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Practice the problems of Math in Focus Grade 5 Workbook Answer Key Chapter 7 Practice 5 Comparing Three Quantities to score better marks in the exam.

Math in Focus Grade 5 Chapter 7 Practice 5 Answer Key Comparing Three Quantities

Find the greatest common factor for each set of numbers.

Question 1.
5, 10 and 20
Answer: The greatest number that divides 5, 10 and 20 is 5, So Greatest common factor of 5,10 and 20 is 5.

Question 2.
3, 9 and 15
Answer: The greatest number that divides 3, 9 and 15 is 3, So Greatest common factor of 3, 9 and 15 is 3.

Question 3.
6, 24 and 27
Answer: The greatest number that divides 6, 24 and 27 is 3, So Greatest common factor of 6, 24 and 27 is 3.

Complete to express each ratio in simplest form.

Question 4.

Answer: 4 : 3 : 2

Explanation:
Given,
All the numbers 16, 12 and 8 can be divided by 4 to get the simplest form in the ratio of 4 : 3 : 2.

Question 5.

Answer: 7 : 5 : 6

Explanation:
Given,
All the numbers 21, 15 and 18 can be divided by 3 to get the simplest form in the ratio of 7 : 5 : 6.

Question 6.

Answer: 4 : 6 : 9

Explanation:
Given,
All the numbers 20, 30 and 45 can be divided by 5 to get the simplest form in the ratio of 4 : 6 : 9.

Question 7.

Answer: 1 : 3 : 5

Explanation:
Given,
All the numbers 7, 21 and 35 can be divided by 7 to get the simplest form in the ratio of 1 : 3 : 5.

Express each ratio in simplest form.

Question 8.
4 : 16 : 18 ___ : ___ : ___
Answer:
All the numbers 4, 16 and 18 can be divided by 2 to get the simplest form in the ratio of 2 : 8 : 9.

Question 9.
27 : 12 : 21 __ : __ : ___
Answer:
Given,
All the numbers 27, 12 and 21 can be divided by 3 to get the simplest form in the ratio of 9 : 4 : 7.

Question 10.
32 : 8 : 20 = ___ : ___ : ____
Answer: All the numbers 32, 8 and 20 can be divided by 4 to get the simplest form in the ratio of 8 : 2 : 5.

Question 11.
63 : 1 8 : 27 = ___ : ___ : ___
Answer: All the numbers 63, 18 and 27 can be divided by 9 to get the simplest form in the ratio of 7 : 2 : 3.

Complete.

Question 12.

Answer:

All the numbers 2, 5 and 7 can be multiplied by 3 to get the simplest form in the ratio of 6 : 15 : 21.

Question 13.

Answer: All the numbers 3, 7 and 11 can be multiplied by 4 to get the simplest form in the ratio of 12 : 28 : 44.

Question 14.

Answer: All the numbers 20, 15 and 30 can be divided to get the simplest form in the ratio of 4 : 3 : 6.

Question 15.

Answer: All the numbers 32, 20 and 28 can be divided by 4 to get the simplest form in the ratio of 8 : 5 : 7.

Complete.

Question 16.
1 : 2 : 5 ___ : 6 : ___
Answer: All the numbers 1, 2 and 5 can be multiplied by 3 to get the ratio of 3 : 6 : 15.

Question 17.
7 : 4 : 3 = 28: ___ : ___
Answer: All the numbers 7, 4 and 3 can be multiplied by four to get the ratio of 28 : 16 : 12.

Question 18.
4 : 5 : 9 = ___ : 25 : ___
Answer: All the numbers 4, 5 and 9 can be multiplied by 5 to get the ratio of 20 : 25 : 45.

Question 19.
16 : 14 : 6 = ___ : ___ : 3
Answer: All the numbers 16, 14 and 6 can be divided by 2 to get the simplest form in the ratio of 8 : 7 : 3.

Question 20.
18 : 24 : 30 = ___ : 4 : ___
Answer: All the numbers 18, 24 and 30 can be divided by 6 to get the simplest form in the ratio of 3 : 4 : 5.

Question 21.
35 : 42 : 56 = 5 : ___ : ___
Answer: All the numbers 35, 42 and 56 can be divided by 7 to get the simplest form in the ratio of 5 : 6: 8.

Practice the problems of Math in Focus Grade 5 Workbook Answer Key Cumulative Review Chapters 5 to 7 to score better marks in the exam.

Math in Focus Grade 5 Cumulative Review Chapters 5 to 7 Answer Key

Concepts and Skills

Write the next three terms of each pattern. Then tell the rule you used. (Lesson 5.1)

Question 1.
1, 5, 25, 125, ____, ___, ____,…
Rule: __________________
Answer:
1, 5, 25, 125, 625, 3125, 15625.
Rule: Multiply each number by 5 to get the next three patterns.

Question 2.
8, 14, 20, 26, ___, ___, ____,…
Rule: __________________
Answer:
8, 14, 20, 26, 32, 38, 44.
Rule: Add 6 to each number to get the next three patterns.

Question 3.
6,236, 6,030, 5,824, 5,618. ___, ___, ___, …
Rule: ________________________
Answer:
6236, 6030, 5824, 5618, 5412, 5206, 5000.
Rule: Subtract 206 from each number to get the next three patterns.

Complete the table. (Lesson 5.1)

Question 4.
The width of a rectangle is 7 centimeters long. Complete the table to find the area as the length increases.

Answer:

Explanation:
Given,
The width of a rectangle is 7 centimeters long,
Multiply the length of the rectangle with 7 to get the area as the length increases.

Complete the table and answer the questions that follow. (Lesson 5.1)

Question 5.

a. How much do 5 boxes weigh? ____
Answer:
5 boxes weigh 1000.
Explanation:
Given,
Each box weighs 200,
Multiply 5 boxes with 200 then we get 1000.

b. How many boxes weigh 600 grams? _____
Answer:3 boxes weigh 600 grams.
Explanation:
Given,
Each box weighs 200,
Multiply 6 boxes with 200 then we get 1200.

c. If 100 grams cost $5, how much will 5 boxes cost? __________
Answer:5 boxes cost $5000.
Explanation:
Given,
Each 100 grams cost $5,
5 boxes contain 1000 grams,
To get the cost of 5 boxes 1000 grams should be multiplied by 5 then we get 5000 as the total sum,
The cost of 5 boxes is $5000.

