounds to 9,000.
5,703 rounds to 6,000.
9,000 + 6,000 = 15,000

Question 12.
6,789 + 4,200
Answer:11000.
Explanation:
Number 6,789 and 4,200 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6 and 4.
Step 2: Hundred’s digit of the number is 7 and 2.
Step 3: The hundred’s digit ‘7’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’and the thousand’s place digit is increased by 1 digit.
Step 4: The hundred’s digit ‘2’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’
6,789 rounding of the nearest 1000 is equal to 7000.
4,200 rounding of the nearest 1000 is equal to 4000.
Now add the rounded figures: 7000+4000=11000.

Question 13.
7,264 + 7,153
Answer:14000
Explanation:
Number 7,264 and 7,153 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 7 and 7.
Step 2: Hundred’s digit of the number is 2 and 1.
Step 3: The hundred’s digit ‘2’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘1’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
7,264 rounding of the nearest 1000 is equal to 7000.
7,153 rounding of the nearest 1000 is equal to 7000.
Now add the rounded figures: 7000+7000=14000.

Question 14.
4,885 + 6,075
Answer: 11000
Number 4,885 and 6,075 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 4 and 6.
Step 2: Hundred’s digit of the number is 8 and 0.
Step 3: The hundred’s digit ‘8’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
Step 4: The hundred’s digit ‘1’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
4,885 rounding of the nearest 1000 is equal to 5000.
6,075 rounding of the nearest 1000 is equal to 6000.
Now add the rounded figures: 5000+6000=11000.

Question 15.
3,105 + 9,940
Answer: 13000
Number 3,105 and 9,940 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 3 and 9.
Step 2: Hundred’s digit of the number is 1 and 9.
Step 3: The hundred’s digit ‘9’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
Step 4: The hundred’s digit ‘1’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
3,105 rounding of the nearest 1000 is equal to 3000.
9,940 rounding of the nearest 1000 is equal to 10000.
Now add the rounded figures: 3000+10000=13,000.

Question 16.
7,083 + 2,607
Answer:10,000
Number 3,105 and 9,940 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 7 and 2.
Step 2: Hundred’s digit of the number is 0 and 6.
Step 3: The hundred’s digit ‘0’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘6’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
7,083 rounding of the nearest 1000 is equal to 7000.
2,607 rounding of the nearest 1000 is equal to 3000.
Now add the rounded figures: 7000+3000=10,000.

Round each number to the nearest thousand. Then estimate the difference

Example
8,156 – 6,109
8,156 rounds to 8,000.
6,109 rounds to 6,000.
8,000 – 6,00 = 2,000

Question 17.
4,924 – 4,127
Answer: 1000
Number 4,924 and 4,127 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 4 and 4.
Step 2: Hundred’s digit of the number is 9 and 1.
Step 3: The hundred’s digit ‘1’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘9’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
4,924 rounding of the nearest 1000 is equal to 5000.
4,127 rounding of the nearest 1000 is equal to 4000.
Now add the rounded figures: 5000-4000=1,000.

Question 18.
7,105 – 3,940
Answer:3000
Number 7,105 and 3,940 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 7 and 3.
Step 2: Hundred’s digit of the number is 9 and 1.
Step 3: The hundred’s digit ‘1’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘9’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
7,105 rounding of the nearest 1000 is equal to 7000.
3,940 rounding of the nearest 1000 is equal to 4000.
Now add the rounded figures: 7000-4000=3000.

Question 19.
4,885 – 1,075 ____
Answer:4000.
Number 4,885 and 1,075 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 4 and 1.
Step 2: Hundred’s digit of the number is 8 and 0.
Step 3: The hundred’s digit ‘0’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘8’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
4,885 rounding of the nearest 1000 is equal to 5000.
1,075 rounding of the nearest 1000 is equal to 4000.
Now add the rounded figures: 5000-4000=1000.

Question 20.
3,522 – 2,815
Answer:1000
Step 1: Thousand’s digit of the number is 3 and 2.
Step 2: Hundred’s digit of the number is 5 and 8.
Step 3: The hundred’s digit ‘8 and 5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
3,522 rounding of the nearest 1000 is equal to 4000.
2,815 rounding of the nearest 1000 is equal to 3000.
Now add the rounded figures: 4000-3000=1000.

Question 21.
6,480 – 1,397
Answer: 5000
Number 6,480 and 1,397 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6 and 1.
Step 2: Hundred’s digit of the number is 4 and 3.
Step 3: The hundred’s digit ‘4 and 3’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
6,480 rounding of the nearest 1000 is equal to 6000.
1,397 rounding of the nearest 1000 is equal to 1000.
Now add the rounded figures: 6000-1000=5000.

Use front-end estimation with adjustment to estimate each sum.

Example
1,963 + 3,290 + 7,837
1,000 + 3,000 + 7,000
= 11,000
900 + 200 – &00
= 1,900
To the nearest thousanci:
1,900 → 2,000
11,000 + 2,000 = 13,000

Question 22.
2,541 + 6,061 + 1,681
Answer: 11000
With front end estimation, we only round and add the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Explanation:
Number 2,541, 6,061 and 1,681 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 2, 6, and 1.
Step 2: Hundred’s digit of the number is 5, 0, and 6.
Step 3: The hundred’s digit  ‘0’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘5 and 6’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
2,541 rounding of the nearest 1000 is equal to 3000.
6,061 rounding of the nearest 1000 is equal to 6000.
1,681 rounding of the nearest 1000 is equal to 2000
The front end estimations are 3000, 6000, 2000.
Now add all those estimations:3000+6000+2000=11000.

