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This handy Math in Focus Grade 1 Workbook Answer Key Chapter 5 Practice 4 Making Pictures and Models with Shapes detailed solutions for the textbook questions.

Math in Focus Grade 1 Chapter 5 Practice 4 Answer Key Making Pictures and Models with Shapes

Find the shapes in the pictures.

Count how many of each shape there are. Write the number.

Question 1.

Answer:

Question 2.

Answer:

Match the pieces to make a shape. Name the shapes. Use the words in the box.

Question 3.

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Cut out the shapes below and make a picture. Paste the picture here or use your own paper. You do not need to use all the shapes.

Question 7.

Answer:

Look at the pictures. Then fill in the blanks.

Question 8.
How many triangles can you see?
I can see ___ triangles.

Answer: In the above figure there are 0 triangles.

Question 9.
A star can be made of triangles.

This star is made of _____ triangles.
This star is made of 10 triangles.
Draw triangles another way to make up this star.

This star is made of ___ triangles.
Answer: This star is made of 5 triangles.

Question 10.
Draw a picture with shapes. Count how many of each shape there are. Write the number.

Answer:

This handy Math in Focus Grade 1 Workbook Answer Key Chapter 5 Shapes and Patterns detailed solutions for the textbook questions.

Math in Focus Grade 1 Chapter 5 Answer Key Shapes and Patterns

Math Journal

Choose two things. Circle them.

Question 1.

Answer:

Now write about them. Use the words in the box to help you.

cylinder sphere cube cone pyramid rectangular prism stacking sliding rolling size shape

Question 2.
The ____________ has the shape of a ____________
Answer: The jar has the shape of a cylinder.

Question 3.
The ______________ has the shape of a ____________
Answer: The sharpener has the shape of a cylinder.

Question 4.
I can move the ____ by ____________
Answer: I can move the cylinder by rolling

Question 5.
I can move the ____ by ____________
Answer: I can move the sphere by sliding

Question 6.
My things are alike because they ____________
Answer: My things are alike because they are different in size.

Question 7.
My things are different because they ____
Answer: My things are different because they are different in shape.

Make a pattern with plane shapes. Read and draw.

Question 8.
The shapes in this pattern are alike. The sizes of the shapes are different.
_________________________
Answer:

Put On Your Thinking cap!

challenging Practice

Solve.

Question 1.
Lee, Jen, Bob, and Dean have some shapes. Find out who has each set of shapes.

• Lee has fewer circles than Bob.
• All of Jen’s shapes have 3 sides or more.
• Bob has four kinds of shapes.
• Dean has no squares.

Write the name that matches each set on the line below.

Answer:

Cut out the pieces of shapes on page 129. Paste the cut-out pieces to fit the two pictures below.

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Put On your Thinking Cap!

Problem Solving

Draw and complete the pattern.

Each row (↔) and column (↕) must have these four shapes,

Question 7.

Answer:

Chapter Review/Test

Vocabulary

Draw the shape.

Question 1.
square
Answer:

Question 2.
rectangle
Answer:

Question 3.
triangle
Answer:

Write the name.
Use the words in the box.

Question 4.

Answer: sphere

Question 5.

Answer: cylinder

Concepts and Skills
Trace the shape.
Write the number of sides and corners.

Question 6.

___ sides
___ corners
Answer: Square has 4 sides and 4 corners.

Question 7.

___ sides
___ corners
Answer: Circle has 0 sides and 0 corners.

Answer the question. Write yes or no.

Question 8.
How are these shapes alike?

a. Same shape ____
Answer: Figure 1 and figure 3 has the same shape

b. same size _______
Answer:

c. same color ________
Answer:

Circle the solid shapes you can roll.

Question 9.

Answer:

How can you move a pyramid? Circle the answer.

Question 10.

stack
slide
roll
Answer: Pyramid can be moved by stacking.

Look at the picture. What shapes do you see? Write the number.

Question 11.

Answer:

Look at the picture. What shapes do you see? Circle the answers.

Question 12.

Answer:

Complete the pattern. Circle the shape that comes next.

Question 13.

Answer:

Question 14.

Answer:

Problem Solving
Draw a line to solve.
Make two shapes that are different in shape and size.

Question 15.

Answer:

Practice the problems of Math in Focus Grade 1 Workbook Answer Key Chapter 11 Practice 2 More Picture Graphs to score better marks in the exam.

Math in Focus Grade 1 Chapter 11 Practice 2 Answer Key More Picture Graphs

Alonso has a coin. Every time he tosses the coin, he gets heads Alonso tosses the coin many times. This is what he gets:

Count the tosses.
Color a for each toss.

Answer:

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Every student in Grade 1 has a pet. The picture shows their pets.

Count the pets and complete the picture graph.

Question 5.

Answer:

Fill in the blanks.

Question 6.
The most popular pet is the ____
Answer: The most popular pet is the goldfish

Question 7 .
There are ___ hamsters.
Answer: There are 2 hamsters.

Question 8.
There are ___ more cats than birds.
Answer: There are 2 more cats than birds.

Question 9.
There are 4 fewer __________ than ______
Answer: There are 4 fewer rabbits than goldfishes

Question 10.
The number of _____________ is the least.
Answer: The number of rabbit is the least.

Question 11.
The number of _____________ is the greatest.
Answer: The number of goldfish is the greatest.

Question 12.
There are equal numbers of ____ and ____.
Answer: There are equal numbers of Dogs and cats.

Look at the picture graph. Then fill in the blanks.

Monica goes to the zoo. She makes a picture graph that shows the animals she sees.

Question 13.
Monica sees ___ tigers.
Answer: Monica sees 3 tigers.

Question 14.
She also sees ___ giraffes.
Answer: She also sees 6 giraffes.

Question 15.
She sees the most ___.
Answer: She sees the most giraffes.

Question 16.
She sees the fewest ____
Answer: She sees the fewest lions

Question 17.
There are ___ more rhinoceroses than lions.
Answer: There are 3 more rhinoceroses than lions.

Question 18.
There are ___ fewer tigers than elephants.
Answer: There are 2 fewer tigers than elephants.

Look at the picture graph. Then fill in the blanks.

This picture graph shows how a group of children goes to school.

Question 19.
How many children walk to school? ________
Answer: 6 children’s go to school by walk

Question 20.
How many children go to school by bus? ________
Answer: 14 children’s go to school by bus

Question 21.
How do most of the children go to school? _________
Answer: Most of the children’s go to school by bus

Question 22.
The fewest children go to school by ____.
Answer: The fewest children go to school by bicycle.

Question 23.
More children walk to school than ride a bicycle. How many more? _______
Answer: 2 more children walk to school than ride a bicycle

Question 24.
Fewer children go to school by car than by bus. How many fewer? ________
Answer: 3 Fewer children go to school by car than by bus

Look at the picture graph. Then fill in the blanks.

Jason invites his friends to a party. This picture graph shows the fruit juices they drink.

Question 25.
The children drink ____ glasses of cranberry juice.
Answer: The children drink 2 glasses of cranberry juice.

Question 26.
What is the most popular juice? ______
Answer: The most popular juice is of apple
Question 27.
They drink fewer glasses of pineapple juice than orange juice. How many fewer? ________
Answer: They drink 4 fewer glasses of pineapple juice than orange juice.

Question 28.
How many types of juices do they drink? _______
Answer: They drink 5 different types of juices

Practice the problems of Math in Focus Grade 1 Workbook Answer Key Chapter 11 Picture Graphs and Bar Graphs to score better marks in the exam.

Math in Focus Grade 1 Chapter 11 Answer Key Picture Graphs and Bar Graphs

Math Journal

Keep a record of how many books you read this week. Include the books you read in class and those your teacher or your family reads to you. Draw to represent 1 book.

Answer:

Look at your graph. Write sentences about the number of books you have read. You may use the words below.

Answer:

Put on your Thinking Cap!

Challenging Practice

Team A, Team B, and Team C play a game. The graph shows the number of points each child on Team A scores.

Answer the questions.

Question 1.
How many points did Team A score in all? _____
Answer: Team A had scored 17 in total

Question 2.
Team B scores 7 points fewer than Team A. How many points does Team B score? _____
Answer:  Team B scored 10 points which is 7 points fewer than Team A.

Question 3.
Team A scores 3 points fewer than Team C. How many points does Team C score? _____
Answer: Team C scored 20 points which is 3 points more than Team A

Complete the tally chart.

Question 4.
Tina and her friends, Eva and Pedro, brought some crackers to school.
The tally chart shows the number of crackers each child brought.

Answer:

Make a bar graph.

Question 5.

Answer:

Question 6.
How many crackers did Pedro bring? _____
Answer: Pedro brought 5 crackers

Question 7.
How many more crackers did Tina bring than Eva? _____
Answer: Tina brought 5 more crackers than Eva

Question 8.
How many crackers did the children bring in all? _____
Answer: In total the children’s brought 15 crackers

Question 9.
Tina brought ___ more crackers than Pedro.
Answer: Tina brought 2 more crackers than Pedro.

Put on Your Thinking cap!

Problem Solving

The Art Club sold boxes of cards to three families along the same street.

Fill in the blanks.

Question 1.
The Bailey family bought ___ boxes of cards.
Answer: The Bailey family bought 7 boxes of cards.

