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This handy Math in Focus Grade 5 Workbook Answer Key Chapter 12 Angles provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 12 Answer Key Angles

Math Journal

Check the box for each correct statement. Then explain your answer.

Question 1.
\(\overleftrightarrow{X Y}\) is a line.

Answer:

Explanation:
The XY is a line and the angle on a straight line is 180°, known as straight angle.
Angle POQ is 90° as per the given information in the diagram.
180° – 90° = 90°
Angle ∠XOP and ∠YOQ are equal angle = 45°

Question 2.
\(\over left right arrow{A B}\) and \(\over left right arrow{C D}\) meet at O.

Answer:

Explanation:
\(\over left right arrow{A B}\) is a line and \(\over left right arrow{C D}\) is a line are crossed at O, the opposite angles are same.
So, m∠e = m∠h and
m∠f + m∠g = m∠j   are true statements.

Put On Your Thinking Cap!

Challenging Practice

Find the unknown angle measures. Explain.

Question 1.
\(\over left right arrow{G J}\) is a line. ∠LHK is a right angle. Find the measure of ∠LHJ.

Answer: 65°
Explanation:
Given information
GJ is a straight line, ∠LHK = 90°
∠JHK = 180° – ∠JHK
= 180° – 155° = 25°
∠JHK = ∠LHK – ∠JHK
= 90° – 25° = 65°

Question 2.
\(\over left right arrow{M N}\) and \(\over left right arrow{X Y}\) meet at O and m ∠a = m ∠b. Find the measure of ∠c.

Answer: 135°
Explanation:
\(\over left right arrow{X Y}\) is a line and \(\over left right arrow{M N}\) is a line are crossed at O, the opposite angles are same.
given information m∠a = m∠b and ∠XOP = 90
as XOY is a straight line, the angle is 180°
90° + m∠a + m∠b = 180°
∠c = 180° -∠XOM= 180 – 45° = 135°

Question 3.
\(\over left right arrow{A C}\) is a line. ∠ABE and ∠DBF are right angles. Find the measure of ∠FBC.

Answer: 26°
Explanation:
∠ABE and ∠DBF = 90°
∠EBF = ∠DBF – ∠DBE
=  90° – 26° = 64°
∠ABD = ∠ABE – ∠DBE
= 90° – 26° = 64°
∠FBC = 180 – (∠ABE + ∠EBF)
= 180° – (90° + 64°)
=180° – 154° = 26°

Question 4.
\(\over left right arrow{A B}\) and \(\over left right arrow{W X}\) meet at O. ∠YOX are right angles. Find the measures of ∠AOX and ∠COY.

Answer:
∠AOX  = 124°
∠COY  =  56°
Explanation:
90° – 56° = 34°
90° – 34° = 56°
∠COY = ∠COB – ∠BOY
= 90° – 34° = 56°
∠AOX = ∠WOX – ∠AOW
=180°- 56° = 124°

Put on Your Thinking cap!

Problem Solving

Solve.

Question 1.
\(\over left right arrow{J K}\) and \(\over left right arrow{L M}\) are lines.
Check the box for each correct statement.

Answer:
\(\over left right arrow{J K}\) and \(\over left right arrow{L M}\) are lines.

Explanation:
\(\over left right arrow{J K}\) is a line and \(\over left right arrow{L M}\) is a line are crossed at O, the opposite angles are same.
so, m∠r + m∠s = m∠p + m∠q is the wrong statement.

Question 2.
\(\over left right arrow{A B}\), \(\over left right arrow{C D}\), and \(\over left right arrow{E F}\) meet at O. Find the sum of the measures of ∠AOC, ∠FOD, and ∠BOE.
m∠AOC + m∠FOD + m∠BOE = _____

Answer: 180°
Explanation:
m∠AOC = 45°

m∠FOD = 45°

m∠BOE = 90°

m∠AOC + m∠FOD + m∠BOE = 180°

Question 3.
ABCD is a square. \(\over right arrow{B E}\) is a ray. Find the measure of ∠x.

Answer: 135°
Explanation:
As BE is a straight line and the angle is 180° at point D
and a square is ABCD is with 90° angle formed at point D
the ange ∠EDC is 135° angle ∠CDB is 45° and ∠ADB is also 45°
now the
∠x =  ∠EDB – ∠ADB
=  180° – 45°  =  135°

Question 4.
How many degrees does the hour hand of a clock turn between 3 P.M. and 7:30 P.M.?
Answer: 135°
Explanation:

Hour hand at 3PM is at 3 and 7:30 as shown in the clock diagram
Total angle is 360°, keep it in mind
and 360° divide in 12 parts
each part is of 30°
from hours hand 3 to 7 :30 its 135°

Question 5.
\(\over left right arrow{A B}\) is a line. The measures of ∠a and ∠b are whole numbers.

If the measure of ∠b is twice that of ∠a, find the measures of ∠a and ∠b.
Answer:
∠a = 60°
∠b = 120°

Explanation:
Here the hint is angle ∠b is twice that of ∠a, and The AB is a line and the angle on a straight line is 180, known as straight angle
∠b + ∠a = 180°
2∠a + ∠a = 180°
3∠a = 180°
∠a = 180°/3 = 60°
∠a = 60°
∠a = 60°
∠b = 2x∠a = 120°

This handy Math in Focus Grade 3 Workbook Answer Key Chapter 17 Practice 2 Right Angles provides detailed solutions for the textbook questions.

Math in Focus Grade 3 Chapter 17 Practice 2 Answer Key Right Angles

Look at these angles. Use a piece of folded paper
to help you answer the questions.

Question 1.
Which angle is less than a right angle?
Angle ________________
Answer:

Angle  C, D and E are angles less then a right angle.
Explanation:
Angle less than a right angles are Acute angles.

Question 2.
Which angle is greater than a right angle?
Angle ________________
Answer:

Angle A is greater then a right angle.
Explanation:
Angle greater than a right angles are Obtuse angles.

Question 3.
Which angles are the same size as right angles?
Angles _________________
Answer:

Angle A and F are the same as right angles.
Explanation:
The angle bounded by two lines perpendicular to each other.
A right triangle has one angle exactly equal to 90 degrees.

Mark all the right angles in each figure.

Question 4.

Answer:

Explanation:
The above figure has,
One right angle is there, which is marked blue color.
The angle bounded by two lines perpendicular to each other.
A right triangle has one angle exactly equal to 90 degrees.

Question 5.