Question 23.
7,823 + 6,848 + 3,310
Answer:
With front end estimation, we only round and add the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Explanation:
Number 7,823, 6,848 and 3,310 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 7, 6, and 3.
Step 2: Hundred’s digit of the number is 8, 8, and 3.
Step 3: The hundred’s digit  ‘3’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘8 and 8’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
7,823 rounding of the nearest 1000 is equal to 8000.
6,848 rounding of the nearest 1000 is equal to 7000.
3,310 rounding of the nearest 1000 is equal to 3000
The front end estimations are 8000, 7000, 3000.
Now add all those estimations:8000+7000+3000=18000.

Question 24.
4,197 + 8,936 + 2,226
Answer:
With front end estimation, we only round and add the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Explanation:
Number 4,197, 8,936 and 2,226 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 4, 8, and 2.
Step 2: Hundred’s digit of the number is 1, 9, and 2.
Step 3: The hundred’s digit  ‘1 and 2’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘9’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
4,197 rounding of the nearest 1000 is equal to 4000.
8,936 rounding of the nearest 1000 is equal to 9000.
2,226 rounding of the nearest 1000 is equal to 2000
The front end estimations are 4000, 9000, 2000.
Now add all those estimations:4000+9000+2000=15000.

Use front-end estimation with adjustment to estimate each difference.

Example .
2,943 – 1,272
2,000 – 1,000
= 1,000
900 – 200 = 700
To the nearest thousand:
700 → 1,000
1,000 + 1,000 = 2,000

Question 25.
6,770 – 3,081
Answer: 4000
Explanation:
With front end estimation, we only round and subtract the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Number 6,770 and 3,081 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6 and 3.
Step 2: Hundred’s digit of the number is 7 and 0.
Step 3: The hundred’s digit ‘7 and 5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
Step 4: The hundred’s digit  ‘0’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
6,770 rounding of the nearest 1000 is equal to 7000.
3,081 rounding of the nearest 1000 is equal to 3000.
The front end estimations are 7000, 3000.
Now add all those estimations:7000-3000=4000.

Question 26.
8,764 – 3,589
Answer: 5000
Explanation:
With front end estimation, we only round and subtract the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Number 8,764and 3,589 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 8 and 3.
Step 2: Hundred’s digit of the number is 7 and 5.
Step 3: The hundred’s digit ‘7 and 5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
8,764 rounding of the nearest 1000 is equal to 9000.
3,589 rounding of the nearest 1000 is equal to 4000.
The front end estimations are 9000, 4000.
Now subtract all those estimations:9000-4000=5000.

Question 27.
7,802 – 4,396
Answer: 4000
Explanation:
With front end estimation, we only round and subtract the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Number 7,802 and 4,396 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 7 and 4.
Step 2: Hundred’s digit of the number is 8 and 3.
Step 3: The hundred’s digit ‘8’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
Step 4: The hundred’s digit  ‘3’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
7,802 rounding of the nearest 1000 is equal to 8000.
4,396 rounding of the nearest 1000 is equal to 4000.
The front end estimations are 8000, 4000.
Now subtract all those estimations:8000-4000=4000.

Use front-end estimation with adjustment to estimate each difference.

Example
7,594 – 2,831
7,000 – 2,000 = 5,000
800 – 500 = 300
To the nearest thouari:
300 → 0
5,000 – 0 = 5,000

Question 28.
5,780 – 3,962
Answer: 2000
Explanation:
With front end estimation, we only round and subtract the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Number 5,780 and 3,962 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 5 and 3.
Step 2: Hundred’s digit of the number is 7 and 9.
Step 3: The hundred’s digit ‘7 and 9’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
5,780 rounding of the nearest 1000 is equal to 6000.
3,962 rounding of the nearest 1000 is equal to 4000.
The front end estimations are 6000, 4000.
Now subtract all those estimations:6000-4000=2000.

Question 29.
9,119 – 4,852
Answer; 4000
Explanation:
With front end estimation, we only round and subtract the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Number 9,119 and 4,852 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 9 and 4.
Step 2: Hundred’s digit of the number is 1 and 8.
Step 3: The hundred’s digit ‘8’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
Step 4: The hundred’s digit  ‘1’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
9,119 rounding of the nearest 1000 is equal to 9000.
4,852 rounding of the nearest 1000 is equal to 5000.
The front end estimations are 9000, 5000.
Now subtract all those estimations:9000-5000=4000.

Question 30.
8,254 – 4,836
Answer: 3000
Explanation:
With front end estimation, we only round and subtract the numbers in the leftmost place or the very last number on the left. This means that all numbers in other places will be zeros except the number in the leftmost place after the numbers are rounded. Having said that, if the numbers have two digits, round to the tens place before adding the leftmost digits or numbers.
Number 8,254 and 4,836 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 8 and 4.
Step 2: Hundred’s digit of the number is 2 and 8.
Step 3: The hundred’s digit ‘8’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
Step 4: The hundred’s digit  ‘2’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
8,254 rounding of the nearest 1000 is equal to 8000.
4,836 rounding of the nearest 1000 is equal to 5000.
The front end estimations are 8000, 5000.
Now subtract all those estimations:8000-5000=3000.

Estimate each product.