Evaluate each expression for z = 5. (Lesson 5.2)

Question 6.
x + 9
Answer: 14

Explanation:
Given,
= x + 9, if x = 5
= 5 + 9
= 14

Question 7.
16 – x
Answer: 11

Explanation:
Given,
= 16 – x, if x = 5
= 16 – 5
= 11

Question 8.
4x
Answer: 20

Explanation:
Given,
= 4x, if x = 5
= 4(5)
= 20

Question 9.
\(\frac{x}{5}\)
Answer: 1

Explanation:
Given,
=> x / 5, if x = 5
=> 5 / 5
=> 1

Simplify each expression. (Lesson 5.3)

Question 10.
y + 3y
Answer: 4y

Explanation:
Given,
=> y + 3y
=> 4y

Question 11.
a + a – 2
Answer: 2a – 2

Question 12.
3b + 5b – 2b
Answer:
Given,
=> 3b + 5b – 2b
=> 8b – 2b
=> 6b

Question 13.
8c + 6 – 1 – c
Answer:
Given,
=> 8c + 6 – 1 – c
=> 8c – c + 6 – 1
=> 7c + 6 – 1
=> 7c + 5

Complete with =, >, or < for d = 7. (Lesson 5.4)

Question 14.
d + 7 15
Answer:
Given,
=> 7 + 7 = 15
=> 14 < 15

Question 15.
3d – 10 11
Answer:
Given,
=> 3d – 10 = 11
=> 3(7) – 10 = 11
=> 21 – 10 = 11
=> 11 = 11

Question 16.
2d + 6 3d – 2
Answer:
Given,
=> 2d + 6 = 3d – 2
=> 2(7) + 6 = 3(7) – 2
=> 14 + 6 = 21 – 2
=> 20 > 19

Question 17.
(35 ÷ d) + 5 d
Answer:
Given,
35 / d, where d = 7,
=> 35 / 7 + 5 = 7,
=> 5 + 5 = 7,
=> 10 > 7

Solve each equation. (Lesson 5.4)

Question 18.
2e = 8
e = ________
Answer:
Given,
=> 2e = 8
=> e = 8/2
=> e = 4

Question 19.
3f + 3 = 18
f = _________
Answer:
Given,
=> 3f + 3 = 18,
=> 3f = 18 – 3
=> 3f = 15
=> f = 15/3
=> f = 5

Question 20.
6g – 5 = 2g + 3
g = _____
Answer:
6g – 5 = 2g + 3
=> 6g – 2g = 3 + 5
=> 4g = 8
=> g = 8 / 4
=> g = 2.

Question 21.
4h – 11 = h + 16
h = ____
Answer:
Given,
=> 4h – 11 = h + 16
=> 4h – h = 16 + 11
=> 3h = 27
=> h = 27 / 3
=> h = 9

Find the area of each rectangle. (Lesson 6.1)

Question 22.

Area: _____
Answer:
Given,
=> Length = 5 / 7 m, Width = 3 / 7 m,
=> Area of rectangle = Length x Width
=> A = 5 / 7 x 3 / 7
=> A = 15 / 49

Question 23.

Answer:
Given,
=> Length = 6 / 8 ft, Width = 2 / 3 ft,
=> Area of rectangle = Length x Width
=> A = 6 / 8 x 2 / 3
=> A = 12 / 24
=> A = 1 / 2

Question 24.
A rectangular tray was placed on a square mat. The tray measures \(\frac{3}{4}\) feet by \(\frac{5}{6}\) feet. what is the area of the tray.

Answer: Area of the rectangular tray = 5 / 8

Explanation:
Given,
=> Area of rectangular tray = Length x Width
=> A = 3 / 4 x 5 / 6
=> A = 15 / 24
=> A = 5 / 8

Complete to give both the base and the height in each triangle. (Lesson 6.2)

Question 25.

Base: ____
Height: _____
Answer: Base = BC, Height = AC

Question 26.

Height: _____
Base: ____
Answer: Base = EF, Height = DG

Question 27.

Base: ____
Height: _____
Answer: Base = BC, Height = AD

Question 28.

Base: ____
Height: _____
Answer: Base = PQ, Height = PS

Find the area of each shaded triangle. (Lesson 6.3)

Question 29.

Area = ___
Answer: Area of the triangle = 2025

Explanation:
Given,
Area of triangle = 1/2 x base x height
=> 1/2 x 150 x 27
=> 1 x 75 x 27
=> 2025

Question 30.

Area = ___
Answer: Area of triangle = 160 square inches

Explanation:
Given,
=> Area of triangle = 1/2 x base x height
=> A = 1/2 x 20 x 16
=> A = 1 x 10 x 16
=> A = 160 square inches

Find the area of each shaded triangle. (Lesson 6.3)

Question 31.

Area = ____
Answer: Area of triangle = 3875 square ft

Explanation:
Given,
Area of triangle = 1/2 x base x height
=> A = 1/2 x 125 x 62
=> A = 1 x 125 x 31
=> A = 3875 square ft

Question 32.

Area = ____
Answer: Area of triangle = 26 square yards

Explanation:
Given,
=> Area of triangle = 1/2 x base x height
=> A = 1/2 x 13 x 4
=> A = 1 x 13 x 2
=> A = 26 sqaure yards.

Question 33.

Area = ____
Answer: Area of triangle = 700 square inches

Explanation:
Given,
=> Area of triangle = 1/2 x base x height
=> A = 1/2 x 40 x 35
=> A = 20 x 35
=> A = 700 square inches

Question 34.

Answer: 6390 square cm

Explanation:
Given,
=> Area of triangle = 1/2 x base x height
=> A = 1/2 x 142 x 90
=> A = 1 x 71 x 90
=> A = 6390 square cm

Find the total area of the shaded parts. (Lesson 6.3)

Question 35.

Area = ____
Answer: Area of shaded parts in the triangle = 120 square cm

Explanation:
Given,
Area of triangle = 1 / 2 x base x height
=> A = 1 / 2 x 24 x 10
=> A = 1 x 24 x 5
=> A = 120 square cm

Complete. (Lesson 7.1)

Question 36.
The ratio of the length of A to the length of B is _________ : ______
Answer: 5 : 11
Explanation:
Given,
Length of A is 5,
Length of B is 11,
Ratio of the length of A to the length of B is 5 : 11.

Question 37.
The ratio of the length of C to the length of A is _________ : _____
Answer: 7 : 5
Explanation:
Given,
Length of C is 7,
Length of A is 5,
Ratio of the length of C to the length of A is 7 : 5

Question 38.
The ratio of the length of B to the total length of A, B, and C is __ : ____
Answer: 11 : 23
Explanation:
Given,
Length of B is 11,
Total length of A, B and C is by adding 5 with 11 we get 16 and add 16 to 7 we get 23,
Ratio of the length of B to th total length of A, B and C is 11 : 23.

Complete. (Lesson 7.2)

Question 39.
The ratio of the number of squares in Set A to the number of squares in Set B is ______ : ___.
Answer: 8 : 20
Explanation:
Given,
Number of squares in Set A is 8,
Number of squares in Set B is 20,
Ratio of the number of squares in Set A to the number of squares in Set B is 8 : 20

Question 40.
The ratio of the number 0f groups in Set A to the number of groups in Set B is ______ : ____.
Answer: 2 : 5
Explanation:
Number of groups in Set A is 2,
Number of groups in Set B is 5,
Ratio of the number of groups in Set A to the number of groups in Set B is 2 : 5

Question 41.
___________ : ___________ ___________ : ___________ in simplest form.
Answer: 8 : 20 = 4 : 10 = 2 : 5
Explanation:
Numbers 8 and 20 are divisible by 2 we get 4 : 10,
4 and 10 are again divisible by 2 we get 2 : 5,
To get into simplest form 8 and 20 should be divisible by 2.

Find the missing number or term in each set of equivalent ratios. (Lesson 7.2)

Question 42.
7 : 4 = 21: ______
Answer: 7 : 4 = 21 : 12
Explanation:
Given,
Both the numbers 7 and 4 can be multiplied by 3, we get 21 : 12

Question 43.
5 : 9 = ______ : 63
Answer: 5 : 9 = 35 : 63
Explanation:
Given,
Both the numbers 5 and 9 can be multiplied by 7, we get 35 : 63

Question 44.
18 : 21 = 6: _____
Answer:18 : 21 = 6 : 7
Explanation:
Given,
Both the numbers 18 and 21 can be divided by 3, we get 6 : 7.