Question 2.
The ___ family bought the fewest boxes of cards.
Answer: The Anderson family bought the fewest boxes of cards.

Question 3.
The ___ family bought the most boxes of cards.
Answer: The Diaz family bought the most boxes of cards.

Question 4.
The Anderson family bought ___ fewer boxes of cards fewer than the Bailey family.
Answer: The Anderson family bought 2 fewer boxes of cards fewer than the Bailey family.

Question 5.
The families bought ___ boxes of cards in all.
Answer: The families bought 20 boxes of cards in all.

Question 6.
Make a bar graph.

Answer:

Chapter Review/Test
Vocabulary
Choose the correct word.

Question 1.
A ____ uses bars and a scale to show data.

Answer:
A librarian uses bars and a scale to show data.

Question 2.
There are ___ girls than boys.
Answer:
There are 3 fewer girls than boys.

Question 3.
There are ___ boys than girls.
Answer: There are 3 more boys than girls.

Concepts and Skills

The tally chart shows some children’s favorite musical instruments.

Question 4.
__________ is the most popular musical instrument.
Answer: Guitar is the most popular musical instrument.

Question 5.
__________ is the favorite musical instrument of the fewest children.
Answer: Drum is the favorite musical instrument of the fewest children.

Problem Solving

A recycling project was carried out in a class. Some children brought bottles for recycling. The tally chart shows the number of bottles each child brought.

Complete the tally chart.

Question 6.

Answer:

Make a bar graph.

Question 7.

Answer:

Fill in the blanks.

Question 8.
How many bottles did Kimberly bring? ____
Answer: Kimberly brought 7  bottles

Question 9.
______ brought the fewest bottles.
Answer: Madison brought the fewest bottles.

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 2 Practice 5 Dividing by Tens, Hundreds, or Thousands to finish your assignments.

Math in Focus Grade 5 Chapter 2 Practice 5 Answer Key Dividing by Tens, Hundreds, or Thousands

Complete.

Question 1.
100 ÷ 10 = _10__
Answer:
10,

Explanation:
100 ÷ 10 = 10

100 is divided by 10 and the result is 10.

Question 2.
670 ÷ 10 = _67__
Answer:
67,

Explanation:
670 ÷ 10

670 is 10 times 67,
670 is 67 x 10.

Question 3.
1,050 ÷ __ = 105
Answer:
105,

Explanation:

1,050 is 105 x 10,
1,050 is divided by 10 and the result is 105.

Question 4.
_1,974__ ÷ 10 = 1,974
Answer:
19,740,

Explanation:

19,740 can be written as 1974 x 10
it can be divided by 10 and the result is 1,974.

Question 5.
52,260 ÷ 10 = _5,260__
Answer:
5,260,

Explanation:

5,2260 can be written as 5,226 x 10 it can be divided by 10 and
the result is 5,2260.

Question 6.
30,500 ÷ _10_ = 3,050
Answer:
3,050,

Explanation:

3,050 can be written as 305 x 10 it can be divided by 10 and
the result is 3,050.

Complete.

5,610 ÷ 30
= (5,610 ÷ 10) ÷ 3
= 561 ÷ 3
= 187

Question 7.
3,000 ÷ 60
= (3,000 ÷ 10) ÷ _6__
= _300__ ÷ 6
= __50__
Answer:
50,

Explanation:

= 3,000 ÷ 10÷ 6
= 300÷ 6
= 50.

Question 8.
1,040 ÷ 40
= (1,040 ÷ __10_) ÷ _4__
= _104__ ÷ __4__
= __26__
Answer:
26,

Explanation:
1,040 ÷ 40,
= 1,040 ÷ 10÷ 4
= 104 ÷ 4
= 26.

Complete.

Question 9.
8,700 ÷ 60
= (8,700 ÷ _10_) ÷ __6_
= _870__ ÷ _6__
= __145__
Answer:
145,

Explanation:
8,700 ÷ 60,
= 8,700 ÷ 10 ÷ 6,
= 870 ÷ 6,
= 145.

Question 10.
3,450 ÷ 50
= (3,450 ÷ _10_) ÷ _5__
= _345___ ÷ __5_
= __69__
Answer:
69,

Explanation:
3,450 ÷  50,
= 3,450 ÷ 10 ÷ 5
= 345 ÷ 5
= 69.

Question 11.
34,230 ÷ 70
= (34,230 ÷ _10__) ÷ _7_
= _3,423__ ÷ _7__
= __489__
Answer:
489,

Explanation:
34,230 ÷ 70,
= 34,230 ÷ 10 ÷ 7,
= 3,423 ÷ 7,
= 489.

Which U.S. president had a sign on his desk that said ‘The buck stops here’?
Write the letters on pages 47 and 48 that match the answers below to find out.

Answer: TRUMAN

Explanation:
The solutions from the above questions from 6 to 11,
according to the answers arrange the given alphabets to find out the word.

Divide.

Question 12.
3,400 ÷ 100 = _34__
Answer:
34,

Explanation:
3,400 ÷ 10 ÷ 10,
= 340 ÷ 10,
= 34.

Question 13.
560,000 ÷ 1,000 = _560__
Answer:
560,

Explanation:
560,000 ÷ 1,000,
= 560,000 ÷ 10 ÷ 10 ÷ 10,
= 56,000 ÷ 10 ÷ 10,
= 5,600 ÷ 10,
= 560.

Question 14.
5,000 ÷ 100 = _50_
Answer:
50,

Explanation:
5,000 ÷ 100,
= 5,000 ÷ 10 ÷ 10,
= 500 ÷ 10,
= 50.

Question 15.
38,000 ÷ 1,000 = __38_
Answer:
38,

Explanation:
38,000 ÷ 1,000,
= 38,000 ÷ 10 ÷ 10 ÷ 10,
= 3800 ÷ 10 ÷ 10,
= 380 ÷ 10,
= 38.

Question 16.
7,700 ÷ 10² = _77__
Answer:
77,

Explanation:
As 100 = 10²,
= 7,700 ÷ 10²,
= 7,700 ÷ 10 ÷ 10,
= 770 ÷ 10,
= 77.

Question 17.
360,000 ÷ 10³ = _360__
Answer:
360,

Explanation:
1000 = 10³,
= 360,000 ÷ 10 ÷ 10 ÷ 10,
= 36,000 ÷ 10 ÷ 10,
= 3,600 ÷ 10,
= 360.

Question 18.
2,000 ÷ 10² = _20__
Answer:
20,
Explanation:
100 = 10²,
2,000 ÷ 10²,
= 2,000 ÷ 10 ÷ 10,
= 200 ÷ 10,
= 20.

Question 19.
415,000 ÷ 10³ = _415__
Answer:
415,

Explanation:
1000 = 10³,
= 415,000 ÷ 10 ÷ 10 ÷ 10,
= 41,500 ÷ 10 ÷ 10,
= 4150 ÷ 10,
= 415.

To which class of animals does the salamander belong?
Write the letters that match the answers below to find out.

Answer:
AMPHIBIANS,

Explanation:
The solutions from the above questions from 12 to 19,
according to the answers arrange the given alphabets to find out the word.

Question 21.
81,000 ÷ 900
= (81,000 ÷ _100_) ÷ __9_
= _810__ ÷ _9__
= _90___
Answer:
90,

Explanation:
= 81,000 ÷ 900,
= 81,000 ÷ 100 ÷ 9,
= 81,000 ÷ 10 ÷ 10 ÷ 9,
= 8,100 ÷ 10 ÷ 9,
= 810 ÷ 9,
= 90.

Complete.

Example . ________
9,000 ÷ 3,000,
= (9,000 ÷ 1000) ÷ 3,
= 9 ÷ 3,
= 3.

Question 22.
31,500 ÷ 500
= (31,500 ÷ _100__) ÷ _5__
= _315__ ÷ _5___
= _63___
Answer:
63,

Explanation:
Given 31,500 ÷ 500,
= 31,500 ÷10  ÷ 10 ÷ 5,
= 3150 ÷ 10 ÷ 5,
= 315 ÷ 5,
= 63,

Question 23.
56,000 ÷ 7,000
= (56,000 ÷ _1000__) ÷ __7____
= _56___ ÷ __7__
= __8__
Answer:
8,

Explanation:
56000 ÷ 1000 ÷ 7,
= 56 ÷ 7 = 8,

Question 24.
133,000 ÷ 7,000
= (133,000 ÷ _1,000__) ÷ __7_
= _133___ ÷ _7__
= _19___
Answer:
19,

Explanation:
Given 133,000 ÷ 1,000 ÷ 7,
= 133 ÷ 7 = 19.

Question 25.
120,000 ÷ 8,000
= (120,000 ÷ __1,000_) ÷ _8__
= _120___ ÷ __8_
= __15__
Answer:
15,

Explanation:
Given 120000 ÷ 8,000,
= 120,000 ÷  1,000 ÷ 8
120 ÷ 8 = 15.

Divide.

Question 26.

Answer: 9

Explanation:
Dividing by tens 360 ÷ 40,
= 360÷10÷4,
= 36÷4,
= 9,
= 3600 ÷ 400
Dividing by hundreds 3600÷100÷4,
= 36÷4
= 9,
Dividing by thousands 36000 ÷ 4000,
= 360÷1000÷4,
= 36÷4,
= 9.

Question 27.