Example
4,512 × 2
4,512 rounds to 5,000.
5,000 × 2 = 10,000

Question 31
3,765 × 7
Answer: 8000
Number 3,765 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 3.
Step 2: Hundred’s digit of the number is 7.
Step 3: The hundred’s digit ‘7’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
3,765 rounding of the nearest 1000 is equal to 4000.
The estimation is 4000
Now multiply with the given number that is 7:
4000×2=8000

Question 32.
2,521 × 5
Answer: 15000
Explanation:
Number 2,521 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 2.
Step 2: Hundred’s digit of the number is 5.
Step 3: The hundred’s digit ‘5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
2,521 rounding of the nearest 1000 is equal to 3000.
The estimation is 3000
Now multiply with the given number that is 5:
3000×5=15000.

Question 33.
5,108 × 6
Answer: 30,000
Explanation:
Number 5,108 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 5.
Step 2: Hundred’s digit of the number is 1.
Step 3: The hundred’s digit  ‘1’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
5,108 rounding of the nearest 1000 is equal to 5000.
The estimation is 5000
Now multiply with the given number that is 6:
5000×6=30,000.

Question 34.
8,497 × 9
Answer: 72,000
Explanation:
Number 8,497 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 8.
Step 2: Hundred’s digit of the number is 4.
Step 3: The hundred’s digit  ‘4’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
8,497 rounding of the nearest 1000 is equal to 8000.
The estimation is 8000
Now multiply with the given number that is 9:
8000×9=72,000.

Question 35.
6,060 × 3
Answer:
Explanation:
Number 6,060 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6.
Step 2: Hundred’s digit of the number is 0.
Step 3: The hundred’s digit  ‘0’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
6,060 rounding of the nearest 1000 is equal to 6000.
The estimation is 6000
Now multiply with the given number that is 3:
6000×3=18,000.

Estimate each quotient.

2,786 ÷ 5
2,500 ÷ 5
2,786 rounds to 3,000.
3,000 ÷ 5 = 600

Look for compatible numbers.

Which number is nearer to 2,786?

Question 36
6,509 ÷ 7
Answer: 1000
Explanation:

Why I choose 7000 to the nearest number I will explain below:
Number 6,509 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6.
Step 2: Hundred’s digit of the number is 5.
Step 3: The hundred’s digit ‘5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
6,509 rounding of the nearest 1000 is equal to 7000.
The estimation is 7000
Now divide with the given number that is 7:
7000÷7=1000.

Question 37.
5,512 ÷ 6
Answer: 1000

Explanation:
Why I choose 6000 to the nearest number I will explain below:
Number 5,512 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 5.
Step 2: Hundred’s digit of the number is 5.
Step 3: The hundred’s digit ‘5’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
5,512 rounding of the nearest 1000 is equal to 6000.
The estimation is 6000
Now divide with the given number that is 6:
6000÷6=1000.

Question 38.
2,785 ÷ 3
Answer: 1000
Explanation:

Number 2,785 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 2.
Step 2: Hundred’s digit of the number is 7.
Step 3: The hundred’s digit ‘7’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
2,785 rounding of the nearest 1000 is equal to 3000.
The estimation is 3000
Now divide with the given number that is 3:
3000÷3=1000.

Question 39.
6,287 ÷ 8
Answer: 750
Explanation:

Number 6,287 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6.
Step 2: Hundred’s digit of the number is 2.
Step 3: The hundred’s digit ‘2’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
6,287 rounding of the nearest 1000 is equal to 6000.
The estimation is 6000
Now divide with the given number that is 8:
6000÷8=750.

Question 40.
2,963 ÷ 9
Answer: 333.33
Explanation:

Number 2,963 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 2.
Step 2: Hundred’s digit of the number is 9.
Step 3: The hundred’s digit ‘9’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
2,963 rounding of the nearest 1000 is equal to 3000.
The estimation is 3000
Now divide with the given number that is 9:
3000÷9=333.33.

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 3 Practice 4 Expressing Fractions, Division Expressions, and Mixed Numbers as Decimals to finish your assignments.

Math in Focus Grade 5 Chapter 3 Practice 4 Answer Key Expressing Fractions, Division Expressions, and Mixed Numbers as Decimals

Write each fraction as a decimal.

Example

\(\frac{3}{5}\) = \(\frac{3}{5}\)
= 0.6

Question 1.
\(\frac{13}{20}\) = ____
= _____
Answer:
\(\frac{13}{20}\) = \(\frac{13}{20}\)
= 0.65
Explanation:
Written the fraction as a decimal.

Question 2.
\(\frac{19}{25}\) = ____
= _____
Answer:
\(\frac{19}{25}\) =\(\frac{19}{25}\)
= 0.76
Explanation:
Written the fraction as a decimal.

Question 3.
\(\frac{47}{50}\) = ____
= _____
Answer:
\(\frac{47}{50}\) = \(\frac{47}{50}\)
= 0.94
Explanation:
Written the fraction as a decimal.

Express each division expression as a mixed number in simplest form and as a decimal.

Explanation:

Question 4.
7 ÷ 2
Answer:
7 ÷ 2 = \(\frac{6}{2}\) + \(\frac{1}{2}\)
= 3 + \(\frac{1}{2}\)
= 3 + 0.5
= 3.5

Explanation:
Converted division expression into mixed fraction and decimal

Question 5.
9 ÷ 4
Answer:
\(\frac{8}{4}\) + \(\frac{1}{4}\)
= 2 + \(\frac{1}{4}\)
= 2 + 0.25
= 2.25

Explanation:
Converted division expression into mixed fraction and decimal

Question 6.
21 ÷ 5
Answer:
\(\frac{20}{5}\) + \(\frac{1}{5}\)
= 4 + \(\frac{1}{5}\)
= 4 + 0.2
= 4.2

Explanation:
Converted division expression into mixed fraction and decimal

Question 7.
101 ÷ 25
Answer:
\(\frac{100}{25}\) + \(\frac{1}{25}\)
= 1 + \(\frac{1}{25}\)
= 4 + 0.04
= 4.04

Explanation:
Converted division expression into mixed fraction and decimal

Express each improper fraction as a decimal.