Answer:

Explanation:
The above figure has,
One right angle is there, which is marked blue color.
The angle bounded by two lines perpendicular to each other.
A right triangle has one angle exactly equal to 90 degrees.

Question 6.

Answer:

Explanation:
The above figure has,
One right angle is there, which is marked blue color.
The angle bounded by two lines perpendicular to each other.
A right triangle has one angle exactly equal to 90 degrees.

Question 7.

Answer:

Explanation:
The above figure has,
One right angle triangles , the angle is marked blue color.
The angle bounded by two lines perpendicular to each other.
A right triangle has one angle exactly equal to 90 degrees.

Question 8.

Answer:

Explanation:
The above figure has,
Two right angle are there, which are marked blue color.
The angle bounded by two lines perpendicular to each other.
A right triangle has one angle exactly equal to 90 degrees.

Question 9.

Answer:

Explanation:
The given figure has,
Two right angle are there, which are marked in blue color.
The angle bounded by two lines perpendicular to each other.
A right triangle has one angle exactly equal to 90 degrees.

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

Math in Focus Grade 5 Chapter 15 Answer Key Surface Area and Volume

Math Journal

This rectangular container is \(\frac{2}{5}\)-filled with water.
How much more water is needed to increase the height of the water level to 3 centimeters?

Show two methods of solving this problem. Which method do you prefer? Why?
Answer:
Given rectangular tank has volume 8 cm X 10 cm X 5 cm = 400 cm³,
Method 1:
Knowing the volume of tank and water filled in it
as the rectangular container is \(\frac{2}{5}\)-filled with water.
\(\frac{2}{5}\) X 400 cm³ = 160 cm³, filled with water.
as 1 cubic centimeter is equal to 1 milliliters,

Put on Your Thinking Cap!

Challenging Practice

Question 1.
A rectangular tank is half-filled with water.
Another 650 cubic centimeters of water are needed to make it \(\frac{3}{5}\) full.
How much water will be in the tank when it is \(\frac{3}{5}\) full?
Answer:
3,900 cubic centimeters of water will be in the tank when it is \(\frac{3}{5}\) full,

Explanation:
Given a rectangular tank is half-filled with water.
Another 650 cubic centimeters of water are needed to make it \(\frac{3}{5}\) full.
Let x cubic centimeters of water so \(\frac{1}{2}\)x + \(\frac{3}{5}\)x = 650 cm³ + x,
\(\frac{5x + 6x}{10}\) = 650 cm³ + x,
\(\frac{11x}{10}\) = 650 cm³ + x,
11 x = 10 X (650 cm³ + x),
11 x =  6500 cm³ + 10 x,
11x – 10 x = 6,500 cm³,
x = 6,500 cm³,
So, water will be in the tank when it is \(\frac{3}{5}\) full is
\(\frac{3}{5}\) x 6,500 cm³ = \(\frac{3 X 6,500}{5}\) cm³,
\(\frac{19,500}{5}\) cm³ = 3,900 cm³,
therefore 3,900 cubic centimeters of water will be in the tank when it is \(\frac{3}{5}\) full.

Question 2.
A cube has a surface area of 21 6 square centimeters.
A second cube has edges that are 3 times as long.
How much greater is the surface area of the second cube than the first cube?
Answer:
1,728 cm² greater is the surface area of the second cube than the first cube,

Explanation:
Given a cube has a surface area of 216 square centimeters as
surface area of cube is 6 X a²= 216 cm²,
a² = 36 cm² = 6 cm X 6 cm,
edge a    = 6 cm,
A second cube has edges that are 3 times long as
6 cm X 3 = 18 cm, Surface area of second cube is 6 x (18)² =
6 X 18 cm X 18 cm = 1,944 cm², Now compairing much greater is the
surface area of the second cube than the first cube is 1,944 cm² – 216 cm² = 1,728 cm².

Put on Your Thinking Cap!

Problem Solving

A prism has a square base whose edges each measure 5 centimeters.
The ratio of its height to its width is 4 : 1.
Find the volume of the rectangular prism in cubic centimeters.

Answer:
Given a prism has a square base whose edge each measure 5 centimeters.
height = 4 cm
width = 1 cm
Volume of the rectangular prism = 2l × 2w × 2h
V = 2 × 5 × 2 × 1 × 2 × 4
V = 80 cubic centimeters

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 15 Practice 4 Understanding and Measuring Volume provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 15 Practice 4 Answer Key Understanding and Measuring Volume

These solids are formed by stacking unit cubes in the corner of a room.
Find the volume of each solid.

Question 1.

Volume = _________ cubic units
Answer:
Volume of give cube has 27 cubic units,

Explanation:
As we know volume of  solid is l X w X h,
so given cube  has 3 unit X 3 unit X 3 unit = 27 cubic units.

Question 2.

Volume = _________ cubic units
Answer:
Volume of give cube has 32 cubic units,

Explanation:
As we know the volume of solid is l X w X h,
so the given cube has 4 units X 4 units X 2 units = 32 cubic units.

Question 3.

Volume = _________ cubic units
Answer:
Volume of given cube has  16 cubic units,

Explanation:
As we know the volume of  solid is l X w X h,
Given cube contains 2 fewer small unit cubes so first we
calculate the total surface and subtract missing cubic units,
Total surface area has 3 units X 2 units X 3 units = 18 cubic units.
the surface area of small unit cubes is 1 unit X 1 unit X 2 units = 2 cubic units,
therefore the volume of the given cube is 18 cubic units – 2 cubic units = 16 cubic units.

Question 4.

Volume = _________ cubic units
Answer:
Volume of 9 cubic units,

Explanation:
Given solid cube has 9 unit cubes with 1 unit X 1 unit X 1 unit each,
So the volume of given cube is 9 X (1 unit X 1 unit X 1 unit)  = 9 cubic units.

These solids are formed by stacking 1-centimeter cubes in the corner of a room.
Find the volume of each solid.

Question 5.

Volume = ______ cm³
Answer:
Volume 11 cm³,

Explanation:
Given solid cube has 11 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 11 X (1 cm X 1 cm X 1 cm)  = 11 cm³.

Question 6.

Volume = _________ cm³
Answer:
Volume 8 cm³,

Explanation:
Given solid cube has 8 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 8 X (1 cm X 1 cm X 1 cm)  = 8 cm³.

Question 7.

Volume = _________ cm³
Answer:
Volume 10 cm³,

Explanation:
Given solid cube has 10 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 10 X (1 cm X 1 cm X 1 cm)  = 10 cm³.