Answer: 17

Explanation:
Dividing by tens 1,190 ÷ 70,
= 1190 ÷ 10÷ 7
= 119 ÷ 7
= 17,
Dividing by hundreds 11,900 ÷ 700,
= 11,900 ÷ 100÷ 7
= 119 ÷ 7
= 17,
Dividing by thousands 1,19000 ÷ 7000,
= 119000 ÷ 1000÷ 7,
= 119 ÷ 7,
= 17.

Question 28.

Answer:
634

Explanation:
Dividing by tens 12,680 ÷ 20,
= 12,680 ÷ 10 ÷ 2,
= 1,268 ÷ 2,
= 634.
Dividing by hundreds 126,800 ÷ 200,
= 126,800÷ 100÷ 2,
= 1,268 ÷ 2,
= 634.
Dividing by thousands 1,268,000 ÷ 2000,
= 1,268,000 ÷ 2,000,
= 12,680 ÷ 1,000 ÷ 2,
=1,268 ÷ 2,
= 634.

Question 29.

Answer:
290

Explanation:
Dividing by tens 23,200 ÷ 80,
= 23,200 ÷ 10 ÷ 8,
= 23,20 ÷ 8,
= 290.
Dividing by hundreds 23,2000 ÷ 800,
= 23,2000 ÷ 100 ÷ 8,
= 2320 ÷ 8,
= 290.
Div iding by thousands 2,320,000 ÷ 8000,
= 2,320,000÷ 1000÷ 8,
= 2320 ÷ 8,
= 290.

Complete.

Question 30.
430 ÷ _10_ = 43
Answer:
10,
Explanation:
Given 430 ÷ 10 = 43.

Question 31.
9,000 ÷ _100_ = 30
Answer:
300,

Explanation:
Given 9,000 ÷ 300,
=9,000 ÷ 100 ÷ 3,
= 90 ÷ 3 = 30.

Question 32.
49,000 ÷ _1,000__ = 7
Answer:
7,000,

Explanation:
49,000 ÷ 7,000,
= 49,000 ÷ 1,000 ÷ 7,
= 49 ÷ 7 = 7.

Question 33.
2,400 ÷ _10__ = 120
Answer:
20,

Explanation:
Given 2,400 ÷ _10__ = 120,
= 2,400 ÷ 120,
= 2,400 ÷ 10 ÷ 12,
= 240 ÷ 12 = 20.

Question 34.
64,000 ÷ _400__ = 160
Answer:
400,

Explanation:
Given 64,000 ÷ 400,
= 64,000 ÷ 100 ÷ 4,
= 640 ÷ 4 = 160.

Question 35.
85,000 ÷ _5,000__ = 17
Answer:
5,000,

Explanation:
Given 85,000 ÷ ____ = 17,
= 85,000 ÷ 17 = 5,000.

Estimate each quotient.

Example
6,452 ÷ 27 rounds to 6,000 ÷ 3 = 200

Question 36.
7,865 ÷ 41 rounds to ____ ÷ ___ = ____
Answer:
7,865 ÷ 41 rounds to 8,000 ÷ 40 = 200,

Explanation:,
Estimate of 7,865 is 8,000,
Estimate of 41 is 40,
So, 8,000 ÷ 40 = 200.

Question 37.
9,125 ÷ 345 rounds to ___ ÷ ___ = ____
Answer:
9,125 ÷ 345 rounds to 9,000 ÷ 300 = 30,

Explanation:
Estimate of 9,125 is 9,000,
Estimate of 345 is 300,
So, 9,000 ÷ 300 = 30.

Question 38.
9,825 ÷ 206 rounds to ___ ÷ ___ = ____
Answer:
9,825 ÷ 206 rounds to 10,000 ÷ 200 = 50,

Explanation:
Estimate of 9,825 is 10,000,
Estimate of 206 is 200,
So, 10,000 ÷ 200 = 50.

Question 39.
7,226 ÷ 871 rounds to ___ ÷ ___ = ____
Answer:
7,226 ÷ 871 rounds to 7200 ÷ 900 = 8,

Explanation:
Estimate of 7,226 is 7,200,
Estimate of 871 is 900,
So, 7,200 ÷ 900 = 8.

Question 40.
5,299 ÷ 49 rounds to ___ ÷ ____ = ____
Answer:
5,299 ÷ 49 rounds to 5,000 ÷ 50 = 100,

Explanation:
Estimate of 5,299 is 5,000,
Estimate of 49 is 50,
So, 5,000 ÷ 50 = 100.

Question 41.
3,654 ÷ 27 rounds to ___ ÷ ___ = ____
Answer:
3,654 ÷ 27 rounds to 3,600 ÷ 30 = 120,

Explanation:
Estimate of 3,654 is 3,600,
Estimate of 27 is 30,
So, 3,600 ÷ 30 = 120.

What number can be evenly divided by 3, 7, and 9?
Color the numbers below that match the answers above to find out.

Answer:

Explanation:
In the above given picture the numbers with green color will divide by 3,
numbers with blue color divide by 7,
numbers with pink color divide by 9.

Practice the problems of Math in Focus Grade 5 Workbook Answer Key Cumulative Review Chapters 8 to 10 to score better marks in the exam.

Math in Focus Grade 5 Cumulative Review Chapters 8 to 10 Answer Key

Concepts and Skills

Mark ✗ to show where each decimal is located on the number line. (Lesson 8.1)

Question 1.
0.032

Answer:

Explanation:
In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.
To represent a decimal on a number line, divide each segment of the number line into ten equal parts.
Then mark the given number on number line.
Question 2.
0.047
Answer:

Explanation:
In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.
To represent a decimal on a number line, divide each segment of the number line into ten equal parts.
Then mark the given number on number line.

Complete. (Lesson 8.1)

Question 3.
3 tenths 5 hundredths = _________ thousandths
Answer:
0.350
3 tenths 5 hundredths = 0.305________ thousandths
Explanation:
Read the whole set of three decimal digits as a number, and say, “tenths”, “hundredths” and “thousandths.” 0.305 has 3 tenths, 0 hundredths, and 5 thousandths. While 0.305 is the sum of 3/10, 0/100, and 5/1000, it is also 305/1000

Just as “ones,” “tens,” and “hundreds” are used to describe place value for whole numbers,
there are terms that describe place value for decimals:
tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, etc.
These terms are used from left to right, starting with the first numeral after the decimal point.

Question 4.
803 thousandths = ______ tenths _______ thousandths
Answer:
803 thousandths = 8 tenths 0 hundredths 3 thousandths
Explanation:
Just as “ones,” “tens,” and “hundreds” are used to describe place value for whole numbers,
there are terms that describe place value for decimals:
tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, etc.
These terms are used from left to right, starting with the first numeral after the decimal point.

Question 5.
0.835 = 8 tenths 3 hundredths _____ thousandths
Answer:
0.835 = 8 tenths 3 hundredths 5 thousandths
Explanation:
Just as “ones,” “tens,” and “hundreds” are used to describe place value for whole numbers,
there are terms that describe place value for decimals:
tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, etc.
These terms are used from left to right, starting with the first numeral after the decimal point.

Write the equivalent decimal. (Lesson 8.1)

Question 6.
8 ones and 214 thousandths = __________
Answer: 8.214
Explanation:
The first digit to the right of decimal point is in the tenths place.
The second digit to the right of decimal point is in the hundredths place.
The third digit to the right of decimal point is in the thousandths place.
So, 8 ones and 214 thousandths.

Question 7.
1,180 thousandths = __________
Answer: 1.180
Explanation:
If you divide 1180 by one thousand you get 1180 thousandths as a decimal which is 1.180.
1180 thousands = 1180/1000 = 1.180

Question 8.
7\(\frac{60}{1000}\) = __________
Answer: 7.06
Explanation:
7 x 1000 + 60 = 7000 + 60 = 7060
\(\frac{7060}{1000}\) = 7.06
7\(\frac{60}{1000}\) = 7.06

Question 9.
\(\frac{6050}{1000}\) = __________
Answer: 6.05
Explanation:
The easiest way to convert a fraction to a decimal is to divide the numerator by the denominator.
Or else count the number of zeros in denominator and place the decimal in the given number by moving from right.
\(\frac{6050}{1000}\) = 6.05

4.526 can be written in expanded form as 4 + 0.5 + 0.02 + 0.006. Write each decimal in expanded notation. (Lesson 8.1)

Question 10.
0.329 = ___ + ___ + ___
Answer:
0.329 = 0.3 + 0.02 + 0.009
Explanation:
Writing decimals in expanded form simply means writing each number according to its place value.
This is done by multiplying each digit by its place value and adding them together.

20.125 = ___ + ___ + ___ + ___
Answer:
20.125 =20 + 0 + 0.1 + .02 + 0.005
Explanation:
Writing decimals in expanded form simply means writing each number according to its place value.
This is done by multiplying each digit by its place value and adding them together.

Complete. (Lesson 8.1)

In 9.168,

Question 12.
the digit 6 is in the ___ place.
Answer:
Hundredths place
Explanation:
Writing decimals in expanded form simply means writing each number according to its place value.
This is done by multiplying each digit by its place value and adding them together.
The digit 6 is in the hundredths place in 9.168.