Example
\(\frac{3}{2}\) = \(\frac{2}{2}\) + \(\frac{1}{2}\)
= 1 + \(\frac{1}{2}\)
= 1 + 0.5
= 1.5
Explanation:
Converted each improper fraction into decimal

Question 8.
\(\frac{22}{5}\)
Answer:
\(\frac{20}{5}\) + \(\frac{2}{5}\)
= 4 + \(\frac{2}{5}\)
= 4 + 0.4
= 4.4
Explanation:
Converted each improper fraction into decimal

Question 9.
\(\frac{47}{20}\)
Answer:
\(\frac{40}{20}\) + \(\frac{7}{20}\)
= 2 + \(\frac{7}{20}\)
= 2 + 0.35
= 2.35
Explanation:
Converted each improper fraction into decimal

Question 10.
\(\frac{32}{25}\)
Answer:
\(\frac{25}{25}\) + \(\frac{7}{25}\)
= 1 + \(\frac{7}{25}\)
= 1 + 0.28
= 1.28
Explanation:
Converted each improper fraction into decimal

Solve. Show your work.

Question 11.
A coil of rope 603 feet long is cut into 25 equal pieces. What is the length of each piece? Express your answer as a mixed number and as a decimal.
Answer:
24.12 in decimal
24\(\frac{3}{25}\) in mixed fraction.
Explanation:
A coil of rope 603 feet long is cut into 25 equal pieces.
603 ÷  25 = \(\frac{600}{25}\) + \(\frac{3}{25}\)
= 24 + \(\frac{3}{25}\)
= 24\(\frac{3}{25}\)
= 24 + 0.12
= 24 .12
24.12 is the length of each piece

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 3 Practice 5 Adding Mixed Numbers to finish your assignments.

Math in Focus Grade 5 Chapter 3 Practice 5 Answer Key Adding Mixed Numbers

Add. Express each sum in simplest form.

Example

Question 1.

Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 2.

Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Add. Express each sum in simplest form

Question 3.
3\(\frac{2}{7}\) + 2\(\frac{5}{14}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 4.
5\(\frac{7}{12}\) + 3\(\frac{1}{4}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 5.
4\(\frac{1}{15}\) + 1\(\frac{3}{10}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 6.
12\(\frac{1}{9}\) + 9\(\frac{5}{6}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Add. Express each sum in simplest form.

Question 7.

Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 8.

Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 9.
2\(\frac{3}{4}\) + 3\(\frac{2}{5}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 10.
2\(\frac{5}{9}\) + 1\(\frac{5}{6}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 11.
7\(\frac{8}{9}\) + 9\(\frac{5}{12}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Question 12.
5\(\frac{7}{12}\) + 1\(\frac{3}{4}\)
Answer:

Explanation:
Made the unlike denominators to like denominators
then added the mixed fractions.

Use benchmarks to estimate each sum.

Example

Question 13.
9\(\frac{6}{7}\) + 7\(\frac{5}{12}\)
Answer:
17\(\frac{1}{2}\)
Explanation:
\(\frac{6}{7}\) is near to the benchmark 1
\(\frac{5}{12}\) is near to the bench mark \(\frac{1}{2}\)
9 + 1 = 10
10 + 7 \(\frac{1}{2}\)
17\(\frac{1}{2}\)

Question 14.
4\(\frac{7}{12}\) + 10\(\frac{1}{9}\)
Answer:
14 \(\frac{1}{2}\)
Explanation:
\(\frac{7}{12}\) is near to the benchmark \(\frac{1}{2}\)
\(\frac{1}{12}\) is near to the bench mark 0
10 + 0 = 10
4\(\frac{1}{2}\) + 10
= 14 \(\frac{1}{2}\)

Go through the Math in Focus Grade 5 Workbook Answer Key Cumulative Review Chapters 3 and 4 to finish your assignments.

Math in Focus Grade 5 Cumulative Review Chapters 3 and 4 Answer Key

Concepts and Skills
Shade and label the model to show the sum of \(\frac{1}{3}\) and \(\frac{3}{5}\).
Then complete the addition sentence. (Lesson 3.1)

Question 1.

Answer:
\(\frac{1}{3}\) + \(\frac{3}{5}\) =
\(\frac{5}{15}\) + \(\frac{9}{15}\).=
\(\frac{14}{15}\)
Explanation:
Making unlike denominators to like denominators.

Explanation:
Making unlike denominators to like denominators.