Question 45.
108 : 72 = _____ : 6
Answer: 108 : 72 = 9 : 6
Explanation:
Given,
Both the numbers 108 and 72 can be divided by 12, we get 9 : 6.

Complete. (Lesson 7.4)

The heights of two buildings are shown.

Question 46.
The ratio of the height of Math Plaza to the height of

Answer:

Question 47.
The height of Math Plaza is ___ times the height of Focus Tower.
Answer: The height of Math plaza is 5 / 9 times the height of focus tower

Explanation:
Given,
Focus tower height as 9,
Math Plaza height as 5,
Therefore, the height of Math plaza is 5 / 9 times the height of focus tower.

Question 48.
The height of Focus Tower is ___ times the height of both buildings.
Answer: The height of focus tower is 9 / 14 times the height of both buildings

Explanation:
Given,
Height of Focus tower is 9,
Height of Math plaza is 5,
By adding 9 with 5 we get 14,
Therefore, the height of focus tower is 9 / 14 times the height of both buildings.

Express each ratio in simplest form. (Lesson 7.5)

Question 49.
8 : 12 : 24 = ____ : ____ : ____
Answer: 8 : 12 : 24 = 2 : 3 : 4
Explanation:
Given,
Numbers 8, 12 and 24 are divisible by 4 to get into simplest form as 2 : 3 : 4.

Question 50.
21 : 9 : 36 = __ : __ : ___
Answer: 21 : 9 : 36 = 7 : 3 : 12
Explanation:
Given,
Numbers 21, 9 and 36 are divisible by 3 tp get into the simplest form as 7 : 3 : 12.

Find the missing numbers or terms in each set of equivalent ratios. (Lesson 7.5)

Question 51.
4 : 6 : 9 = 24: __ : ___
Answer: 4 : 6 : 9 = 24 : 36 : 54
Explanation:
Given,
Ratio 4 : 6 : 9 is multiplied by 6 then we get 24 : 36 : 54

Question 52.
48 : 56 : 28 = ___ : ___ : 7
Answer: 48 : 56 : 28 = 12 : 14 : 7
Explanation:
Given,
Ratio 48 : 56 : 28 is multiplied by 4 then we get 12 : 14 : 7

Problem Solving

Solve. Show your work.

Question 53.
Mandy scores b points in a basketball game. Jay scores 3 points less than Mandy. Kareem scores 2 times as many points as Mandy.

a. Find the number of points that Jay scores in terms of b.
Answer: The number of points that Jay scores is b – 3

Explanation:
Given,
Mandy scores b points in a basketball game,
Jay scores 3 points less than Mandy,
Therefore, Jay scores b – 3 points less than Mandy in terms of b.

b. Find the total number of points the three players score in terms of b.
Answer: The total number of points of three players are Mandy’s scores b, Jay scores b – 3, Kareem scores 2b.

Explanation:
Given,
Mandy scores b points, Mandy scores = b points
Jay scores 3 points less than Mandy, Jay scores = b – 3 points,
Kareem scores 2 times as many points as Mandy, Kareem scores = 2b points.

Question 54.
David reads a book that has (3x + 6) pages. Ellen reads a book that has (4x – 4) pages.

a. If x = 7, whose book has more pages?
Answer: David reads a book which has 27 pages and Ellen reads a book which has 24 pages, So David’s book has more pages than Ellen’s book.

Explanation:
Given,
David’s book:                   Ellen’s book:
=> (3x + 6), If x = 7         => (4x – 4), if x = 7
=> (3(7) + 6)                     => (4(7) – 4)
=> 21 + 6                            => 28 – 4
=> 27                                  => 24

b. For what value of x will the two books have the same number of pages?
Answer: If x = 10, then two books have the same number of pages
Explanation:
Given,
David’s book:                     Ellen’s book:
=> (3x + 6), If x = 10        => (4x – 4), if x = 10
=> (3(10) + 6)                    => (4(10) – 4)
=> 30 + 6                            => 40 – 4
=> 36                                   => 36

Solve. Show your work.

Question 55.
In the figure, BC = 18 cm and AD = BD. The length of BD is twice the length of BC. Find the area of the shaded triangle ABC.

Answer: Area of triangle = 324 square cm

Explanation:
Given,
BC = 18 cm,
BD = twice the length of BC,
BD = 2(18) = 36 cm
AD = BD,
=> Area of triangle = 1/2 x base x height
=> A = 1/2 x BC x AC
=> A = 1/2 x 18 x 36
=> A = 1 x 9 x 36
=> A = 324 square cm

Question 56.
ABCD is a rectangle with a width of 1 2 centimeters. Its length is twice as long as its width. AE = 12 centimeters and AF = BF. Find the area of the shaded triangle CEF.

Answer: Area of triangle = 144 square cm

Explanation:
Given,
Width = 12 cm,
Length is twice as long as width, L = 2 x 12 = 24 cm,
AE = 12 cm,
AF = BF,
=> Area of triangle = 1/2 x base x height
=> A = 1/2 x 24 x 12
=> A = 1 x 12 x 12
=> A = 144 square cm.

Solve. Show your work.

Give your answer in either ratio form or fraction form.

Question 57.
There were 45 pennies in Container A and 79 pennies in Container B at first. Suki took 7 pennies from Container A. She then put them into Container B.

a. What is the ratio of the number of pennies in Container A to that in Container B at first?
Answer: 45 : 79
Explanation:
Given,
There were 45 pennies in Container A,
Pennies in Container B is 79,
The ratio of the number of pennies in Container A to that in Container B at first is 45 : 79

b. Find the ratio of the number of pennies in Container A to that in Container B in the end. Express your answer in simplest form.
Answer: 38 : 79
Explanation:
Given,
There were 45 pennies in Container A at first and Suki took 7 pennies from Container A,
By subtracting 7 from 45 we get 38,
Pennies in Container B is 79,
The ratio of the number of pennies in Container A to that in Container B at the end is 38 : 79.

Solve. Draw a model to help you.

Question 58.
Peggy cycles 3 times as far as Dakota.
a. Find the ratio of the distance that Peggy cycles to the distance that Dakota cycles. Give your answer in fraction form.
Answer: 3 : 1 or 3 / 1 is the ratio of the distance that Peggy cycles to the distance that Dakota cycles.
Explanation:
Given,
Peggy cycles 3 times as far as Dakota,
So Peggy cycles are considered as 3,
Dakota cycle is considered as 1,
Therefore, the ratio of the distance that Peggy cycles to the distance that Dakota cycles is 3 : 1.

b. How many times the combined distance is the distance that Peggy cycles?
Answer: Peggy goes 3 parts of the total distance compared to 1 part for Dakota,
so Peggy accounts for 3/4 of the entire distance,
Dakota does the other part is 1/4.

Solve. Show your work.

Question 59.
A company makes yearly donations to Charities A, B, and C in the ratio 3 : 7 : 9. It donates $5,096 to Charity B in a year.

a. How much does it donate to Charity A in a year?
Answer: Company donates $2,184 to Charity A in a year.
Explanation:
Given,
A company makes yearly donations to Charities A, B and C in the ratio 3 : 7 : 9,
It donates $5,096 to Charity B in a year,
The ratio of A / B is 3 / 7
A / B = 3 / 7 = A / 5,096
Need to cross multiply, then we get
7 A = 3 x 5,096
7 A = 15,288
A = 15288 / 7
A = 2,184

b. How much does it donate to all three charities in a year?
Answer: Company donates to all three charities in a year is $13,832.
Explanation:
Given,
Company donates donation to Charity A is 2184,
Company donates donation to Charity B is 5096,
Company donates donation to Charity C is 6552,
By adding 2184, 5096 and 6552 then we get 13,832.