Question 8.

Volume = ______ cm³
Answer:
Volume 12 cm³,

Explanation:
Given solid cube has 12 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 12 X (1 cm X 1 cm X 1 cm)  = 12 cm³.

Question 9.

Volume = _________ cm³
Answer:
Volume 7 cm³,

Explanation:
Given solid cube has 7 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 7 X (1 cm X 1 cm X 1 cm)  = 7 cm³.

Question 10.

Volume = _________ cm³
Answer:
Volume 11 cm³,

Explanation:
Given solid cube has 11 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 11 X (1 cm X 1 cm X 1 cm)  = 11 cm³.

These solids are built using 1-centimeter cubes. Find the volume of each solid.
Then compare their volumes and fill in the blanks.

Question 11.

Solid _________ has a greater volume than solid _________.
Answer:

Solid B has a greater volume than solid A,

Explanation:
Given solid cube A has 5 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 5 X (1 cm X 1 cm X 1 cm)  = 5 cm³,
and given solid cube B has 8 units cms with 1 cm X 1 cm X 1 cm each,
So the volume of given cubes is 8 X (1 cm X 1 cm X 1 cm)  = 8 cm³.
Solid B has a greater volume than solid A.

These solids are built using 1-meter cubes. Find the volume of each solid.
Then compare their volumes and fill in the blanks.

Question 12.

Solid _________ has less volume than solid _________.
Answer:

Solid 8 m³ has less volume that solid 11 m³,

Explanation:
Given solid cube C has 8 units m’s with 1 m X 1 m X 1 m each,
So the volume of given cubes is 8 X (1 m X 1 m X 1 m)  = 8 m³,
and given solid cube D has 11 units m’s with 1 m X 1 m X 1 m each,
So the volume of given cubes is 11 X (1 m X 1 m X 1 m)  = 11 m³.
Solid 8 m³ has less volume that solid 11 m³.

These solids are built using 1-inch cubes.
Find the volume of each solid.
Then compare their volumes and f411 in the blanks.

Question 13.

Length = __________ in.
Width = __________ in.
Height = _________ in.
Volume = _________ in.³

Length = __________ in.
Width = __________ in.
Height = _________ in.
Volume = _________ in.³
Solid _________ has less volume than solid _________.
Answer:
Solid E has less volume than solid F,

Explanation:
Given the solid cube of E which has a length of 2 in, width 2 in and height 3 in,
so the volume of cube E is 12 in.³,
Given solid cube of F which has a length of 4 in, width of 2 in, and height of 2 in,
so volume of cube F is 16 in.³.
Solid E has less volume than solid F.

These solids are built using 1-foot cubes. Find the volumes of each solid.
Then compare their volumes and fill in the blanks.

Question 14.

Length = _____2_____ ft.
Width = ______2____ ft.
Height = _____2____ ft.
Volume = _____8____ ft.³

Length = ____4______ ft.
Width = _____4_____ ft.
Height = _____4____ ft.
Volume = _____64____ ft.³
Solid _________ has a greater volume than solid _________.
Answer:
Solid H has greater volume than solid G,

Explanation:
Given the solid cube of  G which has a length 2 ft, width 2 ft, and height 2 ft,
so volume of cube G is 8 ft.³,
Given the solid cube of H which has a length 4 ft, width 4 ft and height 4 ft,
so volume of cube H is 64 in.³.
Solid H has a greater volume than solid G.

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 15 Practice 1 Building Solids Using Unit Cubes provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 15 Practice 1 Answer Key Building Solids Using Unit Cubes

Find the number of unit cubes used to build each solid.

Question 1.

__________ unit cubes
Answer:
5 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 5 unit cubes,
So, the volume of a 5 unit cubes = 5 X (Side × Side × Side),
= 5 X (1 unit × 1 unit × 1 unit),
= 5 X (unit cubes).

Question 2.

__________ unit cubes
Answer:
7 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 7 unit cubes,
So, the volume of a 7 unit cubes = 7 X (Side × Side × Side),
= 7 X (1 unit × 1 unit × 1 unit),
= 7 unit cubes.

Question 3.

__________ unit cubes
Answer:
8 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 8 unit cubes,
So, the volume of a 8 unit cubes = 8 X (Side × Side × Side),
= 8 X ( 1 unit × 1 unit × 1 unit),
= 8 unit cubes.

Question 4.

__________ unit cubes
Answer:
6 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 6 unit cubes,
So, the volume of a 6 unit cubes = 6 X (Side × Side × Side),
=6 X (1 unit × 1 unit × 1 unit),
= 6 unit cubes.

Question 5.

__________ unit cubes
Answer:
8 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 8 unit cubes,
So, the volume of a 8 unit cubes = 8 X (Side × Side × Side),
= 8 X (1 unit × 1 unit × 1 unit),
= 8 unit cubes.

Question 6.

__________ unit cubes
Answer:
9 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 9 unit cubes,
So, the volume of a 9 unit cubes = 9 X (Side × Side × Side),
= 9 X (1 unit × 1 unit × 1 unit),
= 9 unit cubes.

Find the number of unit cubes used to build each solid.

Question 7.

__________ unit cubes
Answer:
7 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 7 unit cubes,
So, the volume of a 7 unit cubes = 7 X (Side × Side × Side),
= 7 X ( 1 unit × 1 unit × 1 unit),
= 7 unit cubes.

Question 8.

__________ unit cubes
Answer:
9 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 9 unit cubes,
So, the volume of a 9 unit cubes = 9 X (Side × Side × Side),
= 9 X (1 unit × 1 unit × 1 unit),
= 9 unit cubes.

Question 9.

__________ unit cubes
Answer:
7 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 7 unit cubes,
So, the volume of a 7 unit cubes = 7 X (Side × Side × Side),
= 7 X (1 unit × 1 unit × 1 unit),
= 7 unit cubes.

Question 10.

__________ unit cubes
Answer:
10 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 10 unit cubes,
So, the volume of a 10 unit cubes = 10 X (Side × Side × Side),
= 10 X (1 unit × 1 unit × 1 unit),
= 10 unit cubes.

Question 11.

__________ unit cubes
Answer:
15 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 15 unit cubes,
So, the volume of a 15 unit cubes = 15 X (Side × Side × Side),
= 15 X (1 unit × 1 unit × 1 unit),
= 15 unit cubes.

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 3 Practice 1 Adding Unlike Fractions to finish your assignments.

Math in Focus Grade 5 Chapter 3 Practice 1 Answer Key Adding Unlike Fractions

Find two equivalent fractions for each fraction.