Add. Express each sum in simplest form. (Lesson 3.1)

Question 2.
\(\frac{3}{4}\) + \(\frac{1}{12}\) =
Answer:
\(\frac{3}{4}\) + \(\frac{1}{12}\) =
\(\frac{9}{12}\) + \(\frac{1}{12}\) =
\(\frac{10}{12}\)
Explanation:
Making unlike denominators to like denominators.
And added the fractions

Question 3.
\(\frac{3}{5}\) + \(\frac{2}{7}\) =
Answer:
\(\frac{3}{5}\) + \(\frac{2}{7}\) =
\(\frac{21}{35}\) + \(\frac{10}{35}\) =
\(\frac{31}{35}\)
Explanation:
Making unlike denominators to like denominators.
and added the fractions

Estimate each sum by using the benchmarks, 0, \(\frac{1}{2}\) or 1. (Lesson 3.1)

Question 4.
\(\frac{8}{9}\) + \(\frac{2}{5}\) =
Answer:
= \(\frac{3}{2}\)
Explanation:
Estimating \(\frac{8}{9}\) as 1
and \(\frac{2}{5}\)  as \(\frac{1}{2}\)
1 + \(\frac{1}{2}\)
= \(\frac{3}{2}\)

Question 5.
\(\frac{1}{8}\) + \(\frac{6}{7}\) + \(\frac{1}{6}\) =
Answer:
\(\frac{1}{8}\) + \(\frac{6}{7}\) + \(\frac{1}{6}\) =
Estimated answer = 1
Explanation:
Estimating the bench marks
\(\frac{1}{8}\) = 0
\(\frac{6}{7}\) = 1
\(\frac{1}{6}\) = 0
0 + 1  + 0 = 1

Shade and label the model to show the difference between \(\frac{4}{5}\) and \(\frac{2}{3}\). Then complete the subtraction sentence. (Lesson 3.2)

Question 6.

Answer:

Explanation:
Simplified the fractions.

Subtract. Express each difference in simplest form. (Lesson 3.2)

Question 7.
\(\frac{3}{4}\) – \(\frac{1}{12}\) = \(\frac{2}{3}\)
Answer:
\(\frac{3}{4}\) – \(\frac{1}{12}\) = \(\frac{2}{3}\)
Explanation:

Question 8.
\(\frac{3}{5}\) – \(\frac{3}{9}\) =
Answer:
\(\frac{3}{5}\) – \(\frac{3}{9}\) = \(\frac{4}{15}\)
Explanation:

Estimate each difference by using the benchmarks, 0, \(\frac{1}{2}\) or 1. (Lesson 3.2)

Question 9.
\(\frac{4}{5}\) – \(\frac{3}{8}\)
Answer:
\(\frac{4}{5}\) – \(\frac{3}{8}\) = \(\frac{1}{2}\)
Explanation:
Estimating the fractions to bench marks
\(\frac{4}{5}\) = 1
\(\frac{3}{8}\) = \(\frac{1}{2}\)
1 – \(\frac{1}{2}\)  = \(\frac{1}{2}\)

Question 10.
\(\frac{7}{12}\) – \(\frac{5}{9}\)
Answer:
\(\frac{7}{12}\) – \(\frac{5}{9}\) = 1
Explanation:
Estimating the fractions to bench marks
\(\frac{7}{12}\)  = \(\frac{1}{2}\)
\(\frac{5}{9}\) = \(\frac{1}{2}\)
\(\frac{1}{2}\)  + \(\frac{1}{2}\)  = 1

Write each fraction as a division expression. (Lesson 3.3)

Question 11.

Answer:

Explanation:
\(\frac{4}{9}\)
Fraction into expression.

Question 12.

Answer:

Explanation:
\(\frac{8}{11}\)
Fraction into expression.

Write each division expression as a fraction. (Lesson 3.3)

Question 13.
\(\frac{5}{6}\) = ___ ÷ ___
Answer:
5 ÷ 6
\(\frac{5}{6}\) = 5 ÷ 6
Explanation:
converting division expression as a fraction.

Question 14.
\(\frac{7}{12}\) = ___ ÷ ___
Answer:
7 ÷ 12
\(\frac{7}{12}\) = 7 ÷ 12
Explanation:
converting division expression as a fraction.

Complete. (Lesson 3.3)

Question 15.

Answer:

Explanation:
Converting the division expression to a mixed fraction

Question 16.

Answer:

Explanation:
Converting the division expression to a mixed fraction

Divide. Express each quotient as a mixed number in simplest form. (Lesson 3.3)

Question 17.

Answer:

Explanation:
Converting the division expression to a mixed fraction

Question 18.

Answer:

Explanation:
Converting the division expression to a mixed fraction

Express each fraction as a decimal. (Lesson 3.4)

Question 19.
\(\frac{4}{5}\) = ____
= _________
Answer:
\(\frac{4}{5}\) = 0.8
Explanation:

Question 20.
\(\frac{17}{20}\) = ____
= _________
Answer:

Explanation:
\(\frac{17}{20}\) = 0.85

Express each division expression as a mixed number and as a decimal. (Lessons 3.3 and 3.4)

Explanation:

Question 21.
13 ÷ 4 = 3\(\frac{1}{4}\)
Answer:

Explanation:
13 ÷ 4 = 3.25

Question 22.
23 ÷ 5
Answer:

Explanation:
23 ÷ 5 = 5.6

Add. Express each sum in simplest form. (Lesson 3.5)

Question 23.
2\(\frac{2}{7}\) + 3\(\frac{1}{2}\)
Answer:

2\(\frac{2}{7}\) + 3\(\frac{1}{2}\) = 5\(\frac{11}{14}\)

Question 24.
1\(\frac{1}{2}\) + 1\(\frac{5}{9}\)
Answer:

Explanation:
1\(\frac{1}{2}\) + 1\(\frac{5}{9}\) = 3\(\frac{1}{18}\)

Estimate each sum by using the nearest whole number or half. (Lesson 3.5)

Question 25.
1\(\frac{5}{8}\) + 1\(\frac{1}{5}\)
Answer:

Explanation:
1\(\frac{5}{8}\) + 1\(\frac{1}{5}\) = 3\(\frac{1}{18}\) = 3 + 0 = 3
Converting the fraction into a whole number.