Question 60.
The ratio of the number of boys to the number of girls in a camp is 3 : 7. There are 24 boys in the camp.

a. How many girls are there in the camp?
Answer: 56 number of girls are there in the camp.
Explanation:
Given,
The ratio of the number of boys to the number of girls in a camp is 3 : 7,
There are 24 boys in the camp,
By multiplying 3 and 7 with 8 we get 24 : 56,
Therefore, there are 24 boys and 56 girls in the camp.

b. The camp fee is $50 per person. Find the total amount of fees the girls pay.
Answer: The total amount of fees the girls pay is $2800.
Explanation:
Given,
The number of girls in the camp are 56,
The camp fee is $50 per person,
By multiplying 56 with 50 we get 2800,
Therefore, the total amount of fees the girls pay is $2800.

Practice the problems of Math in Focus Grade 2 Workbook Answer Key Chapter 12 Practice 1 Understanding Fractions to score better marks in the exam.

Math in Focus Grade 2 Chapter 12 Practice 1 Answer Key Understanding Fractions

Put an ✗ in the box if the shape is divided into equal parts.

Example

Question 1.

Answer:
The given circle shape is not divided in the equal parts.
There are 4 parts in the circle. These 4 parts are not in the equal shape.

Question 2.

Answer:

The given circle shape is divided into 4 equal parts.
Question 3.

Answer:
The given triangle shape is not divided in the equal parts.
There are 3 parts in the triangle. These 3 parts are not in the equal shape.

Question 4.

Answer:

The given shape is divided into 3 equal parts.

Question 5.

Answer:
The given rectangular shape is not divided in the equal parts.
There are 4 parts in the rectangle. These 4 parts are not in the equal shape.

Question 6.

Answer:

The given triangle is divided into 3 equal parts.

Question 7.

Answer:

The given square is divided into 4 equal parts.

Look at the pictures. Then fill in the blanks.

Example

Question 8.

The rectangle is divided into ___________ equal parts. ___________ part of the rectangle is shaded.
Answer:
The rectangle is divided into 3 equal parts. 1 part of the rectangle is shaped.

Circle the fraction and words that match the picture.

Example

Question 9.

Answer:

The given circle is divided into 2 parts and 1 part is shaded.
Question 10.

Answer:

The rectangle is divided into 3 parts and 1 part is shaded.

Mark with an ✗ the fractional part that does not belong in each row.

Example

Question 11.

Answer:
In the given figures the wrong image is the circle.

Question 12.

Answer:
In the given figures the wrong image is the triangle that is divided into 4 parts.

Fill in the blanks.

Example

Question 13.

__________ out of ___________ equal parts is shaded.
___________ of the figure is shaded.
Answer:
1 out of 2 equal parts is shaded.
1/2 of the figure is shaded.

Question 14.

___________ out of ___________ equal parts is shaded.
___________ of the figure is shaded.
Answer:
1 out of 3 equal parts is shaded.
1/3 of the figure is shaded.

Question 15.

___________ out of ___________ equal parts is shaded.
___________ of the figure is shaded.
Answer:
1 out of 4 equal parts is shaded.
1/4 of the figure is shsded.

Write a fraction for each shaded part.

Example

Question 16.

Answer:
The Given circle is divided into 4 parts and 1 part is shaded.
The fraction of the figure is 1/4.

Question 17.

Answer:
The given rectangle is divided into 2 parts and 1 part is shaded.
The fraction of the figure is 1/2.

Question 18.

Answer:
The given shape is divided into 3 equal parts and 1 part is shaded.
The fraction of the given figure is 1/3.

Question 19.

Answer:
The given shape is divided into 4 equal parts and 1 part is shaded.
The fraction of the given figure is 1/4.

Shade part(s) of each figure to show the fraction.

Question 20.
\(\frac{1}{3}\)

Answer:
\(\frac{1}{3}\) = 1/3
The given figures is divided into 3 parts. Then shade the 1 part.

Question 21.
\(\frac{1}{4}\)

Answer:
\(\frac{1}{4}\) = 1/4
The given figures is divided into 4 parts. Then shade the 1 part.

Question 22.
\(\frac{1}{2}\)

Answer:
\(\frac{1}{2}\) = 1/2
The given figures are divided into 2 parts. Then shade the 1 part.

Match the words and fractions to the figures.

Question 23.

Answer:

Practice the problems of Math in Focus Grade 2 Workbook Answer Key Chapter 7 Practice 1 Measuring in Meters to score better marks in the exam.

Math in Focus Grade 2 Chapter 7 Practice 1 Answer Key Measuring in Meters

Look at the pictures.

Fill in the blanks with more or less.

Question 1.

The length of the rope ¡s _________ than 1 meter.
Answer: The length of the rope is less than 1 meter.

Question 2.

The length of the slide is ___ than 1 meter.
Answer: The length of the slide is more than 1 meter.

Question 3.

The height of the bookcase is __ than 1 meter.
Answer: The height of the bookcase is more than 1 meter

Fill in the blanks.

Question 4.
Metersticks are placed against two boxes.
a. Which box is about 1 meter long? Box _____
Answer:

Fill in the blanks with more or less.

b. Box A is ___ than 1 meter long.
Answer:

c. Box B is ___ than 1 meter long.
Answer:

Question 5.
Metersticks are placed against a board.

a. Which side of the board is about 3 meters long? Side _____
Answer: Side B of the board is about 3 meters long

b. Side A is shorter than ___ meter.
Answer: Side A is shorter than 1 meter.

c. Side B is shorter than ___ meters.
Answer: Side B is shorter than 3 meters.

Look at the list below.
Check (✓) the columns that are true.
You will need a meterstick or a 1-meter string to measure some items.

Question 6.

Answer:

Name three things that match each length.

Question 7.

Answer:

Fill in the blanks.
Use string and a meterstick.

Question 8.
Mark on the string with a pencil how long you think 1 meter is. Then use a meterstick to measure this length. Did you mark more or less than 1 meter on your string? _____
Answer:

Question 9.
Next, mark on the string how long you think 2 meters are. Then use a meterstick to measure this length.
Did you mark more or less than 2 meters on your string? _____
Answer:

Practice the problems of Math in Focus Grade 2 Workbook Answer Key Chapter 7 Practice 3 Measuring in Centimeters to score better marks in the exam.

Math in Focus Grade 2 Chapter 7 Practice 3 Answer Key Measuring in Centimeters

Check (✓) the correct way to measure the length of the pencil.

Question 1.

Answer:

Use your centimeter ruler to draw.

Question 2.
A line that is 5 centimeters long
___________
Answer:

Question 3.
A line that is 12 centimeters long
_____________
Answer:

Question 4.
A line that is 9 centimeters long
___________
Answer:

Use your centimeter ruler to draw.

Question 5.
A line that is 6 centimeters long
_______________
Answer:

Question 6.
A line that is 2 centimeters shorter than the line in Exercise 4.
_____________
Answer:

Question 7.
A line that is 2 centimeters longer than the line in Exercise 5.
_____________
Answer:

Use a piece of string to find the length.