Question 13.
the value of the digit 8 is ___
Answer:
Thousands place
Explanation:
Writing decimals in expanded form simply means writing each number according to its place value.
This is done by multiplying each digit by its place value and adding them together.
The digit 8 is in the thousandths place in 9.168.

Question 14.
the digit 1 stands for _______
Answer:
Tenths place
Explanation:
Writing decimals in expanded form simply means writing each number according to its place value.
This is done by multiplying each digit by its place value and adding them together.
The digit 1 is in the tenths place in 9.168.

Compare. Write >, <, or =. (Lesson 8.2)

Question 15.
1.07 1.7
Answer: <

Explanation:
The value 1.07 is less than the other value 1.7, we use less than.
The symbol used to represent less than is “<”.
As there is no value for zero after decimal.

Question 16.
3.562 3.526
Answer: >

Explanation:
The value 3.562 is greater than the other value 3.526,
The symbol used to represent greater than is “>”.
The number after decimal is more in 562 than in 526.

Question 17.
15.4 15.40
Answer: =

Explanation:
The value 15.4 is equal to 15.40,
In decimal if zero is present in ones place there is no value.

Order the decimals. (Lesson 8.2)

Question 18.
2.08, 1.973, 6.1
Begin with the least:
_____________
Answer:
1.973 , 2.08, 6.1
Explanation:
Arranging the numbers from least to greatest is known as Ascending order.

Question 19.
1.567, 1.667, 1.376
Begin with the greatest:
________________
Answer:
1.667, 1.567, 1.376
Explanation:
Arranging the numbers from least to greatest is known as Descending order.

Fill in the blanks. (Lesson 8.2)

Question 20.
The mass of a strand of hair is 0.179 gram.
Round the mass to the nearest hundredth of a gram.
0.179 gram rounds to ___ gram.
Answer: 0.18
0.179 gram rounds to 0.18 gram.
Explanation:
For rounding decimal numbers to the nearest hundredth,
we need to know the decimal place values of the digits in the given number.
This refers to the digits given before the decimal point as well as the digits given after the decimal point.
It should be noted that when we round numbers to the nearest hundredth,
we always use the thousandths place to decide whether the hundredths place will round up or will remain the same.

Question 21.
The length of a rope is 2.589 yards.
Round the length to the nearest tenth of a yard.
2.589 yards rounds to ___ yards.
Answer: 2.6
2.589 yards rounds to 2.6 yards
Explanation:
For rounding decimal numbers to the nearest hundredth,
we need to know the decimal place values of the digits in the given number.
This refers to the digits given before the decimal point as well as the digits given after the decimal point.
It should be noted that when we round numbers to the nearest hundredth,
we always use the thousandths place to decide whether the hundredths place will round up or will remain the same.

Write each decimal as a mixed number in simplest form. (Lesson 8.3)

Question 22.
6.2 = ___
Answer:
6\(\frac{1}{5}\)
Explanation:
\(\frac{62}{10}\)
6\(\frac{2}{10}\)
6\(\frac{1}{5}\)

Question 23.
2.16 = _______
Answer:
2\(\frac{4}{25}\)
Explanation:
\(\frac{216}{100}\)
2\(\frac{16}{100}\)
2\(\frac{4}{25}\)

Multiply. (Lessons 9.7 and 9.2)

Question 24.
29.3 × 8 = _______
Answer: 234.4
Explanation:
To multiply decimals, first multiply as if there is no decimal.
Next, count the number of digits after the decimal in each factor.
Finally, put the same number of digits behind the decimal in the product.

Question 25.
12.08 × 5 = _______
Answer: 60.4
Explanation:
To multiply decimals, first multiply as if there is no decimal.
Next, count the number of digits after the decimal in each factor.
Finally, put the same number of digits behind the decimal in the product.

Question 26.
86.4 × 10 = _______
Answer: 864
Explanation:
Separate 10 as 1 ones and 0 tenths,
then multiply with ones first and later tens.
86.4 x 10 = (86.4 x 1) x 10
= 86.4 x 10
= 864
So, 86.4 x 10= 864
Question 27.
13.5 × 30 = ____
Answer: 405
Explanation:
Separate 30 as 3 ones and 1 tenths,
then multiply with ones first and later tens.
13.5 x 30 = (13.5 x 3) x 10
= 40.5 x 10
= 405
So, 13.5 x 30= 405

Question 28.
73.96 × 100 = ___
Answer:7,396
Explanation:
73.96 x 100 = (73.96 x10) x 10
=739.6 x 10
=7396
So, 73.96 x 100 = 7,396

Question 29.
6.2 × 700 = ___
Answer: 4,340
Explanation:
6.2 x 700 = (6.2 x70) x 10
= 434 x 10
=4340
So, 6.2 x 700 = 4,340

Question 30.
9.34 × 1,000 = ___
Answer: 9,340
Explanation:
9.34 x 1000 = (9.34 x 10) x 10 x 10
= 93.4 x 10 x 10
=934 x 10
= 9340
So, 9.34 x 1000 = 9,340

Question 31.
25.6 × 9,000 = ____
Answer: 230,400
Explanation:
25.6 x 1000 = (25.6 x 9) x 10 x 10
= 230.4 x 10 x 10
=2304 x 100
= 230400
So, 25.6 x 1000 = 230,400

Divide. (Lesson 9.3)

Question 32.
0.5 ÷ 5 = _______
Answer: 0.1
Explanation:
0.5 ÷ 5 = 5 tenths ÷ 5
= 1 tenths
= 0.1
So, 0.5 ÷ 5 = 0.1

Question 33.
0.63 ÷ 9 = ___
Answer: 0.07
Explanation:
0.63 ÷ 9 = 63 hundredths ÷ 9
=7 hundredths
= 0.07
So, 0.63 ÷ 9 = 0.07

Question 34.
36.8 ÷ 4 = ___
Answer: 9.2
Explanation:
Step 1
Divide the ones by 4.
36 ones ÷ 4 = 9 ones R 0 ones
Regroup the remainder into tenths.
0 ones = 0 tenths
Add the tenths.
0 tenths + 8 tenths = 8 tenths
Step 2
Divide the tenths by 4.
8 tenths ÷ 4 = 2 tenths
So, 36.8 ÷ 4 = 9.2

Question 35.
96.3 ÷ 5 = ___
Answer: 19.26
Explanation:
Step 1
Divide the ones by 5.
96 ones ÷ 5 = 19 ones R 2 ones
Regroup the remainder into tenths.
192 = 19 ones and 2 tenths
Step 2
Divide the tenths by 5.
10 tenths ÷ 5 = 2 tenths
So, 96.3 ÷ 5 = 19.26

Question 36.
3.36 ÷ 4 = ___
Answer: 0.84
Explanation:
Step 1
Divide the ones by 4.
3 ones ÷ 4 = 8 ones R 7 ones
Regroup the remainder into tenths.
0 ones = 0 tenths
Add the tenths.
0 tenths + 8 tenths = 8 tenths
Step 2
Divide the tenths by 4.
8 tenths ÷ 4 = 2 tenths
So, 3.36 ÷ 4 = 0.84

Question 37.
1.92 ÷ 8 = ___
Answer: 24
Explanation:
Step 1
Divide the ones by 8.
9 ones ÷ 8 = 1 ones R 1 ones
Regroup the remainder into tenths.
1 ones = 10 tenths
Add the tenths.
10 tenths + 9 tenths = 19 tenths
Step 2
Divide the tenths by 4.
19 tenths ÷ 8 = 4 tenths
So, 1.92 ÷ 8 = 24

Divide. Round the quotient to the nearest tenth and nearest hundredth. (Lesson 9.3)

Question 38.
19 ÷ 7 = ___ to the nearest tenth
19 ÷ 7 = ___ to the nearest hundredth
Answer:
19 ÷ 7 = 2.7 to the nearest tenth
19 ÷ 7 = 0.27 to the nearest hundredth
Explanation:
19 ÷ 7 = 2.7 to the nearest tenth

19 ÷ 7 = 0.27 to the nearest hundredth

19 ÷ 7 = 2.7_ to the nearest tenth
First, divide to two decimal places.
Then round the answer to the nearest tenth.
Explanation:
19 ÷ 7 = ___ to the nearest hundredth
First, divide to three decimal places.
Then round the answer to the nearest hundredth.

Divide. (Lesson 9.4)

Question 39.
3.8 ÷ 10 = ___
Answer: 0.38
Explanation:
3.8 ÷ 10 = (4.8 ÷ 1 ) ÷ 10
= 3.8 ÷ 10
= 0.38
So, 3.8 ÷ 10 = 0.38

Question 40.
19.6 ÷ 20 = ___
Answer: 0.98
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,
19.6 ÷ 20 = (19.6 ÷ 2 ) ÷ 10
= 9.8 ÷ 10
= 0.98
So, 19.6 ÷ 10 = 0.98

Question 41.
4.5 ÷ 100 = ___
Answer: 0.045
Explanation:
4.5 ÷ 100 = (4.5 ÷ 10 ) ÷ 10
= 0.45 ÷ 10
= 0.045
So,  4.5 ÷ 100 = 0.045

Question 42.
375 ÷ 300 = ___
Answer: 1.25
Explanation:
375 ÷ 300 = (375 ÷ 30 ) ÷ 10
= 12.5 ÷ 10
= 1.25
So,  375 ÷ 300 = 1.25

Question 43.
5,030 ÷ 1,000 = ___
Answer: 5.03
Explanation:
5030 ÷ 1000 = (5030 ÷ 10 ) ÷ 10 ÷ 10
= 503 ÷ 10÷ 10
= 50.3÷ 10
=5.03
So, 5030 ÷ 1000 = 5.03

Question 44.
2,506 ÷ 7,000 = ___
Answer: 0.358
Explanation:
2506 ÷ 7000 = (2506 ÷ 70 ) ÷ 10 ÷ 10
= 35.8 ÷ 10÷ 10
= 3.58÷ 10
=0.358
So, 2506 ÷ 7000 = 0.358

Estimate each answer by rounding the numbers to an appropriate place. (Lesson 9.5)

Question 45.
91.2 + 25.9
Answer: 117.1
Estimate: 117
Explanation:
91.2 + 25.9
91.2 rounds to 91.
25.9 rounds to 26.
91 + 26 = 10
91.2 + 25.9 is about 117.