Example

Question 1.
\(\frac{3}{4}\) = ___ = ____
Answer:

Question 2.
\(\frac{2}{5}\) = ___ = ____
Answer:

Question 3.
\(\frac{5}{6}\) = ___ = ____
Answer:

Question 4.
\(\frac{1}{7}\) = ___ = ____
Answer:

Express each fraction in simplest form.

Question 5.
\(\frac{6}{8}\) = ___
Answer:

Question 6.
\(\frac{8}{20}\) = ___
Answer:

Question 7.
\(\frac{10}{15}\) = ___
Answer:

Question 8.
\(\frac{9}{21}\) = ___
Answer:

Rewrite each pair of unlike fractions as like fractions.

Example

Question 9.
\(\frac{1}{4}\) = ___ \(\frac{5}{12}\) = ___
Answer:

Question 10.
\(\frac{1}{10}\) = ___ \(\frac{2}{5}\) = ___
Answer:

Question 11.
\(\frac{5}{9}\) = ___ \(\frac{2}{3}\) = ___
Answer:

Question 12.
\(\frac{3}{8}\) = ___ \(\frac{9}{16}\) = ___
Answer:

Write equivalent fractions for each fraction. Then find the least common denominator of the fractions.

Example
\(\frac{1}{2}\) = \(\frac{2}{4}\) = \(\frac{3}{6}\)
\(\frac{2}{3}\) = \(\frac{4}{6}\)
The least common denominator is 6.

Question 13.
\(\frac{2}{3}\) =
\(\frac{3}{4}\) =
The least common denominator is ____
Answer:

Question 14.
\(\frac{1}{4}\) =
\(\frac{5}{6}\) =
The least common denominator is ____
Answer:

Question 15.
\(\frac{5}{6}\) = ____
\(\frac{3}{8}\) = ____
The least common denominator is ____
Answer:

Shade and label each model to show the tractions. Then complete the addition sentence.

Example

Question 16.
\(\frac{1}{5}\), \(\frac{1}{2}\)

Answer:

Look at the model. Write two addition sentences.

Question 17.
\(\frac{1}{6}\), \(\frac{1}{4}\)

\(\frac{1}{6}\) + \(\frac{1}{4}\) = ___ + ___
= ____
Answer:

Question 18.
\(\frac{1}{5}\), \(\frac{2}{3}\)

\(\frac{1}{5}\) + \(\frac{2}{3}\) = ____ + ___
= ____
Answer:

Question 19.
Addition sentence 1:

Answer:

Question 20.
Addition sentence 2 (fractions in simplest form):
____ + ____ = ____
Answer:

Add. Express each sum in simplest form.

Question 21.
\(\frac{1}{3}\) + \(\frac{1}{9}\) =
Answer:

Question 22.
\(\frac{5}{8}\) + \(\frac{2}{4}\) =

Question 23.
\(\frac{1}{2}\) + \(\frac{6}{7}\) =
Answer:

Question 24.
\(\frac{4}{8}\) + \(\frac{1}{5}\) =
Answer:

Use benchmarks to estimate each sum.

Example

Question 25.
\(\frac{2}{3}\) + \(\frac{2}{9}\)
Answer:

Question 26.
\(\frac{7}{9}\) + \(\frac{1}{7}\) + \(\frac{3}{5}\)
Answer:

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 1 Practice 3 Place Value to finish your assignments.

Math in Focus Grade 5 Chapter 1 Practice 3 Answer Key Place Value

Complete. Use the place-value chart.

In 345,201:

Question 1.
a. the digit 3 stands for ___________
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

The digit 3 stands for a hundred thousand.

b. the value of the digit 3 is _____
Answer:
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.
The value of the digit is 300,000.

Question 2.
a. the digit 4 stands for ___.
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

The digit 4 stands for ten thousand.

b. the value of the digit 4 is ______
Answer:
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.
The value of digit 4 is 40,000.

Question 3.
a. the digit 5 stands for ___.
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

The digit 5 stands for thousands.

b. the value of the digit 5 is ______
Answer:
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.
The value of digit 5 is 5000.

Write the value of each digit in the correct box.

Question 4.

Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

Complete.

In 346,812:

Question 5.
the digit 3 stands for ____
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

The digit 3 stands for a hundred thousand.

Question 6.
the digit 6 stands for ____
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

The digit 6 stands for thousand.

Write the value of the digit 2 in each number.

Question 7.
329,051 ____
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The value of digit 2 is 20,000 because it represents the ten thousand places.

Question 8.
903,521 ____
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The value of digit 2 is 20 because it represents the tens place.

Question 9.
712,635 ___
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The value of digit 2 is 2000 because it represents the thousands place.

Question 10.
258,169 ____
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The value of digit 2 is 200,000 because it represents the hundred thousand place.

Complete.

Question 11.
In 320,1 87, the digit ___ is in the thousands place.
Answer: 0
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The value of digit present in the thousands place is 0.

Question 12.
In 835,129, the digit 8 is in the ____ place.
Answer: Hundred thousand place.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The place value of 8 in the given number is a hundred thousand and its digit value is 800,000.

Question 13.
In 348,792, the digit 4 is in the ____ place.
Answer: Ten thousand place.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The place value of the 4 in the given number is ten thousands place and its digit value is 40,000.

Complete to express each number in expanded form.

Question 14.
153,420 = 100,000 + ___ + 3,000 + 400 + 20
Answer:
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
How to write numbers in expanded form:
Go through the below steps to write the numbers in expanded form:
Step 1: Get the standard form of the number.
Step 2: Identify the place value of the given number using the place value chart.
Step 3: Multiply the given digit by its place value and represent the number in the form of (digit × place value).
Step 4: Finally, represent all the numbers as the sum of (digit × place value) form, which is the expanded form of the number.
Now write the expanded form for the given number by using the above steps:
Step 1: The standard form of the number is 153,420.
Step 2: The place value of the given number is:
1 – Hundred thousand
5 – Ten thousand
3 – Thousands
4 – Hundreds
2 – Tens
0 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 1×100,000, 5×10,000, 3×1000, 4×100, 2×10, 0×1
Step 4: Expanded form is 100,000+50,000+3000+400+20+0
Finally, the expanded form of the number 100,000+50,000+3000+400+20+0.