Question 8.

Answer: 7.1 cm

Question 9.

Answer: 7 cm

Question 10.

Answer: 3.1 cm

Cut a piece of string as long as the drawing below. Then place the string on a centimeter ruler to find its length.

Question 11.
a. How long is the string? ___ cm

Answer: The string is 8.5 cm long

b. This string is used to form the following shapes. Use a string and a centimeter ruler to measure each of them.

Do they all have the same length? ____
Explain your answer.
Answer:

Find the missing numbers.

Question 12.
The pencil is _________ centimeters long.
Answer: The pencil is 8 centimeters long.

Question 13.
The eraser is _________ centimeters long.
Answer: The eraser is 3 centimeters long.

Question 14.
The length of the comb is ___ centimeters.
Answer: The length of the comb is 5 centimeters

Question 15.
The length of the ribbon is ___ centimeters.
Answer: The length of the ribbon is 7 meters centimeters.

Question 16.
The length of the eraser is ____ centimeters.
Answer: The length of the eraser is 2 centimeters.

Practice the problems of Math in Focus Grade 2 Workbook Answer Key Chapter 7 Metric Measurement of Length to score better marks in the exam.

Math in Focus Grade 2 Chapter 7 Answer Key Metric Measurement of Length

Put on Your Thinking cap!

Challenging Practice

Solve.

Question 1.
There are three drawings—A, B, and C. Drawing A is shown below.
________ Drawing A
Drawing B is 2 centimeters longer than Drawing A. Drawing C is 3 centimeters shorter than Drawing B. How long is Drawing C?
Answer:
Drawing A is 2.5 cm,
Drawing B is 2 centimeters longer than Drawing A,
By adding 2 centimeters to 2.5 we get 4.5 cm as Drawing B,
Drawing C is 3 centimeters shorter than Drawing B,
By subtracting 3 cm from 4.5 cm we get 1.5 cm as Drawing C,
Therefore,Drawing A is 2.5cm,Drawing B is 4.5cm and Drawing C is 1.5cm.

Question 2.
Sara bought three pieces of ribbon. She bought 90 centimeters of ribbon in all. Check (✓) to show which three pieces of ribbon she bought.

Answer:
Given,
Sara bought three pieces of ribbon,
She bought 90 centimeters of ribbon,
By adding 42 with 38 we get 80 and adding 80 with 10 we get 90,
Therefore, first ribbon is 42 cm, second ribbon is 38 cm and third ribbon is 10 cm.

Put on Your Thinking Cap!

Problem Solving

The picture shows the shadows of two trees.

Look at the shadows. Which tree is taller? Tree ____
Explain your answer.
___________________
___________________
___________________
Answer: Tree B is taller than Tree A
Explanation:
Given,
Tree A, Tree B Shadows and a Sun,
Tree B’s shadow is bigger than Tree A,
Therefore, Tree B is taller than Tree A.

Chapter Review/Test

Vocabulary

Fill in the blanks with the words in the box.

Question 1.

To find how high this bookcase is, I need to find its ___________________
Answer: To find how high this bookcase is, I need to find its Height.

Question 2.
An earthworm is about 10 ____ long.
Answer: An earthworm is about 10 centimeters long.

Question 3.

This is a ________
Answer: This is a meterstick.

Fill in the blanks with the words in the box.

Question 4.

Jose is trying to find the ___ of the door.
Answer: Jose is trying to find the width of the door.

Question 5.
A whiteboard is about 3 ____ long
Answer: A whiteboard is about 3 meters long

Question 6.

The _________ of this truck is about 6 meters.
Answer: The length of this truck is about 6 meters.

Concepts and Skills

Check (✓) the correct answers.

Question 7.
What is the length of your math textbook?

Answer: Less than meter

Question 8.
What is the height of your desk?

Answer: Less than meter

Question 9.
What is the height of your classroom?

Answer: More than 8 meters

Look at the objects measured. Then fill in the blanks.

Question 10.
spoon: ___ cm
Answer: 6 cm

Question 11.
brush: ___ cm
Answer: 9cm

Question 12.
craftstick: ___ cm
Answer: 10 cm

Question 13.
The craftstick is ___ centimeters longer than the spoon.
Answer:
The craftstick is 4 centimeters longer than spoon.
Explanation:
Given,
Craftstick is 10 centimeters,
Spoon is 6 centimeters,
By subtracting 6 from 10 we get 4,
Therefore, the craftstick is 4 centimeters longer than spoon.

Question 14.
The ___ is the shortest.
Answer: The Spoon is the shortest.
Explanation:
Given,
Spoon is 6 centimeters,
Brush is 9 centimeters,
Craftstick is 10 centimeters.

Solve.

Question 15.
Shane has 5 meters of cloth. He needs 16 meters more cloth to make some curtains. How many meters of cloth are needed to make the curtains?
____ meters of cloth are needed to make the curtains.
Answer:
21 meters of cloth are needed to make the curtains.
Explanation:
Given,
Shane has 5 meters of cloth,
He needs 16 meters more cloth,
By adding 5 with 16 we get 21,
Therefore, 21 meters of cloth are needed to make the curtains.

Question 16.
Two boards are 26 meters long altogether. One board is 8 meters long. How long is the other board?
The other board is ____ meters long.
Answer:
The other board is 18 meters long.
Explanation:
Given,
Two boards are 26 meters long altogether,
One board is 8 meters long,
By subtracting 8 from 26 we get 18,
Therefore, the other board is 18 meters long.

Question 17.
Bella is 161 centimeters tall. She is 12 centimeters taller than Joshua. How tall is Joshua?
Joshua is ___ centimeters tall.
Answer:
Joshua is 149 centimeters tall.
Explanation:
Given,
Bella is 161 centimeters tall,
She is 12 centimeters taller than Joshua,
By subtracting 12 from 161 we get 149,
Therefore, Joshua is 149 centimeters tall.

Question 18.
Raul has a box that is 9 centimeters wide. Ling’s box is 3 centimeters wider than Raul’s box. Will both their boxes fit on a shelf that is 30 centimeters wide? Explain why.
Answer:
Yes, both their boxes will fit on a shelf that is 30 centimeters wide.
Explanation:
Raul has a box that is 9 centimeters wide,
Ling’s box is 3 centimeters wider than Raul’s box,
By adding 9 with 3 we get 12 which is the width of Ling’s box,
Then, Raul’s box and Ling’s box will make by adding 12 with 9 we get 21,
Width of both boxes is shorter than the Shelf’s width,
Therefore, both the boxes will fit on a shelf.

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 5 Practice 3 How to Divide to finish your assignments.

Math in Focus Grade 2 Chapter 5 Practice 3 Answer Key How to Divide

Example

Divide 10 snails into 2 equal groups.

10 ÷ 2 = 5
There are 5 snails ¡n each group.

Question 1.
Divide 15 books into 3 equal stacks.

15 ÷ ______ = ______
There are ________ books in each stack.
Answer:
Given that number of books are 15
The 15 books are divided into 3 equal stacks.
Number of books in each stack is 15 ÷ 3 = 5
There are 5 books in each stack.

Question 2.
Divide 15 eggs equally info 5 nests.

15 ÷ ______ = ______
There are ___ eggs in each nest.
Answer:
Given that there are 15 eggs.
15 eggs are divided into 5 nests.
Number of eggs in each nest is 15 ÷ 5 = 3
There are 3 eggs in each nest.