Question 46.
37.4 – 11.7
Answer: 25.7
Estimate: 25
Explanation:
37.4 – 11.7
37.4 rounds to 37.
11.7 rounds to 12.
37 – 12 = 25
37.4 – 11.7 is about 25.

Question 47.
21.63 × 5
Answer: 108.15
Estimate: 110
Explanation:
21.63 × 5
21.63 rounds to 22.
22 × 5 = 110
21.63 × 5 is about 110.

Question 48.
7.05 ÷ 8
Answer: 0.88
Estimate: 1
Explanation:
7.05 ÷ 8
7.05 is about 8.
8 ÷ 8 = 1
7.05 ÷ 8 is about 1.

Write each ratio in three ways. Complete the table. (Lesson 10.1)

Question 49.

Answer:

Explanation:
Ratios are smaller to fractions, and each fraction can be written as a fraction.
Divide the first number 23 by the second number 100.
Multiply by 100 to convert to a percentage.
Add the percent symbol (%) to the output.
To change a percent to a decimal we divide by 100.
This is the same as moving the decimal point two places to the left.

Question 50.

Answer:

Explanation:
Ratios are smaller to fractions, and each fraction can be written as a fraction.
Divide the first number 23 by the second number 100.
Multiply by 100 to convert to a percentage.
Add the percent symbol (%) to the output.
To change a percent to a decimal we divide by 100.
This is the same as moving the decimal point two places to the left.

Express each fraction as a percent. (Lesson 10.2)

Question 51.
\(\frac{88}{200}\) =
Answer: 44%
Explanation:
To convert a fraction to a percent, first divide the numerator by the denominator.
Then multiply the answer by 100 .
It can be converted to percent by multiplying the decimal by 100 .

Question 52.
\(\frac{204}{400}\) =
Answer: 51%
Explanation:
To convert a fraction to a percent, first divide the numerator by the denominator.
Then multiply the answer by 100 .
It can be converted to percent by multiplying the decimal by 100 .

Question 53.
\(\frac{6}{20}\) =
Answer: 30%
Explanation:
To convert a fraction to a percent, first divide the numerator by the denominator.
Then multiply the answer by 100 .
It can be converted to percent by multiplying the decimal by 100 .

Question 54.
\(\frac{7}{50}\) =
Answer: 14%
Explanation:
To convert a fraction to a percent, first divide the numerator by the denominator.
Then multiply the answer by 100 .
It can be converted to percent by multiplying the decimal by 100 .

Question 55.
\(\frac{13}{20}\) =
Answer: 65%
Explanation:
To convert a fraction to a percent, first divide the numerator by the denominator.
Then multiply the answer by 100 .
It can be converted to percent by multiplying the decimal by 100 .

Question 56.
\(\frac{16}{25}\) =
Answer: 64%
Explanation:
To convert a fraction to a percent, first divide the numerator by the denominator.
Then multiply the answer by 100 .
It can be converted to percent by multiplying the decimal by 100 .

Problem Solving

Solve.

Question 57.
Hazel saves $5.75 each week.

a. How much does she save in 2 weeks?
Answer: $11.5
Estimate: 12
Explanation:
Hazel saves $5.75 each week.
Total amount she saves in two weeks
5.75 x 2 = 11.5
5.75 is rounded as 6
6 x 2 = 12
So, 5.75 x 2 is about 12.

b. She spends $23.83 on a book and $9.12 on a wallet. How much does she spend on the two items?
Answer: $32.95
Estimate: 33
Explanation:
Hazel spends $23.83 on a book and $9.12 on a wallet.
Total amount she spend on the two items
23.83 + 9.12
23.83 rounds as 24
9.12 rounds as 9
So, 24 + 9 = 33
23.83 + 9.12 = 32.95

Question 58.
Evelyn has 12.7 quarts of fruit punch in a cooler. She pours the fruit punch into glasses. She fills 5 glasses, each with a capacity of 0.36 quart. Then she fills 8 glasses, each with a capacity of 0.52 quart. How much fruit punch is left in the cooler?
Answer:
Explanation:
total fruit punch = 12.7 quarts
she fills 5 glasses with 0.36 quart
she fills 8 glasses with 0.52 quart
totalt fruit punch that she filled in glasses = 5 x 0.36 + 8 x 0.52
= 1.8 + 4.16 = 5.96 quarts
total fruit punch left in cooler = 12.7 – 5.96 = 6.74 quarts

Solve. Use models to help you.

Question 59.
The total weight of three tables is 16.9 pounds. The first table is twice as heavy as the second table. The weight of the third table is \(\frac{1}{3}\) the weight of the second table. What is the weight of the first table?
Answer:
weight of first table = 10.14 pounds
Explanation:
let weight of second table is x
weight of first table = 2 x weight of second table
weight of first table = 2x
weight of third table = \(\frac{1}{3}\) of weight of third table
weight of third table =  \(\frac{1}{3}\) x
So we get,
weight of first table = 2x
weight of second table = x
weight of third table =  \(\frac{1}{3}\) x
total weight = 16.9 pounds
first table + second table + third table = 16.9 pounds
2x + x + \(\frac{1}{3}\) x = 16.9
3x + \(\frac{1}{3}\) x = 16.9
\(\frac{3 x (3x) + x}{3}\) = 16.9
9x + x = 16.9 x 3
10x = 50.7
x = \(\frac{50.7}{10}\)
x = 5.07
weight of first table = 2x = 2 x 5.07
weight of first table = 10.14 pounds

Question 60.
There are 950 seats in a theater. 82% of the seats are occupied. How many seats are not occupied?
Answer:
151 seats
Explanation:
Total number of seats = 950
Occupied seats = 950 x \(\frac{82}{100}\)  = 799
Seats not occupied =  950 – 799 =  151 seats

Solve. Use models to help you.

Question 61.
Rahul spends 10% of his weekly allowance on Monday. On Wednesday, he spends \(\frac{1}{3}\) of the remainder. What percent of his allowance is left at the end of Wednesday?
Answer: 60%
Explanation:
x 100% –  x10% =x 90%
x 90% x \(\frac{1}{3}\)
x 30% he spent on Wednesday
total he spent 10% + 30% = 40%
percent of his allowance is left at the end of Wednesday is 60%

Question 62.
Ms. Jones buys a violin for $860. In addition, she has to pay 7% sales tax. How much does she pay in all?
Answer: $920.2
Estimate: $920
Explanation:
860 x \(\frac{7}{100}\) = 60.2 tax
she pay in all $860 + $60.2 = $920.2

Solve.

Question 63.
The regular price of a television set is $1,200. Albert buys the television set at a discount of 35%. How much does he pay for the television set?
Answer: $780
Explanation:
1200 x \(\frac{35}{100}\) = 420
1200 – 420 = 780
Albert pay for the television set $780

Question 64.
A school band gives a year-end concert. It is held in a 400-seat auditorium. Each concert ticket sells for $10, and 85% of the tickets are sold. How much money does the band earn from the sale of the tickets?
Answer: $3 400
Explanation:
total money to be collected by selling 400 tickets @$10
400 x 10 = 4000
4000 x 85%
4000 x \(\frac{85}{100}\) = 3400
$3400 much money does the band earn from the sale of the tickets.

Practice the problems of Math in Focus Grade 5 Workbook Answer Key Chapter 10 Practice 4 Real-World Problems: Percent to score better marks in the exam.

Math in Focus Grade 5 Chapter 10 Practice 4 Answer Key Real-World Problems: Percent

Solve. Show your work.

Question 1.
Jennifer bought a printer that cost $240. There was a 7% sales tax on the printer.

a. How much sales tax did Jennifer pay?

Answer: $16.8
Explanation:
240 x 7%
= (240  x 7)/100
=$16.8

b. How much did Jennifer pay for the printer with tax?
Answer: $256.8
Expanation:
Printer cost $240
Tax paid 7% = &16.8
Tota amount paid = $240 + $16.8 = $256.8

Question 2.
A company invests $8,000 in an account that pays 6% interest per year.

a. How much interest will the company earn at the end of 1 year?
Answer: $480
Explanation:
$8000 x 6%
= (8000 x 6)/100 = 480

b. How much money will the company have in the account at the end of 1 year?
Answer: $8480
Explanation:
invested amount = $8000
interest 6%
the company have in the account at the end of 1 year
$8000 + $480 = 8480

Solve. Show your work.