Question 15.
760,300 = ____ + 60,000 + 300
Answer: 700,000
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 760,300.
Step 2: The place value of the given number is:
7 – Hundred thousand
6 – Ten thousand
0 – Thousands
3 – Hundreds
0 – Tens
0 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 7×100,000, 6×10,000, 0×1000, 3×100, 0×10, 0×1
Step 4: Expanded form is 700,000+60,000+0+300+0+0
Finally, the expanded form of the number 700,000+60,000+300.

Question 16.
700,000 + 8,000 + 500 + 4 = ____
Answer: 708,504
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 760,300.
Step 2: The place value of the given number is:
7 – Hundred thousand
0 – Ten thousand
8 – Thousands
5 – Hundreds
0 – Tens
4 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 7×100,000, 0×10,000, 8×1000, 5×100, 0×10, 4×1
Step 4: Expanded form is 700,000+0+8000+500+0+4
Finally, the expanded form of the number 700,000+8000+500+4.
The number is 708,504.

Question 17.
200,000 + 2,000 + 10 = ____
Answer:
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 202,010.
Step 2: The place value of the given number is:
2 – Hundred thousand
0 – Ten thousand
2 – Thousands
0 – Hundreds
1 – Tens
0 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 2×100,000, 0×10,000, 2×1000, 0×100, 1×10, 0×1
Step 4: Expanded form is 200,000+0+2000+0+10+0
Finally, the expanded form of the number 200,000+2000+10
The number is 202,010.

Complete. Use the place-value chart.

In 1,508,369.
Question 18.
a. the digit 1 stands for ____
Answer:
In Mathematics, place value charts help us to make sure that the digits are in the correct places. To identify the positional values of numbers accurately, first, write the digits in the place value chart and then write the numbers in the usual and the standard form.

The place value of the 1 in the given number 1,508,369 is millions.

b. the value of the digit 1 is ____
Answer: 1,000,000.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use

The value of digit of 1 in the given number 1,508,369 is 1,000,000.

Complete

Question 19.
a. the digit 8 stands for _____
Answer: Thousands place.
In Mathematics, place value charts help us to make sure that the digits are in the correct places. To identify the positional values of numbers accurately, first, write the digits in the place value chart and then write the numbers in the usual and the standard form.

The place value of 8 in the given number 1,508,369 is thousand place.

b. the value of the digit 8 is ________________
Answer: 8000
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The value of digit 8 in the given number 1,508,369 is 8000.

Question 20.
the digit 0 is in the ___ place.
Answer:
In Mathematics, place value charts help us to make sure that the digits are in the correct places. To identify the positional values of numbers accurately, first, write the digits in the place value chart and then write the numbers in the usual and the standard form.

The digit 0 in the given number 1,508,369 is ten thousands place.

Write the value of each digit in the correct box.

Question 21.

Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

Complete

Question 22.
In 5,420,000, the digit 5 is in the ____ place.
Answer: Millions place.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The place value of the 5 in the given number 5,420,000 is millions place.

Question 23.
In 1,077,215, the digit in the hundred thousand place is ____
Answer: 0
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

In the given number 1,077,215, the hundred thousand place is 0.

Question 24.
In 9,400,210, the digit 9 stands for _____
Answer: Millions place.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

The place value of the 9 in the given number 9,400,210 is millions place.

Complete to express each number in expanded form.

Question 25.
4,130,000 = ___ + 100,000 + 30,000
Answer: 4,000,000
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 4,130,000.
Step 2: The place value of the given number is:
4 – Millions
1 – Hundred thousand
3 – Ten thousand
0 – Thousands
0 – Hundreds
0 – Tens
0 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 4×1,000,000,  1×100,000, 3×10,000, 0×1000, 0×100, 0×10, 0×1)
Step 4: Expanded form is 4,000,0000+100,000+30,000+0+0+0+0
Finally, the expanded form of the number 4,000,0000+100,000+30,000
The number is 4,130,000.

Question 26.
6,123,750 = 6,000,000 + 100,000 + 20,000 + 3,000 + 700 + ____
Answer: 50
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 6,123,570.
Step 2: The place value of the given number is:
6 – Millions
1 – Hundred thousand
2 – Ten thousand
3 – Thousands
5 – Hundreds
7 – Tens
0 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 6×1,000,000,  1×100,000, 2×10,000, 3×1000, 7×100, 5×10, 0×1)
Step 4: Expanded form is 6,000,0000+100,000+20,000+3,000+700+50+0
Finally, the expanded form of the number 6,000,0000+100,000+20,000+3,000+700+50
The number is 6,123,750.

Question 27.
7,550,100 = 7,000,000 + ___ + 50,000 + 100
Answer: 500,000
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 7,550,100.
Step 2: The place value of the given number is:
7 – Millions
5 – Hundred thousand
5 – Ten thousand
0 – Thousands
1 – Hundreds
0 – Tens
0 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 7×1,000,000,  5×100,000, 5×10,000, 0×1000, 1×100, 0×10, 0×1)
Step 4: Expanded form is 7,000,0000+500,000+50,000+0+100+0+0
Finally, the expanded form of the number 7,000,0000+500,000+50,000+100.
The number is 7,550,100.

Question 28.
5,000,000 + 200,000 + 7,000 + 70 = ____
Answer: 5,207,070.
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 5,207,070.
Step 2: The place value of the given number is:
5 – Millions
2 – Hundred thousand
0 – Ten thousand
7 – Thousands
0 – Hundreds
7 – Tens
0 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 5×1,000,000,  2×100,000, 0×10,000, 7×1000, 0×100, 7×10, 0×1)
Step 4: Expanded form is 5,000,0000+200,000+0+7,000+0+70+0
Finally, the expanded form of the number 5,000,000+200,000+7,000+70
The number is 5,207,070.

Question 29.
3,000,000 + 20,000 + 9,000 + 100 + 5 = ____
Answer: 3,029,105.
Expanded form definition: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
Step 1: The standard form of the number is 3,029,105.
Step 2: The place value of the given number is:
3 – Millions
0 – Hundred thousand
2 – Ten thousand
9 – Thousands
1 – Hundreds
0 – Tens
5 – Ones
Step 3: Multiply the given number by its place value.
(i.e., 3×1,000,000,  0×100,000, 2×10,000, 9×1000, 1×100, 0×10, 5×1)
Step 4: Expanded form is 3,000,0000+0+20,000+9,000+100+0+5
Finally, the expanded form of the number 3,000,000+20,000+9,000+100+5
The number is 3,029,105.

Read the clues to find the number.