Find the number of groups.
Fill in the blanks.

Example

Divide 15 pancakes so there are 3 pancakes in each group.

Subtract groups of 3 until there is nothing left.
15 ÷ 3 – 3 – 3 – 3 – 3 = 0
How many times do you subtract groups of 3? 5
15 ÷ 3 = 5
There are 5 groups.

Question 3.
Divide 12 beads into groups of 4.
12 – ______ – ___ – ___ = 0
12 ÷ ___ = ____
There are ___ groups of 4 beads.
Answer:
Given that number of beads are 12.
They are divided into 4 groups.
The number of breads are
12 – 4 – 4 – 4 = 0
12 ÷ 4 = 3
There are 3 groups of 4 beads.

Question 4.
Divide 14 frozen yogurt cones into groups of 7.

14 – ___ – ___ = 0
14 ÷ ___ = ____
There are ___ groups of 7 frozen yogurt cones.
Answer:
Given that there are 14 frozen yogurt cones.
These 14 frozen yogurt cones are 7 of each group.
Number of groups are
14 – 7 – 7 = 0
14 ÷ 2 = 7
There are 2 groups of 7 frozen yoghurt cones.

Question 5.
Put 20 oranges onto plates with 5 on each plate.

20 – _______ – _______ — _______ — _______ =0
20 ÷ ______ = ______
There are ___ plates of 5 oranges.

Answer:
Given that total number of oranges are 20
The 20 oranges are put in a 5 plates.
Number of oranges on each plate are
20 – 5 – 5 – 5 – 5 = 0
20 ÷ 5 = 4
There are 4 plates of 5 oranges.

Fill in the blanks.

Question 6.
Put 16 glasses onto trays with 4 on each tray.

16 – _______ — _______ — _______ — _______ = 0
16 ÷ ______ = ______
There are ___ trays of 4 glasses.
Answer:
Given that there are 16 glasses.
Each tray has 4 glasses.
Number of trays are
16 – 4 – 4 – 4 – 4 = 0
16 ÷ 4 = 4
There are 4 trays of 4 glasses.

Question 7.
Put 8 cookies onto plates with 2 on each tray.

8 – ___ – ___ – ____ – ___ = 0
8 ÷ ___ = ____
There are ___ plates of 2 cookies.
Answer:
Given that the total number of cookies are 8.
Each of 2 cookies are putted in a plate as a group.
Number of plates are 8 – 2 – 2 – 2 – 2 = 0
8 ÷ 2 = 4
Therefore there are 4 plates of 3 cookies.

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 5 Practice 5 Real-World Problems: Algebra to finish your assignments.

Math in Focus Grade 5 Chapter 5 Practice 5 Answer Key Real-World Problems: Algebra

Solve. Show your work.

Question 1.
Raul has 5 boxes of golf balls. Each box contains y golf balls. His father gives him another 8 golf balls.

a. Find the total number of golf balls Raul has in terms of y.
Answer:
Number of boxes of golf balls Raul has = 5
As each box contains ‘y’ balls, total number of balls Raul has = 5y
Number of balls given by Raul’s father = 8
So, total number of golf balls does Raul has = 5y+8

b. If y = 4, how many golf balls does Raul have altogether?
Answer:
Total number of golf balls Raul has = 5y+8
If y=4, then total number of golf balls Raul has = (5×4)+8 = 20+8 = 28
So, Raul altogether has 28 balls.

Question 2.
Glenda bought z containers of laundry detergent at $9 each. She gave the cashier $50.

a. Find the change Glenda received in terms of z.
Answer:
Total number of laundry detergent containers bought = z
Cost of all containers bought = (9×z) $
Cash given to cashier = 50 $
Change received by Glenda = [50 – (9×z)] $

b. If z = 3, how much change did Glenda receive?
Answer:
If z=3. then total change received = [50-(9×3)] $ = [50-27]$ = 23$

Question 3.
Garrett is w years old. His mother is 4 times his age. His father is 3 years older than his mother.

a. How old is Garrett’s father in terms of w?
Answer:
Age of Garrett = w years
Age of Garrett’s mother = (4×w) years
Age of Garrett’s father = [(4×w)+3] years

b. If w = 9, how old is Garrett’s father?
Answer:
Age of Garrett’s father = [(4×w)+3] years
If w=9, then age of Garrett’s father = [(4×9)+3] = 39 years

Question 4.
An office manager bought 16 boxes of pens, each containing m pens. Workers took 10 pens from the supply room.

a. How many pens were left? Give your answer in terms of m.
Answer;
Total number of boxes of pens bought = 16
Number of pens each box contains = m
So, total number of pens bought = 16×m
Number of pens workers took from supply room = 10
So. then number of pens left = total number of pens – pens taken by workers
=(16×m)-10

b. If m = 5, how many pens were left in the supply room?
Answer:
Total number of pens left in supply room = (16×m)-10
If m=5, then total number of pens left = (16×5)-10 = 80-10= 70

Solve. Show your work.

Question 5.
Sarah has a box containing x ribbons and 4 extra ribbons. Jill has 1 2 ribbons.

a. Express the number of ribbons that Sarah has in terms of x.
Answer:
Number of ribbons Sarah has in box = x
Number of extra ribbons Sarah has = 4
So, total number of ribbons Sarah has= x+4

b. For what value of x will Sarah and Jill have the same number of ribbons?
Answer:
Number of ribbons Sarah has = x+4
Number of ribbons Jill has = 12
If we need to have same number of ribbons for Sarah and Jill, then
x+4 =8
x=8-4 = 4
So, for the value of x as 4, Sarah and Jill have the same number of ribbons

Question 6.
Henry made (2y + 4) paper cranes. Elise made (3y – 9) paper cranes.

a. If y = 6, who would have made more paper cranes?
Answer:
If y=6,
Paper cranes made by Henry = (2y+4) = [(2×6)+4] = 12+4 = 16
Paper cranes made by Elise= (3y-9) = [(3×6)-9] = 18-9 = 9

b. For what value of y will they have made the same number of paper cranes?
Answer:
Number of paper cranes Henry has = 2y+4
Number of paper cranes Elise has = 3y-9
If we need to have same number of paper cranes for Henry and Elise, then
3y-9 = 2y+4
3y-2y = 4+9
y=13
So, for the value of y as 13, Henry and Elise will have the same number of paper cranes

Solve. Show Your Work

Question 7.
Mary has y yards of fabric. She used 2 yards to sew a skirt. She used the remaining fabric to make 5 jackets.

a. Find the amount of material that was used to make each jacket in terms of y.
Answer:
Total number of yards of fabric = y
Total yards used to sew a skirt = 2
So, total number of yards left = y-2
Number of jackets made with remaining fabric = 5
So, amount of material that was used to make each jacket  = (y-2)/5

b. If she has 17 yards of fabric, how much material was used for each jacket?
Answer:
If y=17, then material used for each jacket = (y-2)/5 = (17-2)/5 = 15/5 = 3

Question 8.
A magazine costs half as much as a book. The book costs p dollars. A pen costs $2 more than the magazine.
a. How much does the pen cost in terms of p?
Answer:
Cost of book = p$
A magazine costs half as much as a book which implies a book is twice the cost of a magazine.
So, cost of magazine = 2p $
A pen costs $2 more than the magazine.
So, cost of pen = 2p$ + 2$ = (2p+2) $

b. If the book costs $5, how much does the pen cost?
Answer:
If book costs $5,
cost of pen = (2p+2) $ = [(2×5)+2] $ = (10+2) $ = 12$

Practice the problems of Math in Focus Grade 5 Workbook Answer Key Chapter 6 Practice 3 Finding the Area of a Triangle to score better marks in the exam.