Question 3.
The regular price of a digital camera was $250. Tyrone bought the digital camera at a discount of 40%. How much did Tyrone pay for the digital camera?

Answer:
$150 Tyrone pay for the digital camera.
Explanation:
camera price is $250
40% of 250 is
(250 x 40)/100 = 25 x 4
= $100
Tyrone pay for the digital camera
$250 – $100 = $150

Question 4.
Len bought a new car for $22500. After o few years, he sold the car at a discount of 25%. What was the selling price of the car?
Answer: $16875
Explanation:
new car cost =  $22500
sold at a discount of 25%
25% of $22500
=(22500 x 25)/100
=225 x 25
= $5625
the selling price of the car is
$22500 – $5625 = $16875

Solve. Show your work.

Question 5.
The price for dinner in a restaurant was $80. The customer paid on additional 7% meals tax and left o $15 tip.

a. How much meals tax did the customer pay?
Answer: $5.6
Explanation:
Dinner cost = $80
Tax = 7%
80 x 7% =
(80 x 7)/100 = $5.6

b. How much did the customer spend altogether in the restaurant?
Answer: $100.6
Explanation:
Dinner cost = $80
Tip = $15
meal tax =$5.6
the customer spend altogether in the restaurant
=$80 + $15 + $5.6 = $100.6

Question 6.
The regular price of a pair of hockey skates was $250. Ron bought the skates at a discount of 8%. However, he had to pay 5% sales tax on the skates after the discount.

a. What was the selling price of the skates?
Answer: $230
Explanation:
hockey skates cost= $250
8% of $250=
(250 x 8)/100 = $20
the selling price of the skates is
$250 – $20 = $230

b. How much did Ron pay for the skates in total?
Answer: $241.5
Explanation:
5% sales tax on the skates after the discount
5% of $230
(230 x 5)/100 = 11.5
Ron pay for the skates in total
$230 + $11.5 = $241.5

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 12 Practice 1 Angles on a Line provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 12 Practice 1 Answer Key Angles on a Line

In each figure, \(\overleftrightarrow{A C}\) is a line. Use a protractor to find the unknown angle measures.

Question 1.

m∠DBC = ____
m∠DBA = ____
m∠DBC + m∠DBA = ___ + _____
= _____
Answer:
m∠DBC = 60°
m∠DBA = 120°
m∠DBC + m∠DBA = 60° + 120°= 180°
Explanation:

To determine to measure of the unknown angle, be sure to use the total sum of 180°.
Then take a protractor and measure m∠DBC = 60°
Then subtract m∠DBC = 60° from 180°,
We get m∠DBA = 120°

Question 2.

m∠x = ____
m∠y = ____
m∠x + m∠y = ___ + ___
= _____
Answer:
m∠x = 70°
m∠y = 110°
m∠x + m∠y = 70° + 110° =  180°
Explanation:

To measure the unknown angles, first take a protractor and measure m∠x = 70°
Then measure m∠y = 110°
Add both the angles m∠x + m∠y = 70° + 110° =  180°

\(\overleftrightarrow{A C}\) is a line. Use a protractor to find the unknown angle measures.

Question 3.

m∠p = ____
m∠q = ____
m∠r = ____
m∠p + m∠q + m∠r = ___ + ___ + ___
= ____
Answer:
m∠p = 20°
m∠q = 100°
m∠r =  60°
m∠p + m∠q + m∠r = 20° + 100° + 60°= 180°
Explanation:

To measure the unknown angles, first take a protractor and measure m∠p = 20°
Then measure m∠q = 100°
Then measure m∠r = 60°
Add all the angles m∠p + m∠q + m∠r = 20° + 100° + 60° =  180°

Name the angles on each line.

Question 4.
\(\overleftrightarrow{X Z}\) is a line.

Answer:
m∠XYW = 40°
m∠WYZ = 140°
m∠XYW + m∠WYZ = 40°+ 140° = 180°
Explanation:

To determine to measure of the unknown angle, be sure to use the total sum of 180°.
Then take a protractor and measure m∠XYW = 40°, an angle less than 90° is acute angle.
Then take a protractor and measure m∠WYZ = 140°, an angle more than 90° is obtuse angle.
Add both the angles m∠XYW + m∠WYZ = 40°+ 140° = 180°

Question 5.
\(\overleftrightarrow{P R}\) is a line.

Answer:
m∠PQS = m∠a = 40° Acute Angle
m∠TQS = m∠b = 90° Right Angle
m∠TQR = m∠c = 50° Acute Angle
m∠PQS + m∠TQS + m∠TQR = 40°+ 90° + 50° = 180° Straight Angle
Explanation:

To determine to measure of the unknown angle, be sure to use the total sum of 180°.
Then take a protractor and measure m∠PQS = m∠a = 40° Acute Angle, an angle less than 90° is acute angle.
Then take a protractor and measure m∠TQS = m∠b = 90° Right Angle.
Then take a protractor and measure m∠TQR = m∠c = 50° Acute Angle
Add all the angles m∠PQS + m∠TQS + m∠TQR = 40°+ 90° + 50° = 180° Straight Angle.

Name each set of angles on a line.

Question 6.
\(\overleftrightarrow{A C}\) is a line.

Answer:
m∠p = 50°
m∠q = 120°
m∠r =  60°
m∠s =  60°
m∠t =  70°
∠p + ∠q + ∠r + ∠s + ∠t = 50° + 120° + 60°+ 60°+ 70° = 360°
Explanation:

m∠p and m∠q are Vertical angles where the two angles cross each other.
m∠r , m∠t and m∠s are acute angle, where the angle is less than 90°

Question 7.
\(\overleftrightarrow{A B}\) and \(\overleftrightarrow{C D}\) are line.

Answer:
∠p = 60°
∠q = 100°
∠r =  20°
∠s =  160°
∠t =  20°
∠p + ∠q + ∠r + ∠s + ∠t = 60° + 100° + 20°+ 160°+ 20° = 360°
Explanation:

∠p, ∠r and ∠t are acute angles, where the angle is less than 90°
∠q and ∠s are obtuse angles, where the angles is more than 90°

Find the unknown angle measures.

Question 8.
\(\overleftrightarrow{A C}\) is a line. Find the measure of ∠DBC.

Answer:

Explanation:
To determine to measure of the unknown angle, be sure to use the total sum of 180°.
Given m∠DBC + 125° = 180°
m∠DBC – 180° = 125° = 55°

Question 9.
\(\overleftrightarrow{E G}\) is a line. Find the measure of ∠HFE.

Answer:

Explanation:
To determine to measure of the unknown angle, be sure to use the total sum of 180°.
Given ∠FIG = 42° = 180°
∠HFI = 90°
∠EFH = 180° – (42° + 90°)
= 180° – 132° = 48°

Find the unknown angle measures.

Question 10.
\(\overleftrightarrow{O Q}\) is a line. Find the measure of ∠SPT.

Answer:
m∠SPT =180° – (15°+70°+39°) =  56°

Explanation:
To determine to measure of the unknown angle, be sure to use the total sum of 180°.
Given ∠POR = 15°
∠RPS = 70°
∠TPQ = 39°
m∠SPT = 180° – (∠POR +∠RPS +∠TPQ )
m∠SPT =180°- (15°+70°+39°) =  56°

Question 11.
\(\overleftrightarrow{A C}\) is a line. Find the measure of ∠EBF.

Answer:
m∠EBF =180° – (41° + 27° + 90°) = 180° – 158° = 22°

Explanation:
To determine to measure of the unknown angle, be sure to use the total sum of 180°.
Given ∠DBA = 41°
∠DBE = 27°
∠FBC = 90°
m∠EBF = 180° – (∠DBA +∠DBE +∠FBC )
m∠EBF =180°- (41°+27°+90°) =  22°

Question 12.
\(\overleftrightarrow{J K}\) is a line. Find the measure of ∠y and ∠z.

Answer:

Explanation:
Angles formed by two rays lie in the plane that contains the rays.
Angles are also formed by the intersection of two planes.
Given:
∠JOI = 80°
∠JOG = 36°
∠GOH= 72°
m∠y = 180° – (∠JOG+∠GOH)
m∠y =180°- (36°+72°)
=180°- 108°
= 72°
m∠z =180°- ∠JOI
= 180° – 80°
= 100°

Question 13.
\(\overleftrightarrow{E F}\) and \(\overleftrightarrow{G H}\) are line. Find the measure of ∠a and ∠b.

Answer:

Explanation:
Angles formed by two rays lie in the plane that contains the rays are called vertex of the angle.
Angles are also formed by the intersection of two planes.
Given:
∠GOF = 160°
∠FOH = 20°
∠HOJ= 50°
∠JOI = 90°
m∠a =180°- ∠GOF
= 180° – 160°
= 20°
m∠b= 180° – (∠HOJ+∠FOH+∠JOI )
=180°- (50°+20°+90°)
=180°- 160°
= 20°

This handy Math in Focus Grade 3 Workbook Answer Key Cumulative Review Chapters 16 to 19 detailed solutions for the textbook questions.