Question 26.
2\(\frac{1}{6}\) + 3\(\frac{4}{5}\)
Answer:

Explanation:
2\(\frac{1}{6}\) + 3\(\frac{4}{5}\) = 5\(\frac{29}{30}\)
Converting the fraction into a whole number.
5 + 1 = 6

Subtract. Express each difference in simplest form. (Lesson 3.6)

Question 27.
5\(\frac{8}{9}\) – 3\(\frac{5}{6}\)
Answer:

Explanation:
5\(\frac{8}{9}\) – 3\(\frac{5}{6}\) = 2\(\frac{1}{18}\)
2 + 0 = 2

Question 28.
4\(\frac{2}{7}\) – 2\(\frac{7}{8}\)
Answer:

Explanation:
4\(\frac{2}{7}\) – 2\(\frac{7}{8}\) = 1\(\frac{23}{56}\)
= 1 + \(\frac{1}{2}\)
= \(\frac{3}{2}\)

Estimate difference by using the nearest whole number or half. (Lesson 3.6)

Question 29.
2\(\frac{1}{10}\) – 1\(\frac{4}{7}\)
Answer:

Explanation:
2\(\frac{1}{10}\) – 1\(\frac{4}{7}\) = \(\frac{37}{70}\) = \(\frac{1}{2}\)
Converting the fraction into a half

Question 30.
3\(\frac{3}{8}\) – 1\(\frac{7}{12}\)
Answer:

Explanation:
3\(\frac{3}{8}\) – 1\(\frac{7}{12}\) = 1\(\frac{19}{24}\)
= 1 + 1 = 2

Find the product in simplest form. (Lesson 4.1)

Question 31.
\(\frac{6}{7}\) × \(\frac{5}{8}\) =
Answer:

Explanation:
\(\frac{6}{7}\) × \(\frac{5}{8}\) = \(\frac{15}{28}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Question 32.
\(\frac{4}{5}\) × \(\frac{10}{12}\) =
Answer:

Explanation:
\(\frac{4}{5}\) × \(\frac{10}{12}\) = \(\frac{2}{3}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Question 33.
\(\frac{2}{5}\) of \(\frac{10}{11}\) =
Answer:

Explanation:
\(\frac{2}{5}\) of \(\frac{10}{11}\) =\(\frac{4}{11}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Question 34.
\(\frac{8}{9}\) of \(\frac{5}{12}\) =
Answer:

Explanation:
\(\frac{8}{9}\) of \(\frac{5}{12}\)  = \(\frac{10}{27}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Multiply. Express the product in simplest form. (Lesson 4.3)

Question 35.
\(\frac{2}{5}\) × \(\frac{15}{7}\) =
Answer:

Explanation:
\(\frac{2}{5}\) × \(\frac{15}{7}\) = \(\frac{6}{7}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Question 36.
\(\frac{9}{5}\) × \(\frac{5}{12}\) =
Answer:

Explanation:
\(\frac{9}{5}\) × \(\frac{5}{12}\) = \(\frac{3}{4}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Multiply. Express the product as a whole number or a mixed number in simplest form. (Lesson 4.3)

Question 37.
\(\frac{4}{3}\) × \(\frac{7}{6}\) =
Answer:

Explanation:
\(\frac{4}{3}\) × \(\frac{7}{6}\) = \(\frac{14}{9}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Question 38.
\(\frac{8}{3}\) × \(\frac{9}{12}\) =
Answer:

Explanation:
\(\frac{8}{3}\) × \(\frac{9}{12}\)= 2
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Question 39.
\(\frac{7}{8}\) × \(\frac{6}{5}\) =
Answer:

Explanation:
\(\frac{7}{8}\) × \(\frac{6}{5}\) = \(\frac{21}{20}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Question 40.
\(\frac{25}{4}\) × \(\frac{10}{8}\) =
Answer:

Explanation:
\(\frac{25}{4}\) × \(\frac{10}{8}\) = \(\frac{125}{16}\)
Multiplication in fractions we have to directly multiply
Numerator x Numerator
and Denominator x Denominator.

Multiply. Express the product as a whole number or a mixed number in simplest form. (Lesson 4.4)

Question 41.
2\(\frac{1}{4}\) × 16 =
Answer:

Explanation:
Converting the mixed fraction in to a fraction then multiply with 16
And done the simplest form to make into a whole number

Question 42.
27 × 1\(\frac{2}{9}\) =
Answer:

Explanation:
Converting the mixed fraction in to a fraction then multiply with 27
And done the simplest form to make into a whole number

Multiply. Express the product as a whole number or a mixed number in simplest form. (Lesson 4.4)

Question 43.
5\(\frac{3}{6}\) × 42 =
Answer:

Explanation:
Converting the mixed fraction in to a fraction then multiply with 42
And done the simplest form to make into a whole number

Question 44.
2\(\frac{5}{6}\) × 15 =
Answer:

Explanation:
Converting the mixed fraction in to a fraction then multiply with 15
And done the simplest form to make into a whole number

Divide. Express each quotient in simplest form. (Lesson 4.6)

Question 45.
3 ÷ \(\frac{1}{9}\) =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Question 46.
6 ÷ \(\frac{1}{8}\) =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Question 47.
5 ÷ \(\frac{1}{5}\) =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Question 48.
2 ÷ \(\frac{1}{10}\) =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Question 49.
\(\frac{7}{8}\) ÷ 5 =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Question 50.
\(\frac{5}{8}\) ÷ 4 =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Question 51.
\(\frac{4}{7}\) ÷ 12 =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Question 52.
\(\frac{2}{9}\) ÷ 6 =
Answer:

Explanation:
Converting the whole number as a fraction
To divide a fraction with a whole number,
we multiply the given whole number with the denominator of the fraction.