Math in Focus Grade 5 Chapter 6 Practice 3 Answer Key Finding the Area of a Triangle

Example

Question 1.

Area of a triangle = _____
= ________
Answer:
Height = 26 m
Base = 17m
Area of the triangle = 1/2 × b × h
= 1/2 × 17 × 26
= 221 m²

Question 2.

Area of a triangle = _____
= ________
Answer:
From the above figure Base of the triangle is 72 cm. Height of the triangle is 54 cm.
Area of the triangle = 1/2 × b × h
= 1/2 × 72 × 54
= 1,944 cm²

Question 3.

Area of triangle = ____
= _______
Answer:
From the above figure Base of the triangle is 38 ft. Height of the triangle is 45 ft.
Area of the triangle = 1/2 × b × h
= 1/2 × 38 × 45
= 855 ft²

Find the area of each shaded triangle.

Example

Question 4.

Area = ____
= ______
Answer:
From the above figure Base of the triangle is 12 in. Height of the triangle is 4 in.
Area of the triangle = 1/2 × b × h
= 1/2 × 12 × 4
= 24 in²

Question 5.

Area = _____
= ______
Answer:
From the above figure Base of the triangle is 28 in. Height of the triangle is 18 in.
Area of the triangle = 1/2 × b × h
= 1/2 × 28 × 18
= 252 in²

Question 6.

Area = _____
= ______
Answer:
From the above figure Base of the triangle is 5 cm. Height of the triangle is 5 cm.
Area of the triangle = 1/2 × b × h
= 1/2 × 5 × 5
= 25/2 cm²

Question 7.

Area = ____
= ______
Answer:
From the above figure Base of the triangle is 7 in. Height of the triangle is 4 in.
Area of the triangle = 1/2 × b × h
= 1/2 × 7 × 4
= 14 in²

Question 8.

Area = _____
= _______
Answer:
From the above figure Base of the triangle is 14 in. Height of the triangle is 15 in.
Area of the triangle = 1/2 × b × h
= 1/2 ×14 × 15
= 105 in²

Practice the problems of Math in Focus Grade 5 Workbook Answer Key Chapter 9 Practice 4 Dividing by Tens, Hundreds, and Thousands to score better marks in the exam.

Math in Focus Grade 5 Chapter 9 Practice 4 Answer Key Dividing by Tens, Hundreds, and Thousands

Complete. Draw chips and use arrows to show how the chips move. Then fill in the blanks.

Question 1.

Answer:
140 ÷ 10 = 14
20 ÷ 10 = 2
6 ÷ 10 = 0.6
0.3 ÷ 10 = 0.03
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.

Divide.

Question 2.

Answer:0.6

Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.
So, 6 is written as 0.6.

Question 3.

Answer:5.4

Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.
So, 5.4 is written as 0.54.

Question 4.

Answer: 21.5

Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.
So, 215 will be come 21.5.

Question 5.

Answer:0.52

Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.
So, 5.2 can be written as 0.52.

Question 6.
64.6 ÷ 10 = ______
Answer:6.46

Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
So, 64.6 can be written as 6.46.

Question 7.
4.08 ÷ 10 = ______
Answer: 0.408

Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
So, 4.08 can be written as 0.408.

Question 8.
180.4 ÷ 10 = ______
Answer: 18.04

Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number,
after dividing by 10 , 180.4 is written as 18.04.

Question 9.
1.84 ÷ 1o = ______
Answer:0.184

Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number,
after dividing by 10 , 1.84 is written as 0.184.

Complete.

Question 10.
23.7 ÷ ___ = 2.37
Answer:
23.7 ÷ 10 = 2.37
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number,
after dividing by 10 , 23.7 is written as 2.37.

Question 11.
0.78 ÷ __ = 0.078
Answer: 10
0.78 ÷ 10 = 0.078
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number,
after dividing by 10 , 0.78 is written as 0.078.

Question 12.
____ ÷ 10 = 4.106
Answer: 41.06
41.06 ÷ 10 = 4.106
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number,
after dividing by 10 , 41.06 is written as 4.106.

Question 13.
___ ÷ 10 = 6.4
Answer: 64
64 ÷ 10 = 6.4
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number,
after dividing by 10 , 64 is written as 6.4.

Divide

Example
9 ÷ 30 = (9 ÷ 3) ÷ 10
= 3 ÷ 10
= 0.3
So, 9 ÷ 30 = 0.3

Question 14.
0.09 ÷ 30 = (0.09 ÷ ___) ÷ 10
= ___ ÷ 10
= ______
So, 0.09 ÷ 30 = __
Answer:
0.09 ÷ 30 = (0.09 ÷ 3) ÷ 10
= 0.03 ÷ 10
= 0.003
So, 0.09 ÷ 30 = 0.003
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number,
after dividing by 10.

Question 15.
0.09 ÷ 30 = (0.09 ÷ ___) ÷ 10
= ___ ÷ 10
= ______
So, 0.09 ÷ 30 = ____
Answer: 0.003
0.09 ÷ 30 = (0.09 ÷ 3) ÷ 10
= 0.03 ÷ 10
= 0.003
So, 0.09 ÷ 30 = 0.003
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number,
after dividing by 10.

Question 16.
1.8 ÷ 90 = (1.8 ÷ ___ ) ÷ 10
= ___ ÷ 10
= ____
So, 1.8 ÷ 90 = ____
Answer: 0.02
1.8 ÷ 90 = (1.8 ÷ 9 ) ÷ 10
= 0.2 ÷ 10
= 0.02
So, 1.8 ÷ 90 = 0.02
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number,
after dividing by 10.

Divide.

Question 17.
4.8 ÷ 20 = ___
Answer: 0.24
Explanation:
4.8 ÷ 20 = (4.8 ÷ 2 ) ÷ 10
= 2.4 ÷ 10
= 0.24
So, 4.8 ÷ 20 = 0.24
Question 18.
0.32 ÷ 40 = ___
Answer: 0.008
Explanation:
0.32 ÷ 40 = (0.32 ÷ 4 ) ÷ 10
= 0.08 ÷ 10
= 0.008
So, 0.32 ÷ 40 = 0.008
Question 19.
2.08 ÷ 80 = ___
Answer: 0.026
Explanation:
2.08 ÷ 80 = (2.08 ÷ 8 ) ÷ 10
= 0.26 ÷ 10
= 0.026
So, 2.08 ÷ 80 = 0.026
Question 20.
2.55 ÷ 50 = ____
Answer: 0.051
Explanation:
2.55 ÷ 50 = (2.55 ÷ 5 ) ÷ 10
= 0.51 ÷ 10
= 0.051
So, 2.55 ÷ 50 = 0.051
Question 21.
3.5 ÷ 70 = __
Answer: 0.05
Explanation:
3.5 ÷ 70 = (3.5 ÷ 7 ) ÷ 10
= 0.5 ÷ 10
= 0.05
So, 3.5 ÷ 70 = 0.05
Question 22.
0.3 ÷ 60 = ___
Answer: 0.005
Explanation:
0.3 ÷ 60 = (0.3 ÷ 6 ) ÷ 10
= 0.05 ÷ 10
= 0.005
So, 0.3 ÷ 60 = 0.005
Divide.