Math in Focus Grade 3 Cumulative Review Chapters 16 to 19 Answer Key

Fill in the blanks with past or to. (Lesson 16.1)

Question 1.
12 minutes __________ 8 is 8:12.
Answer:
12 minutes past 8

Question 2.
10 minutes ___________ 3 is 2:50.
Answer:
10 minutes to 3

Fill in the blanks. (Lesson 16.2)

Question 3.
4 h 25 min = ___________ min
Answer: 265 min
Explanation:

Question 4.
210 min = ___________ h __________ min
Answer: 3h 30 min
Explanation:

Circle the correct number. (Lesson 16.6)

Question 5.
Jamie is playing basketball. The temperature outside is about (32, 72, 120) °F.
Answer: 72°F
Explanation:
In lesson 6.6 the temperature scale is given,
by using the given data we can solve.
The suitable temperature to play outside is about ( 72) °F

Question 6.
Water freezes at (0, 10, 32) °F.
Answer: 32°F
Explanation:
Fahrenheit temperature scale, scale based on 32° for the freezing point of water
and 212° for the boiling point of water,
the interval between the two being divided into 180 equal parts.

Question 7.
Gary puts on his jacket before he leaves the house. The temperature outside is about (50, 72, 105) °F.
Answer: 50 °F
Explanation:
The temperature outside is about (50) °F.
Gary puts on his jacket before he leaves the house.

Complete. Look at the angle. (Lesson 17.1)

Question 8.
Circle the angles below that are greater than the given angle.

Answer:

Explanation:
Given angle is 90° Right angle.
The angles first and last are below that are greater than the given angle.

Question 9.
Name the pairs of perpendicular and parallel line segments.

Perpendicular line segments: (Lesson 17.4)
_______________________
Parallel line segments: (Lesson 17.6)
_______________________
Answer:
Perpendicular line segments
HO perpendicular to ON
HI perpendicular to IJ
MN perpendicular to ON

Parallel line segments
HO and KL are Parallel line segments
HI  and  JK are Parallel line segments
Explanation:
Perpendicular line segments are line segments that intersect and make 90 degree angles.
Parallel line segments are always the same distance apart, they will never meet. 

Question 10.
Mark the right angles in each figure. (Lesson 17.3)

Answer:

Explanation:
When two straight lines intersect each other at 90˚or perpendicular to each other at the intersection,
they form the right angle.
A right angle is represented by the symbol ∟.

Circle the polygons. (Lesson 18.1)

Question 11.

Answer: polygons

Explanation:
A polygon is a closed shape with straight sides.
Rectangles, triangles, hexagons, and octagons are all examples of polygons.
It simply means many (poly) angles (gon).

Write true or false. (Lesson 18.1)

Question 12.
A trapezoid has four angles. ___________
Answer: True
Explanation:
A trapezoid is a quadrilateral, which means it has four sides.
Two sides must be parallel to each other for it to be a trapezoid.
A trapezoid also has four angles.

Question 13.
A circle is a quadrilateral. ____________
Answer: False
Explanation:
A quadrilateral is a polygon in Euclidean plane geometry with four edges (sides) and four vertices (corners).
Other names for quadrilateral include quadrangle and tetragon.

Question 14.
A rhombus has only one pair of parallel lines. ____________
Answer:
False (2 pairs of parallel lines)
Explanation:
In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length.
Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length.
A rhombus with right angles is a square.

Question 15.
An octagon has eight sides. ____________
Answer: True
Explanation:
An octagon is an eight-sided polygon or 8-gon.
A regular octagon has Schläfli symbol {8} and can also be constructed as a quasiregular truncated square, t{4}, which alternates two types of edges.

Question 16.
A square is not a rectangle. ____________
Answer: True
Explanation:
A square is a figure with four equal sides and four right angles.
It’s a popular shape for windows and record albums, among many other things.

Does the figure show a flip? Write yes or no. (Lesson 18.2)

Question 17.

Answer: YES
Explanation:
A flip is also called a reflection.
You can see the result of a flip or a reflection in a shape that has line symmetry,
so line symmetry is related to the movement that is a reflection or a flip.

Question 18.

Answer: NO
Explanation:
The above image does not show flip.
We cannot draw line symmetry and it is not a reflection of image.

Does the figure show a flip? Write yes or no. (Lesson 18.2)

Question 19.

Answer: YES
Explanation:
A flip is also called a reflection.
You can see the result of a flip or a reflection in a shape that has line symmetry,
so line symmetry is related to the movement that is a reflection or a flip.

Question 20.

Answer: YES
Explanation:
A flip is also called a reflection.
You can see the result of a flip or a reflection in a shape that has line symmetry,
so line symmetry is related to the movement that is a reflection or a flip.

Circle the congruent shapes. (Lesson 18.2)

Question 21.

Answer:

Explanation:
If two figures or objects have the same shape and size or known as congruent,
or if one has the same shape and size as the mirror image of the other.

Decide if each figure is symmetric. Write yes or no. (Lesson 18.3)

Question 22.

Answer: YES
Explanation:
Symmetry defines that one shape is exactly like the other shape when it is moved, rotated, flipped.
Which can exactly divide into two equal halves.

Question 23.

Answer: NO
Explanation:
The given image is not symmetry.
We can’t divide into two equal halves.

Question 24.

Answer: NO
Explanation:
The given image is not symmetry.
We can’t divide into two equal halves.

Decide if each figure show a line of symmetry. Write yes or no.

Question 25.

Answer: YES
Explanation:
The line of symmetry is the imaginary line that divides an object into two identical halves,
either horizontally or vertically.

Question 26.

Answer: YES
Explanation:
The line of symmetry is the imaginary line that divides an object into two identical halves,
either horizontally or vertically.

Question 27.

Answer: YES
Explanation:
The line of symmetry is the imaginary line that divides an object into two identical halves,
either horizontally or vertically.

Find the area of each figure. (Lesson 19.2)

Answer:

Explanation:
In the above picture each area of the square is measured as 1 square centimeter.
In figure A there are 5 full square units and 2 half square units.
In figure B there are 6 full square units and 2 half square units.
In figure C there are 6 full square units and 4 half square units.

Question 28.
Which figure has the greatest area? Figure ____________
Answer:
Figure C
Explanation:
By comparing the above given figures,
figure C has the greatest area.
Question 29.
Which figure has the least area? Figure ____________
Answer:
Figure A
Explanation:
By comparing the above given figures,
figure A has the least area.

Complete. (Lesson 19.5)

Question 30.
Measure in inches.

__________ in.
Answer: 5 in.

Explanation:
The Area of a rectangle is the total distance covered by its boundaries or the sides.
Since there are four sides of a rectangle,
Area of the rectangle length x width.
A = 3 + 2 = 5 cm

Question 31.
The perimeter of the rectangle is _____________
Answer: 10 in
Explanation:
The perimeter of a rectangle is the total distance covered by its boundaries or the sides.
Since there are four sides of a rectangle,
thus, the perimeter of the rectangle will be the sum of all four.
P = 3 + 2 + 3 + 2 = 10 in.

Problem Solving

Complete. Draw two different rectangles with a perimeter of 10 feet each.

Question 32.


Answer:

Explanation:
Perimeter is the distance around the edge of a shape.
Area is used to define the amount of space taken up by a 2D shape or surface.
We measure area in square units : cm² or m².
Area is calculated by multiplying the length of a shape by its width.
Question 33.
Are the areas of the two rectangles the same? ___________
Answer: yes
Explanation:
Both the rectangles have the same number of square units.

Question 34.
If their areas are the same, what is the area? _____________
Answer:
6 Square feet
Explanation:
Each square unit represent 1 square unit.
So, there are 6 units in each rectangle.

Question 35.
If their areas are not the same, what is the difference in their areas?
Answer:
Might be the difference is there size and shape.
Explanation:
If we take different number of square boxes in both the rectangles,
then we find the difference in their areas.

Complete.

Question 36.
Look at the shape in a.
How many sides and angles are there?
Answer:
6 sides are there.
Explanation:
It represents hexagon.
A hexagon can be defined as polygon with six sides.
The two-dimensional shape has 6 sides, 6 vertices and 6 angles.

Question 37.
Draw another shape that has the same number of sides and angles.

Answer:

Explanation:
It represents hexagon.
A hexagon can be defined as polygon with six sides.
The two-dimensional shape has 6 sides, 6 vertices and 6 angles.

Solve. Show your work.

Question 38.
On Monday, Samantha spent 8 hours 10 minutes in school. On Tuesday, she spent 6 hours 55 minutes in school. How much longer did she spend in school on Monday than on Tuesday?
Answer:
1h: 15 min
Explanation:
8 : 10 –  6 : 55
6 : 55 is subtracted from 8 : 10 min time
7 : 60 – 6 : 55
= 1 : 10 + 5
= 1:15min
On Monday, Samantha spent 8 hours 10 minutes in school.
On Tuesday, she spent 6 hours 55 minutes in school.
Total time she spent in school on Monday than on Tuesday

Solve. Show your work.

Question 39.
Laura sews six square patches to make a quilt, as shown below. The side of each square patch is 15 inches long. What is the perimeter of the quilt?

Answer: 75 in.
Explanation:
Perimeter of a rectangle = P
P = 2l + 2w
P = 2 x 45 + 2 x 30 = 90 + 60 = 150 square inches.
Solve. Draw a time line to help you.