Problem Solving

Solve. Show your work.

Question 53.
Ron used \(\frac{3}{5}\) pound of flour to bake bread and \(\frac{2}{7}\) pound of flour to bake scones. How many more pounds of flour did he use to bake bread than scones?
Answer: \(\frac{11}{35}\) more pounds of flour he used to bake bread than scones
Explanation:
Subtract them…
But to subtract fractions you need a common denominator (the smallest thing that 5 and 7 both go into)
Remember when making equivalent fractions with your common denominator (which is 7×5 = 35) make sure you multiply the top by whatever you multiplied the bottom by.

Question 54.
Tina uses 4\(\frac{5}{12}\) yards of wire for her science project. Kelvin uses 1\(\frac{2}{3}\) yards of wire for his project. How many yards of wire do they use altogether?
Answer: 6\(\frac{1}{12}\) yards of wire used altogether
Explanation:

Solve. Show your work

Question 55.
Rosa poured 1\(\frac{3}{4}\) quarts of grape juice into a container. She added 3\(\frac{1}{3}\) quarts of apple juice. She then poured 2\(\frac{2}{3}\) quarts of the mixed juice into a pitcher. How many quarts of mixed juice were left in the container?
Answer: 2\(\frac{5}{12}\)
Explanation:
1\(\frac{3}{4}\) =1\(\frac{9}{12}\)
3\(\frac{1}{3}\) = 3\(\frac{4}{12}\)

1\(\frac{9}{12}\)+ 3\(\frac{4}{12}\) = 4\(\frac{13}{12}\) = 5\(\frac{1}{12}\)

4\(\frac{13}{12}\) – 2\(\frac{8}{12}\) = 2\(\frac{5}{12}\)

Question 56.
A race was \(\frac{11}{12}\) mile long. Hamish ran \(\frac{4}{5}\) of the distance.

a. Without multiplying, explain how you know that the answer must be less than \(\frac{11}{12}\).
Answer:
With the help of bench mark. Both the values are lesser than 1. So he ran less than \(\frac{11}{12}\).

b. How far did he run?
Answer: \(\frac{7}{60}\)
Explanation:

Solve. Show your work.

Question 57.
Ashley uses \(\frac{1}{4}\) package of raisins for o fruit cake. She then uses \(\frac{1}{9}\) of the remainder for muffins. What fraction of the package of raisins does she have left?
Answer: \(\frac{23}{36}\) of the package of raisins she have left
Explanation:

Question 58.
Mrs. Vernon used 4\(\frac{3}{8}\) pounds of meat in each of her 12 pots of soup. How many pounds of meat did she use for the 12 pots of soup?
Answer: 52\(\frac{1}{2}\) pounds of meat she used.
Explanation:

Solve. Show your work.

Question 59.
A custodian pours \(\frac{1}{8}\) gallon of cleaning solution into each pail of water that she uses.

a. How many pails of water and cleaning solution can the custodian make using 16 gallons of cleaning solution?
Answer:

b. Find the volume of solution in two of these pails.
Answer:

 

 

 

Question 60.
A carnival sold 135 bottles of juice in one day. They sold \(\frac{1}{3}\) of the bottles in the first hour and \(\frac{2}{5}\) of the bottles in the second hour. How many bottles of juice did they sell altogether in these two hours?
Answer: 99 bottles sold altogether in these two hours
Explanation:

Solve. Show your work.

Question 61.
Ms. Li spent $840 on a vacation. She spent \(\frac{2}{3}\) of the amount on a plane ticket and \(\frac{1}{2}\) of the remaining amount on food. How much did she spend on the ticket and food altogether?
Answer: So she spent $560+$140 = $ 700  on the ticket and food altogether
Explanation:
Ms. Li spent $840 on a vacation. She spent \(\frac{2}{3}\) of the amount on a plane ticket. So she spent $560 for plane ticket.

She spent \(\frac{1}{2}\) of the remaining amount on food.
Remaining amount is $280.
So she spent $ 140 on food

So she spent $560+$140 = $ 700  on the ticket and food altogether

Question 62.
Sam traveled \(\frac{3}{4}\) of a journey by bus. He jogged \(\frac{1}{2}\) the remaining distance and walked the rest of the way. If he walked 800 feet, what was the total distance he traveled?
Answer: 6400 feet he traveled
Explanation:
Total Distance = x
Sam traveled \(\frac{3}{4}\) of a journey by bus. So it is \(\frac{3}{4}\) x
So remaining distance is x – \(\frac{3}{4}\) x =\(\frac{1}{4}\) x
He jogged \(\frac{1}{2}\) the remaining distance. So he jogged \(\frac{1}{8}\) x

walked the rest of the way . So remining is x – \(\frac{3}{4}\) x + \(\frac{1}{8}\) x  =800

Solve. Show your work.

Question 63.
Matthew used \(\frac{1}{5}\) of a box of flour for cooking and \(\frac{3}{4}\) of the remainder to make bread. The rest of the flour was packed equally into 5 containers. What fraction of the total amount of flour was in each container? r
Answer: \(\frac{1}{100}\) fraction of the total amount of flour was in each container
Explanation:
Matthew used \(\frac{1}{5}\) of a box of flour for cooking. So remaining flour is

\(\frac{3}{4}\) of the remainder to make bread

The rest of the flour was packed equally into 5 containers

Question 64.
A bus driver filled up \(\frac{7}{8}\) of her fuel tank for a trip. She used \(\frac{6}{7}\) of the fuel by the end of the trip. The capacity of her tank is 70 gallons. How much fuel did she use for the trip? Express your answer as a decimal.
Answer: 52.5gallons of fuel she used for the trip
Explanation:
The capacity of her tank is 70 gallons.
A bus driver filled up \(\frac{7}{8}\) of her fuel tank for a trip

So she filled 61.25 gallons of fuel in tank.
She used \(\frac{6}{7}\) of the fuel by the end of the trip.