It is a 7-digit number.
The value of the digit 7 is 700.
The greatest digit is in the millions place.
The digit 1 is next to the digit in the millions place. The value of the digit 8 is 8 tens.
The value of the digit 3 is 3 ones.
The digit 5 is in the thousands place.
The digit 6 stands for 60,000.

Question 30.
The number is ____
Answer: 8,165,783
The greatest digit in the given clue is the number 8. So I kept 8 in the millions place.
The hundred thousand place is the digit 1. In the clue already given that 1 is next to the millions place.
The ten thousand place is the digit 6.
The thousands place is the digit 5.
The hundreds place is the digit 7.
The tens place is the digit 8.
The units place is the digit 3.

This handy Math in Focus Grade 4 Workbook Answer Key Chapter 13 Practice 3 Making Symmetric Shapes and Patterns detailed solutions for the textbook questions.

Math in Focus Grade 4 Chapter 13 Practice 3 Answer Key Making Symmetric Shapes and Patterns

Each figure below is half of a symmetric shape with the dotted line as a line of symmetry. Complete each symmetric shape.

Example

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Each figure below is half of a symmetric shape with the dotted line as a line of symmetry. Complete each symmetric shape.

Question 4.

Answer:

Question 5.

Answer:

Shade four more squares in each figure so that the pattern of shaded squares has rotational symmetry.

Example

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Shade four more squares in each figure so that the pattern of shaded squares has rotational symmetry.

Example

Question 9.

Answer:

Question 10.

Answer:

Question 11.

Answer:

This handy Math in Focus Grade 4 Workbook Answer Key Chapter 14 Practice 1 Identifying Tessellations detailed solutions for the textbook questions.

Math in Focus Grade 4 Chapter 14 Practice 1 Answer Key Identifying Tessellations

In each tessellation, color the repeated shape.

Example

Question 1.

Answer:

Explanation:
The repeated shape is colored in the above tessellation.

Question 2.

Answer:

Explanation:
The repeated shape is colored in the above tessellation.

Question 3.

Answer:

Explanation:
The repeated shape is colored in the above tessellation.

Is each pattern a tessellation of a single repeated shape? Write yes or no. Explain your answer.

Example

Yes. It is made up of a single repeated shape. The repeated shapes do not have gaps between them and they do not overlap.

Question 4.

Answer:
Yes. It is made up of a single repeated shape. The repeated shapes do not have gaps between them and they do not overlap.

Question 5.

Answer:
No. It is not made up of a single repeated shape. Because the repeated shapes have overlaps between them.

Question 6.

Answer:
No. It is not made up of a single repeated shape. Because the repeated shapes have gaps between them.

Add eight more of the repeated shapes to each tessellation.

Question 7.

Answer:

Explanation:
Added eight more repeated shapes to the above tessellation

Question 8.

Answer:

Explanation:
Added eight more repeated shapes to the above tessellation

Use each shape to make a tessellation in the space provided.

Question 9.

Answer:

Question 10.

Answer:

Use each shape to make a tessellation in the space provided.

Question 11.
Tessellate this shape by rotating it.

Answer:

The above shape is tessellated by rotating it.

Question 12.
Tessellate this shape by flipping it.

Answer:

The above shape is tessellated by flipping it.

Use the shape to make a tessellation in the space provided.

Question 13.
Tessellate this shape by rotating or hipping and sliding it.

Answer:

This handy Math in Focus Grade 4 Workbook Answer Key End of Year Review detailed solutions for the textbook questions.

Math in Focus Grade 4 End of Year Review Answer Key

Test Prep

Multiple Choice

Fill in the circle next to the correct answer.

Question 1.
The digit 9 in 89.4 stands for _________. (Lesson 7.2)
(A) 9 hundredths
(B) 9 tenths
(C) 9 ones
(D) 9 tens
Answer:

So, Option C is correct.

Question 2.
Find 9.50 – 2.63. (Lesson 8.2)
(A) 5.07
(B) 5.73
(C) 6.67
(D) 6.87
Answer:

9.50 – 2.63 = 6.87
Option C is correct.
Explanation:
Perform subtraction operation on above two numbers. Subtract 2.63 from 9.50 the difference is 6.87. So, draw a circle for option C.

Question 3.
The product of 9 and ____________ is 1,1 07. (Lesson 3.1)
(A) 123
(B) 1,098
(C) 1,116
(D) 9,963
Answer:

The product of 9 and 123 is 1,1 07.
Option C is correct.
Explanation:
Multiply 9 with 123 the product is 1,107. So draw a circle for option C.

Question 4.
The table shows the number of fruits and biscuits a group of students have. Some numbers in the table are missing. Use the information in the table to answer the question. (Lesson 4.1)

The total number of fruits and biscuits is 120. How many fruits does Crystal have?
(A) 6
(B) 23
(C) 37
(D) 97
Answer:


The total number of fruits and biscuits is 120.
The total number of fruits and biscuits of Annabel and Mandy  having are calculated by adding 59 and 38.
59 + 38 = 97
Subtract the total fruits and biscuits of Annabel and Mandy from total number of fruits and biscuits.
120 – 97 = 23
Subtract number of biscuits that Crystal having from the total number of fruits and biscuits
23 – 17 = 6
Crystal have 6 fruits.
So, drawn a circle for option A.

Question 5.
The stem-and-leaf plot shows the points scored by Jason in nine basketball games. (Lesson 5.3)

What is the outlier of the set of data?
(A) 40
(B) 26
(C) 23
(D) 10
Answer:

Question 6.
Peter draws one of these number cards from a bag. (Lesson 5.5)

What is the probability that he draws a number less than 10?
(A) \(\frac{1}{2}\)
(B) \(\frac{1}{3}\)
(C) \(\frac{1}{4}\)
(D) \(\frac{1}{6}\)
Answer:

Explanation:
Total number of cards are 6.
Number of cards which are having a number less than 10 are 3.
So, the probability the peter draws a number less than 10 = 3/6 = 1/2

Question 7.
Subtract \(\frac{2}{4}\) from \(\frac{7}{12}\). Express your answer in simplest form. (Lesson 6.2)
(A) \(\frac{1}{12}\)
(B) \(\frac{2}{15}\)
(C) \(\frac{2}{5}\)
(D) \(\frac{11}{15}\)
Answer:

7/12 – 2/4 = (7 – 6)/12 = 1/12
So, drawn a circle for Option A.

Question 8.
4\(\frac{3}{5}\) = ____________ (Lesson 6.3)
(A) \(\frac{12}{5}\)
(B) \(\frac{20}{5}\)
(C) \(\frac{23}{5}\)
(D) \(\frac{43}{5}\)
Answer:

4 3/5 = (20 + 3)/5 = 23/5
Option C is correct.