Question 23.

Answer: 0.075
Explanation:
7.5 ÷ 100 = (7.5 ÷ 10 ) ÷ 10
= 0.75 ÷ 10
= 0.075
So,  7.5 ÷ 100 = 0.075
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.

Question 24.

Answer: 0.493
Explanation:
49.3 ÷ 100 = (49.3 ÷ 10 ) ÷ 10
= 4.93 ÷ 10
= 0.493
So,  49.3 ÷ 100 = 0.493
Question 25.
6,000 ÷ 100 = ___
Answer: 60
Explanation:
6000 ÷ 100 = (6000 ÷ 10 ) ÷ 10
= 600 ÷ 10
= 60
So,  6000 ÷ 100 = 60
Question 26.
708.2 ÷ 100 = ___
Answer: 7.082
Explanation:
708.2 ÷ 100 = (708.2 ÷ 10 ) ÷ 10
= 70.82 ÷ 10
= 7.082
So,  708.2 ÷ 100 = 7.082
Question 27.

Answer: 0.9
Expalnation:
900 ÷ 1000 = (900 ÷ 10 ) ÷ 10 ÷ 10
= 90 ÷ 10÷ 10
= 9÷ 10
=0.9
So, 9000 ÷ 1000 = 0.9
Question 28.

Answer: 4.103
Explanation:
4103 ÷ 1000 = (4103 ÷ 10 ) ÷ 10 ÷ 10
= 410.3 ÷ 10÷ 10
=41.03 ÷ 10
=4.103
So, 9000 ÷ 1000 = 4.103

Question 29.
909 ÷ 1,000 = ___
Answer: 0.909
Explanation:
909 ÷ 1000 = (909 ÷ 10 ) ÷ 10 ÷ 10
= 90.9 ÷ 10÷ 10
= 9.09÷ 10
=0.909
So, 909 ÷ 1000 = 0.909

Question 30.
9,009 ÷ 1,000 = _______
Answer: 9.009
Explanation:
9009 ÷ 1000 = (9009 ÷ 10 ) ÷ 10 ÷ 10
= 900.9 ÷ 10÷ 10
= 90.09÷ 10
=9.009
So, 9009 ÷ 1000 = 9.009

Complete.

Question 31.
86.2 ÷ _______ = 0.862
Answer: 100
Explanation:
86.2 ÷ 100 = 0.862
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.

Question 32.
275 ÷ _______ = 0.275
Answer: 1000
Explanation:
275 ÷1000 = 0.275
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.

Question 33.
______ ÷ 100 = 0.006
Answer: 0.6
Explanation:
0.6 ÷ 100 = 0.006
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.

Question 34.
______ ÷ 1,000 = 3.082
Answer: 3.082
Explanation:
3082 ÷ 1,000 = 3.082
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.

Complete.

Example
0.07 = 0.7 ÷ 10
= 7 ÷ 100
= 70 ÷ 1,000

Question 35.
0.31 = 3.1 ÷ ______
= 31 ÷ ___
= 310 ÷ ____
Answer:
0.31 = 3.1 ÷ 10
= 31 ÷ 100
= 310 ÷ 1000
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.
When dividing by 1000, move the decimal place three places to the left.

Question 36.
8.06 = ___ ÷ 10
= 806 ÷ ____
= 8,060 ÷ ___
Answer:
8.06 = 80.6÷ 10
= 806 ÷ 100
= 8,060 ÷ 1000
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.
When dividing by 1000, move the decimal place three places to the left.

Question 37.
5.115 = ______ ÷ 10
= ___ ÷ 100
= 5,115 ÷ ______
Answer:
5.115 = 51.15 ÷ 10
= 511.5 ÷ 100
= 5,115 ÷ 1000
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.
When dividing by 1000, move the decimal place three places to the left.

Complete.

Example
42 ÷ 200 = (42 ÷ 2) ÷ 100
= 21 ÷ 100
= 0.21
So, 42 ÷ 200 = 0.21

Question 38.
18.9 ÷ 900 = (18.9 ÷ ___) ÷ 100
= ___ ÷ 100
= ____
So, 18.9 ÷ 900 = ____
Answer:
18.9 ÷ 900 = (18.9 ÷ 9) ÷ 100
= 2.1 ÷ 100
= 0.021
So, 18.9 ÷ 900 = 0.021
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.
When dividing by 1000, move the decimal place three places to the left.

Question 39.
2 ÷ 2,000 = (2 ÷ ___) ÷ 1,000
= ____ ÷ 1,000
= ____
So, 2 ÷ 2,000 = ____
Answer:
2 ÷ 2,000 = (2 ÷ 2) ÷ 1,000
= 1 ÷ 1,000
= 0.001
So, 2 ÷ 2,000 = 0.001
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.
When dividing by 1000, move the decimal place three places to the left.

Question 40.
1,500 ÷ 6,000 = (1,500 ÷ ___) ÷ 1,000
= ______ ÷ 1,000
= ____
So, 1,500 ÷ 6,000 = ____
Answer:
1,500 ÷ 6,000 = (1,500 ÷ 6) ÷ 1,000
= 250 ÷ 1,000
= 0.25
So, 1,500 ÷ 6,000 = 0.25
Explanation:
When dividing by ten, move the decimal point one place to the left.
Place value is the value of a digit based on its location in the number.
When dividing by 100, move the decimal place two places to the left.
When dividing by 1000, move the decimal place three places to the left.

Divide.

Question 41.
306 ÷ 600 = _______
Answer: 0.51
Explanation:
306 ÷ 600 = (306 ÷ 6) ÷ 100
= 51 ÷ 100
= 0.51
Question 42.
29.7 ÷ 900 = ___
Answer: 0.033
Explanation:
29.7 ÷ 900 = (29.7 ÷ 9) ÷ 100
= 3.3 ÷ 100
= 0.033
Question 43.
1.056 ÷ 800 = _______
Answer: 0.00132
Explanation:
1.056 ÷ 800 = (1.056 ÷ 8) ÷ 100
= 0.132 ÷ 100
= 0.00132
Question 44.
48 ÷ 2,000 = _______
Answer: 0.024
Explanation:
48 ÷ 2000 = (48 ÷ 2 ) ÷ 10 ÷ 10 ÷ 10
= (24 ÷ 10) ÷ 10÷ 10
= (2.4 ÷ 10) ÷ 10
= (0.24 ÷ 10)
=0.024
So, 48 ÷ 2000 = 0.024
Question 45.
408 ÷ 3,000 = _______
Answer: 0.136
Explanation:
408 ÷ 3000 = (408 ÷ 3 ) ÷ 10 ÷ 10 ÷ 10
= (136 ÷ 10) ÷ 10÷ 10
= (13.6 ÷ 10) ÷ 10
= (1.36 ÷ 10)
=0.136
So, 408 ÷ 3000 = 0.136
Question 46.
805 ÷ 7,000 = _______
Answer: 0.115
805 ÷ 7000 = (805 ÷ 7 ) ÷ 10 ÷ 10 ÷ 10
= (115 ÷ 10) ÷ 10÷ 10
= (11.5 ÷ 10) ÷ 10
= (1.15 ÷ 10)
=0.115
So, 805 ÷ 7000 = 0.115