Question 65.
Sergio walked to and from school on \(\frac{3}{5}\) of the days in one month. He got a ride to school on \(\frac{7}{8}\) of the remaining days. On the one remaining school day that month, he stayed home with a cold. How many school days were there that month?
Answer: 20 days
Explanation:
Total Days = x
Sergio walked to and from school on \(\frac{3}{5}\) of the days in one month = \(\frac{3}{5}\)x
So remaining days = x – \(\frac{3}{5}\)x = \(\frac{2}{5}\)x
He got a ride to school on \(\frac{7}{8}\) of the remaining days. = \(\frac{7}{20}\)x .Since

On the one remaining school day that month, he stayed home with a cold.
So

x =20

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 3 Practice 7 Subtraction with Regrouping in Hundreds, Tens, and Ones to finish your assignments.

Math in Focus Grade 2 Chapter 3 Practice 7 Answer Key Subtraction with Regrouping in Hundreds, Tens, and Ones

Regroup.
Then subtract.

Question 1.
241 – 173 = ?
241 – 173
= 2 hundreds 4 tens 1 one – 1 hundred 7 tens 3 ones
= 2 hundreds ________ tens 11 ones – 1 hundred 7 tens 3 ones
= _________ hundred 13 tens 11 ones – 1 hundred 7 tens 3 ones
= _________ hundreds _________ tens _________ ones
241 – 173 = ____
Use addition to check your answer.

Answer:
241-173 = 68,
173+68 = 241.

Explanation:
Given that 241 – 173 which is 68. So to check the answer we will perform addition, which is 173+68 = 241.
241 – 173
= 2 hundreds 4 tens 1 one – 1 hundred 7 tens 3 ones
= 2 hundreds 3 tens 11 ones – 1 hundred 7 tens 3 ones
= 1 hundred 13 tens 11 ones – 1 hundred 7 tens 3 ones
= 0 hundreds 6 tens 8 ones.

Question 2.

Answer:
478 – 199 = 279,
279+199 = 478.

Explanation:
Given that 478 – 199 which is 279. So to check the answer we will perform addition, which is
279+199 = 478.

Question 3.

Answer:
555-457 = 98,
457+98 = 555.

Explanation:
Given that 555 – 457 which is 98. So to check the answer we will perform addition, which is
457+98 = 555.

Question 4.
924 – 886 = ___

Answer:
924-886 = 38,
38+886 = 924.

Explanation:
Given that 924-886 which is 38. So to check the answer we will perform addition, which is
38+886 = 924.

Question 5.
818 – 669 = ___

Answer:
818-669 = 149,
149+669 = 818.

Explanation:
Given that 818-669 which is 149. So to check the answer we will perform addition, which is
149+669 = 818.

Help Daryl ride past these rocks to reach the shore. Subtract and write the correct answer on each rock.

Question 6.

Answer:

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 2 Practice 5 Addition with Regrouping in Tens to finish your assignments.

Math in Focus Grade 2 Chapter 2 Practice 5 Answer Key Addition with Regrouping in Tens

Add and regroup the tens.

Question 1.
534 + 283 = ?
Add the ones.
4 ones + 3 ones = ones
Add and regroup the tens.
3 tens + 8 tens = ___ tens

= ___ hundred ___ ten
Add the hundreds.
1 hundred + 5 hundreds + 2 hundreds = ___ hundreds
534 + 283 = ____
Answer:
534 + 283 = 817
Explanation:
4 ones + 3 ones = 7 ones
Add and regroup the tens.
3 tens + 8 tens = 11 tens
= 1 hundred 1 ten
Add the hundreds.
1 hundred + 5 hundreds + 2 hundreds = 8 hundreds

Question 2.

Answer:

Explanation:
2  ones + 5 ones = 7 ones
Add and regroup the tens.
6 tens + 7 tens = 13 tens
= 1 hundred 3 ten
Add the hundreds.
1 hundred + 4 hundreds + 1 hundreds = 6 hundreds

Question 3.

Answer:

Explanation:
8 ones + 1 ones = 9 ones
Add and regroup the tens.
4  tens + 6 tens = 10 tens
= 1 hundred 0 ten
Add the hundreds.
1 hundred + 6 hundreds + 1 hundreds = 8 hundreds

Question 4.
295 + 633 = ___

Answer:

Explanation:
5 ones + 3 ones = 8 ones
Add and regroup the tens.
9 tens + 3  tens = 12 tens
= 1 hundred 2 ten
Add the hundreds.
1 hundred + 2 hundreds + 6 hundreds = 9 hundreds

Question 5.
462 + 456 = ___

Answer:

Explanation:
2 ones + 6 ones = 8 ones
Add and regroup the tens.
6 tens + 5 tens = 11 tens
= 1 hundred 1 ten
Add the hundreds.
1 hundred + 4 hundreds + 4 hundreds = 9 hundreds

Add.

Question 6.

Answer:

Kim lost her robots.
Her robots have the same answer.
To help her find her robots, color the robots with the same answer.
Explanation:
no matches were found
for Kim’s lost robots.