Question 40.
Mr. Jones takes 2 hours 30 minutes to drive from San Diego to Los Angeles. He reaches Los Angeles at 4:25 p.m. What time did he leave San Diego?
Answer:  1:55 pm
Explanation:
Mr. Jones takes 2 hours 30 minutes to drive from San Diego to Los Angeles.
He reaches Los Angeles at 4:25 p.m.
Total time did he leave San Diego
4:25pm – 2 :30pm  = 1:55 pm

Solve. Draw a time line to help you.

Question 41.
Rhonda read a book from 8:45 A.M. to 10:50 A.M.
a. How long did she spend reading the book?
Answer:
2h:05 min
Explanation:

b. She continues reading for another 1 hour 25 minutes. What time will she stop reading?
Answer:
12:15pm
Explanation:

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 1 Whole Numbers to finish your assignments.

Math in Focus Grade 5 Chapter 1 Answer Key Whole Numbers

Math Journal

Question 1.
Kim and Dominic found the sum of 8,642 and 9,328.

One of their answers is incorrect.
Show how you could use estimation to check which answer is reasonable.
Answer: Dominic’s answer is incorrect, Kim’s answer is correct.
Explanation:
If we add the given two numbers:8,642+9,328=17,970.
For this, we need to check estimation.
The numbers are 8,642 and 9,328
1. First, Find out the thousand’s digit in the number.
2. Next, choose the next smallest number (that is the hundredth digit of the number).
3. Now, check the hundred’s digit is either <5 (That means 0, 1, 2, 3, 4) or > = 5 (That is 5, 6, 7, 8, 9).
(i) If the digit is < 5, then the hundreds place is replaced with the digit ‘0’.
(ii) If the digit is > = 5, then the hundred’s digit is replaced with the digit ‘0’, and the thousand’s place digit is increased by 1 digit.
Step 1: Thousand’s digit of the number is 8 and 9.
Step 2: Hundred’s digit of the number is 6 and 3.
Step 3: The hundred’s digit ‘3’ is <5, then we have to apply 3(i) conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
Step 4: The hundred’s digit ‘6’ is >=5, then we have to apply 3(ii) conditions. That is, the hundred’s placed is replaced with the digit ‘0’, and the thousand’s place digit is increased by 1 digit.
8,642 rounding of the nearest 1000 is equal to 9000.
9,328 rounding of the nearest 1000 is equal to 9000.
If we add both estimations then we get:
9000+9000=18000, which is near to Kim’s answer.
This is the process to estimate the value.

Question 2.
Samantha found these quotients.
a. 7,986 ÷ 8 = 998 R 2
Answer: 1000
998 is near to 1000 and this is the estimation process.
Number 7,986 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 7.
Step 2: Hundred’s digit of the number is 9.
Step 3: The hundred’s digit ‘9’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
7,986 rounding of the nearest 1000 is equal to 8000.
The estimation is 8000
Now divide with the given number that is 8:
8000÷8=1000.

b. 2,659 ÷ 3 = 264 R 3
Answer:1000
If we divide 2,659 with 3 then the quotient is 886.3333…
Number 2,659 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 2.
Step 2: Hundred’s digit of the number is 6.
Step 3: The hundred’s digit ‘6’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’ and the thousand’s place digit is increased by 1 digit.
2,659 rounding of the nearest 1000 is equal to 3000.
The estimation is 3000
Now divide with the given number that is 3:
3000÷3=1000.

Show how you could check whether the quotients are reasonable.
State in each case whether the quotient is reasonable.
Answer:
The quotients of the given numbers are 998.25 and 886.33
Step 1: For the first number that is (a) sum: 7,986 ÷ 8 = 998.
– Divide the given number by 8 then we will get the quotient of 998.25.
Step 2: For the second number that is (b) sum: 2,659 ÷ 3 = 264
– Divide the given number by 3 then we will get the quotient of 886.333.
If we take step 1 then the quotient is reasonable according to the given division and the estimation is also checked in the above sum(a). The estimation is 1000 which is near to 998.
If we take step 2 then the given quotient is wrong and the correct quotient for the sum (b) is 886.33. The estimation is also checked in the above sum (b). For this also the estimation is 1000 which is near to 886.

Question 3.
Liso was asked to round
a. 763 to the nearest hundred.
Answer:800
Explanation:
Number 763 Round to the Nearest 100:
Step 1: Hundred’s digit of the number is 7.
Step 2: Ten’s digit of the number is 6.
Step 3: The hundred’s digit ‘6’ is >=5, then we have to apply some conditions. That is, the ten’s placed is replaced with the digit ‘0’ and the hundred’s place digit is increased by 1 digit.
763 rounding of the nearest 100 is equal to 800.

b. 3,730 to the nearest thousand.
Answer: 4000
Explanation:
The number is 3730
Step 1: Thousand’s digit of the number is 3.
Step 2: Hundred’s digit of the number is 7.
Step 3: The hundred’s digit ‘7’ is >=5, then we have to apply conditions. That is, the hundred’s placed is replaced with the digit ‘0’, and the thousand’s place digit is increased by 1 digit.
3,730 rounding of the nearest 1000 is equal to 4000.

Lisa rounded 763 to 700 and 3,730 to 3,000. What mistakes did she make?
What should the correct answer in each case have been?
Answer: Both answers are wrong.
Explanation:
The first number Lisa rounded for 763=700
The second number Lisa rounded for 3,730=3000
The mistake she had done was rounding down the values that are 700 and 3000.
There are some conditions to round up and down the values. The conditions are:
1. First, Find out the thousand’s digit in the number.
2. Next, choose the next smallest number (that is the hundredth digit of the number).
3. Now, check the hundred’s digit is either <5 (That means 0, 1, 2, 3, 4) or > = 5 (That is 5, 6, 7, 8, 9).
(i) If the digit is < 5, then the hundreds place is replaced with the digit ‘0’.
(ii) If the digit is > = 5, then the hundred’s digit is replaced with the digit ‘0’, and the thousand’s place digit is increased by 1 digit.
According to the above conditions we need to round the nearest values.
The correct answers for 763 and 3,730 are 800 and 4000.

put on your thinking cap!

Challenging Practice

Arrange the digits to form three 6-digit numbers that will round to 756,000 when rounded to the nearest thousand.

Answer:
The number is 756,000
Number 756,000 Round to the Nearest 1000:
Step 1: Thousand’s digit of the number is 6.
Step 2: Hundred’s digit of the number is 0.
Step 3: The hundred’s digit ‘0’ is <5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’
756,000 rounding of the nearest 1000 is equal to 756,000.
The three 6-digit numbers are 755,678, 756,052, 756,275.
If we calculate these 3 numbers these all are round to 756,000 when rounded to the nearest thousand.
Take number 755,678:
Step 1: Thousand’s digit of the number is 5.
Step 2: Hundred’s digit of the number is 6.
Step 3: The hundred’s digit ‘6’ is >=5, then we have to apply some conditions. That is, the hundred’s placed is replaced with the digit ‘0’, and the thousand’s place digit is increased by 1 digit.
So the number is 756,000. The hundred thousand and ten thousand places will not change because in the question asked round the number nearest to thousand.
According to the above conditions we need to round the nearest values. Likewise, write the other two numbers also.

put on your Thinking cap

Problem Solving

Question 1.
What number can you subtract from 3,200 so that their difference is a 4-digit number that has: the digit 2 in the thousands place, the digit 3 in the hundreds place and zeros in the tens and ones place?
Answer: 900
Explanation:
The given number=3,200
The number we need to subtract to get the number 2,300=X
The number need to come if we subtract X and 3,200=2,300.
If we take 2,300: The value of digits are 0-ones place, 0-tens place, 3-hundreds place, 2-thousands place.
So, If we subtract 3,200 from 900 then we get the 2,300 because we need to take borrow from another number.

Here I take borrow 1 from 3 because we cannot subtract 9 from 2. If we take borrow from another number then it will become 12, from 12 we can easily subtract 9. Then it becomes 3. Finally, if we subtract 900 from 3,200 then we get 2,300.
Therefore, the value of X is 900.
Another method:
By math sentence, we can write as:
3200-X=2300
Taking X to the right side then it becomes:
3200=2300+x
If we take all the numbers into one side then it becomes:
3200-2300=X
900=X
Therefore, X=900.

Question 2.
A 3-digit number when divided by 5 has an even quotient. When it is divided by 3, it also has an even quotient.
a. What is the digit in the one’s place?
Answer: 0
Explanation:
It has to be a multiple of 5. All multiples of 5 either end in 0 or 5. Since it has to be even it has to end in 0, since if it ended in 5 it would be odd. Therefore, the answer to this must be 0, because the digit on the right end of the number is one’s digit.

b. What can the number be?
Answer:
Since it ends with a zero it is divisible by 10. So if you divide it by 10, the quotient will be a two-digit number which is the same as the number without the 0 on the right end.
But the quotient will still be divisible by 3.
So the number could be any two-digit number that is multiple of 3 with a zero on the right end of it for its one’s digit.
The smallest two-digit number that is multiple of 3 is 12. So the smallest number could be is 120.
The largest two-digit number that is a multiple of 3 is 99. So the largest number could be is 990.
So it could be any of these thirty 3-digit numbers:
120, 150, 180, 210, 240,270, 300, 330, 360, 390, 420, 450, 480, 510, 540, 570, 600, 630, 660, 690, 720, 750, 780, 810, 840, 870, 900, 930, 960, 990.