Question 9.
Which of the shaded parts represents \(\frac{4}{5}\) of a set? (Lesson 6.7)

Answer:

Option A:
15 circles are shaded out of 20.
15/20 = 3/4
The simplified form of 15/20 is 3/4.
Option B:
12 circles are shaded out of 20.
12/20 = 3/5
The simplified form of 12/20 is 3/5.
Option C:
12 circles are shaded out of 15.
12/15 = 4/5
The simplified form of 12/15 is 4/5.
Option D:
10 circles are shaded out of 15.
10/15 = 2/3
The simplified form of 10/15 is 2/3.
So, drawn a circle for Option C.

Question 10.

The arrow is pointing at __________. (Lesson 7.1)
(A) 0
(B) 1.2
(C) 1.3
(D) 4
Answer:


The arrow is pointing at 1.2.
So, draw a circle for option B.

Question 11.
Ava’s mass is 45.0 kilograms when rounded to 1 decimal place. What is her least possible mass? (Lesson 7.4)
(A) 45.01 kilograms
(B) 44.95 kilograms
(C) 44.99 kilograms
(D) 44.55 kilograms
Answer:

Ava’s mass is 45.0 kilograms and it is rounded to 1 decimal place.
The least possible mass is 44.95.
So, draw a circle for option B.

Question 12.
0.55 is not equal to _________. (Lesson 7.5)
(A) \(\frac{11}{20}\)
(B) \(\frac{55}{100}\)
(C) \(\frac{550}{1,000}\)
(D) \(\frac{55}{10}\)
Answer:

Option A:
11/20 = 0.55
Option B:
55/100 = 0.55
Option C:
550/1,000 = 0.55
Option D:
55/10 = 5.5
0.55 is not equal to 55/10.
So, option D is correct.

Question 13.
4.6 – 0.46 is equal to _________. (Lesson 8.2)
(A) 0
(B) 4.14
(C) 4.20
(D) 4.26
Answer:

4.6 – 0.46 is equal to 4.14.
So, option B is correct.

Question 14.
Which of these angles is an acute angle? (Lesson 9.1)

Answer:

Option A is correct.

Question 15.

Sam needs to draw an angle of 1 25° from point X. He must join point X to point __________. (Lesson 9.2)
(A) A
(B) B
(C) C
(D) D
Answer:


Sam drawn an angle of 125° from point X to point D. So, option D is correct.

Question 16.
Refer to the figure to answer Exercises 15 and 16.

Which line segment is perpendicular to \(\overline{\mathrm{AH}}\)? (Lesson 10.1)
(A) HG
(B) BE
(C) FE
(D) AD
Answer:

The line segment perpendicular to AH is AD.
So, option D is correct.

Question 17.
Which line segment is parallel to \(\overline{\mathrm{CD}}\)? (Lesson 10.2)
(A) AD
(B) GH
(C) BE
(D) FG
Answer:

The line segment parallel to CD is BE.
So, option C is correct.

Question 18.
In the square below, find the measure of ∠a. (Lesson 11.2)

(A) 30°
(B) 45°
(C) 60°
(D) 90°
Answer:

The measure of ∠a is 45°.
So, option B is correct.

Question 19.
The perimeter of a rectangle is 24 centimeters. The length of one of its sides is 5 centimeters. What is the area? (Lesson 12.1)
(A) 7 cm²
(B) 14 cm²
(C) 35 cm²
(D) 49 cm²
Answer:

The perimeter of a rectangle is 24 centimeters.
The length of one of its sides is 5 centimeters.
Width = ?
Perimeter of a rectangle = 2 (l + w)
24 cm = 2 (5 cm+ w)
24 cm = 10 cm + 2w
24 cm – 10 cm = 2w
14 cm = 2w
7 cm = w
Area of the rectangle = l × w
= 5 cm × 7 cm
= 35 cm²
Area of the rectangle is equal to 35 square centimeters.
So, option C is correct.

Question 20.
All line segments on the figure meet at right angles. Find EF. (Lesson 12.1)

(A) 4 cm
(B) 6 cm
(C) 8 cm
(D) 10 cm
Answer:

From the above figure AB = EF
HG = AB + CD + EF
12 cm = 2 EF + 4 cm
8 cm = 2 EF
4 cm = EF
So, option A is correct.

Question 21.
Which pair of figures are symmetric? (Lesson 13.1)

(A) A and B
(B) B and C
(C) C and D
(D) D and A
Answer:


The figures A and B are symmetric. So option A is correct.

Question 22.
What is the repeated shape used in the tessellation? (Lesson 14.1)

Answer:

The figure in option D is the repeated shape used in the tessellation.

Question 23.
Which of these shapes has rotational symmetry? (Lesson 13.2)

Answer:

Question 24.
This shape can be tessellated by ___________. (Lesson 14.2)

(A) sliding
(B) rotation
(C) flipping
(D) All of the above
Answer:

The shape can be tessellated by sliding, rotating, and flipping. So, option D is correct.

Question 25.

From position A to B, the unit shape has been ___________
(A) slid
(B) rotated
(C) flipped
(D) none of the above
Answer:

From position A to B, the unit shape has been flipped. So, option C is correct.

Short Answer

Read each question carefully. Write your answers in the space given. Give your answers in the correct units.

Question 26.
I am a number between 30 and 50. I am a multiple of 8. My greatest common factor with 25 is 5. What number am I? (Lessons 2.2 and 2.3)
Answer:
I am a number between 30 and 50.
I am a multiple of 8.
My greatest common factor with 25 is 5.
5 x 8 = 40
The number is 40.

Question 27.
The table shows the number of marbles Anthony and Michelle have. Complete the table and answer the questions. (Lesson 4.1)


a. What was the total number of red marbles?
Answer:
The number of red marbles does Anthony have is 18.
The number of red marbles does Michelle have is 37.
18 + 37 = 55
The total number of red marbles are 55.

b. What fraction of the total number of marbles were blue?
Answer:
The total number of red marbles and blue marbles are 105.
44 + 61 = 105
The total number of red marbles are 55.
18 + 37 = 55
The fraction form of the total number of blue marbles.
55/105 = 10/21

Question 28.
The graph shows the amount of water used by the residents of an apartment block over a morning. (Lesson 4.3)

a. At which two times was the same amount of water used?
Answer:
The same amount of water used at 9 A.M and 1 P.M

b. At what time was the amount of water used twice that used at noon?
Answer:
At 12 P.M the volume of water used is 2,500.
2 x 2,500 = 5,000
At 10 A.M the amount of water used twice that used at noon.

Question 29.
A bag has 5 pink balls, 8 yellow balls, and 4 blue balls. What is the probability of drawing a pink ball from the bag? (Lesson 5.5)
Answer:
5/(5 + 8 + 4) = 5/17
The probability of drawing a pink ball from the bag is 5/17.

Question 30.
What is \(\frac{7}{12}\) – \(\frac{2}{6}\)? Express your answer in simplest form. (Lesson 6.2)
Answer:
7/12 – 2/6 = (7 – 4)/12 = 3/12 = 1/4
The simplest form of 7/12 – 2/6 is 1/4.

Question 31.
Express \(\frac{30}{7}\) as a mixed number. (Lesson 6.5)
Answer:
The mixed number for 30/7 is 4 2/7.

Question 32.
Find the difference between \(\frac{5}{8}\) and 3. (Lesson 6.6)
Answer:
3 – (5/8) = (24 – 5)/8 = 19/8
The difference between 5/8 and 3 is 19/8.

Question 33.
How many grey squares must be replaced by white squares so that \(\frac{2}{3}\) of the total number of squares are grey? (Lesson 6.7)

Answer:

Total number of squares = 15
Total number of grey squares = 12
If 2/3 of the total number of squares should be grey then number of grey squares should be = 2/3 x 15 = 10
As total number of grey squares are currently 12. S0, the number of squares to be whitened = 12 – 10 = 2

Question 34.
What is the number in the box? (Lesson 7.2)
6.34 = 6 + 0.3 + ___________
Answer:
6.34 = 6 + 0.3 + 0.04

Question 35.
Li Li is 1.85 meters tall. Round her height to the nearest tenth of a meter. (Lesson 7.4)
Answer:
Round her height to the nearest tenth of a meter 1.9.

Question 36.
Express 5\(\frac{6}{25}\) as a decimal. (Lesson 7.5)
Answer:
5 6/25 = (125 + 6)/25 = 131/25 = 5.24

Question 37.
Draw and label a line segment BC such that the measure of angle ABC is 167°. Line segment AB is given. (Lesson 9.2)

Answer:

Drawn and labeled a line segment BC such that the measure of angle ABC is 167°.

Question 38.
Draw a line segment perpendicular to AB through point O. (Lesson 10.1)

Answer:

Drawn a line segment perpendicular to AB through point O as we can observe in the above image.

Question 39.
Draw a line parallel to \(\overleftrightarrow{C D}\) passing through point X. (Lesson 10.2)

Answer:

Drawn a line parallel to CD passing through point X.

Question 40.
AB is a vertical line segment and BC is a horizontal line segment. Find the measure of ∠ABC. (Lesson 10.3)
Answer:

Explanation:
AB is a vertical line segment and BC is a horizontal line segment. The measure of ∠ABC is 90°.

Question 41.
Look at the figure below to answer the question. (Lesson 12.3)

X, Y, and Z are squares. The length of each side of X is 5 centimeters and the length of each side of Y is 3 centimeters. AB = CD. Find the total length of the thick lines in the figure.
Answer:

In the above image we can observe X, Y, and Z are squares.
The length of each side of X is 5 centimeters and the length of each side of Y is 3 centimeters.
AB = CD.
AB = 5 cm – 3 cm
AB = 2 cm
The total length of the thick line in the figure = 5 + 2 + 3 + 2 + 1 = 13 cm

Question 42.
Shade some squares and half-squares to make a symmetric pattern in the figure. (Lesson 13.3)

Answer:

Question 43.
In the tessellation below, the unit shape is . Extend the tessellation in the space provided by adding four more unit shapes. (Lesson 14.2)

Answer:

By adding four more unit shapes the tessellation is extended in the space provided above.

Question 44.
Complete the tessellation by adding three more unit shapes. (Lesson 14.2)

Answer:

Question 45.
Complete the figure so that it has rotational symmetry about point O. (Lesson 13.3)

Answer:

The above figure has rotational symmetry at point O.

Question 46.
a. Does the word have rotational symmetry? (Lesson 13.3)
Answer:
No, The word ‘NO’ doesn’t have a rotational symmetry.

b. Fill in the box with a letter so that will have rotational symmetry. (Lesson 13.3)
Answer:

The letter NON have rotational symmetry.

Extended Response

Solve. Show your work.

Question 47.
Jane used \(\frac{1}{4}\) of the flour to make biscuits. She used \(\frac{1}{2}\) of the flour to bake a cake. What fraction of the flour was left?
Answer:
Jane used 1/4 of the flour to make biscuits.
She used 1/2 of the flour to bake a cake.
The fraction of flour left = 1/2 – 1/4 = 1/4

Question 48.
Mr. Lim has some savings. If he gives $40 to one brother, he will have $6,145 left. But he decides to give all his savings to his 5 brothers equally. How much will each brother get?
Answer:
$40 + $6,145 = $6,185
He decides to give all his savings to his 5 brothers equally.
$6,185/5 = $1237
Each brother will get $1237.

Question 49.
Rita bought fabric and ribbon from a store. The ribbon cost $18.50. Rita paid the cashier $50.00 and received a change of $5.25. How much did the fabric cost?
Answer:
The ribbon cost $18.50.
The fabric cost = ?
Rita paid the cashier $50.00 and received a change of $5.25.
Rita received change from cashier = Amount paid to the cashier – Ribbon cost – Fabric cost
$5.25 = $50.00 – $18.50 – Fabric cost
Fabric cost = $50.00 – $18.50 – $5.25
Fabric cost = $26.25

Question 50.
The area of a rectangle is 98 square centimeters, and its width is 7 centimeters. Find the length.
Answer:
The area of a rectangle is 98 square centimeters.
Width = 7 cm
Length = ?
Area of the rectangle = l × w
98 cm²= l × 7 cm
14 cm = l
The length of a rectangle is 14 cm.

Question 51.
Richard planted some grass on a rectangular plot of land which measures 1 2 meters by 8 meters. He left a margin of 0.5 meters around the grass, as shown in the figure below. Find the area of land covered by grass. (Lesson 12.4)

Answer:
Length of the grass = 11 m
Width of the grass = 7 m
Area of land covered by grass = length x width
= 11 m x 7 m
= 77 square meters
Area of land covered by grass is 77 square meters.