Math in Focus

Practice the problems of Math in Focus Grade 4 Workbook Answer Key Cumulative Review Chapters 7 and 8 to score better marks in the exam.

Math in Focus Grade 4 Cumulative Review Chapters 7 and 8 Answer Key

Concepts and Skills

write each fraction or mixed number as a decimal. (Lesson 7.1)

Question 1.
\(\frac{4}{10}\) = ____
Answer:
\(\frac{4}{10}\) =  0.4.

Explanation:
\(\frac{4}{10}\) = 4 ÷ 10 = 2 ÷ 5 = 0.4.

Question 2.
3\(\frac{3}{10}\) = ____
Answer:
3\(\frac{3}{10}\) = 0.9.

Explanation:
3\(\frac{3}{10}\) = 3(3 ÷ 10) = 3(0.3) = 0.9.

Question 3.
\(\frac{18}{10}\) = ____
Answer:
\(\frac{18}{10}\) = 1.8.

Explanation:
\(\frac{18}{10}\) = 18 ÷ 10 = 9÷ 5 = 1.8.

Write each decimal in tenths. (Lesson 7.1)
Question 4.
0.6 = ___ tenths
Answer:
0.6 = 6 tenths.

Explanation:

0.6 = 6 tenths.

Question 5.
1.7 = ___ tenths
Answer:
1.7 = 17 tenths.

Explanation:
1.7 = 17 tenths.

Question 6.
9.5 = ___ tenths
Answer:
9.5 = 95 tenths.

Explanation:
9.5 = 95 tenths.

Question 7.
4.2 = ___ tenths
Answer:
4.2 = 42 tenths.

Explanation:
4.2 = 42 tenths.

write each of these as a decimal. (Lesson 7.1)
Question 8.
3 ones and 4 tenths = ___
Answer:
3 ones and 4 tenths = 3.4.

Explanation:
3 ones and 4 tenths = 3.4.

Question 9.
8 ones and 1 tenth = ____
Answer:
8 ones and 1 tenth = 8.1.

Explanation:
8 ones and 1 tenth = 8.1.

Question 10.
77 tenths = ___
Answer:
77 tenths = 7.7.

Explanation:
77 tenths = 7.7.

Question 11.
19 tenths = ____
Answer:
19 tenths = 1.9.

Explanation:
19 tenths = 1.9.

Fill in the blanks. (Lesson 7.1)
Question 12.
22 tenths = 2 ones and ___ tenths
Answer:
22 tenths = 2 ones and  2 tenths.

Explanation:
22 tenths = 2 ones and 2 tenths.

Question 13.
3.2 = 3 ones and ___ tenths
Answer:
3.2 = 3 ones and 2 tenths.

Explanation:
3.2 = 3 ones and 2 tenths.

Write the correct decimal in each box. (Lesson 7.1)
Question 14.

Answer:

Explanation:
1. 1 tenths.
2.1 one.
3. 1 one 3 tenths.
4. 2 one o tenths.
5. 2 one 8 tenths.

Complete the expanded form of each decimal. (Lesson 7.1)
Question 15.
5.4 = 5 + ___
Answer:
5.4 = 5 + 4 tenths.

Explanation:
5.4 = 5 + 4 tenths.

Question 16.
7.1 = 7 + ___
Answer:
7.1 = 7 + 1 tenths.

Explanation:
7.1 = 7 + 1 tenths.

Question 17.
3.6 = 3 + __.
Answer:
3.6 = 3 + 6 tenths.

Explanation:
3.6 = 3 + 6 tenths.

Question 18.
10.2 = 10 + ___
Answer:
10.2 = 10 + 2 tenths.

Explanation:
10.2 = 10 + 2 tenths.

Fill in the blanks. (Lesson 7.1)
Question 19.
In 22.3, the digit 3 is in the ___ place. Its value is ____.
Answer:
In 22.3, the digit 3 is in the tenths place. Its value is 3 ÷ 10.

Explanation:
In 22.3,
the digit 3 is in the tenths place.
Its value is \(\frac{3}{10}\) = 3 ÷ 10.

Write each fraction or mixed number as a decimal. (Lesson 7.2)
Question 20.
\(\frac{9}{100}\) = ____
Answer:
\(\frac{9}{100}\) = 0.09.

Explanation:
\(\frac{9}{100}\) = 9 ÷ 100 = 0.09.

Question 21.
2\(\frac{26}{100}\) = ____
Answer:
2\(\frac{26}{100}\) = 0.52.

Explanation:
2\(\frac{26}{100}\) = 2(26 ÷ 100)
= 2 × 0.26
= 0.52.

Question 3.
\(\frac{105}{100}\) = ____
Answer:
\(\frac{105}{100}\) = 1.05.

Explanation:
\(\frac{105}{100}\) = 105 ÷ 100 = 1.05.

Write each decimal in hundredths. (Lesson 7.2)
Question 23.
0.06 = ___ hundredths
Answer:
0.06 = 6 hundredths.

Explanation:
0.06 = 6 hundredths.

Question 24.
1.33 = ___ hundredths
Answer:
1.33 = 133 hundredths.

Explanation:
1.33 = 133 hundredths.

Question 25.
2.5 = ___ hundredths
Answer:
2.5 = 250 hundredths.

Explanation:
2.5 = 250 hundredths.

Write each of these as a decimal. (Lesson 7.2)
Question 26.
2 ones and 6 hundredths = ____
Answer:
2 ones and 6 hundredths = 2.06.

Explanation:
2 ones and 6 hundredths = 2.06.

Question 27.
5 tenths 5 hundredths = ____
Answer:
5 tenths 5 hundredths = 0.55.

Explanation:
5 tenths 5 hundredths = 0.55.

Question 28.
7 ones and 3 tenths 4 hundredths = ___
Answer:
7 ones and 3 tenths 4 hundredths = 7.34

Explanation:
7 ones and 3 tenths 4 hundredths = 7.34.

Fill in the blanks. (Lesson 7.2)
Question 29.
16 hundredths = 1 tenth ___ hundredths
Answer:
16 hundredths = 1 tenth 6 hundredths.

Explanation:
16 hundredths = 1 tenth 6 hundredths.

Question 30.
0.45 = 4 tenths ___ hundredths
Answer:
0.45 = 4 tenths 5 hundredths.

Explanation:
0.45 = 4 tenths 5 hundredths.

Mark ✗ to show where each decimal is located on the number line. Label its value. (Lesson 7.2)

Question 31.
0.04
Answer:
0.04 = 4 hundredths.

Explanation:

Question 32.
0.15
Answer:
0.15 = 0 ones 1 tenths 5 hundredths.

Explanation:

Question 33.
0.26
Answer:
0.26 = 0 ones 2 tenths 6 hundredths.

Explanation:

Complete.
Question 34.
5.2 = __________ ones and __________ tenths
Answer:
5.2 = 5 ones and 2 tenths.

Explanation:
5.2 = 5 ones and 2 tenths.

Question 35.
0.86 = ___________ tenths ___________ hundredths
Answer:
0.86 = 8 tenths 6 hundredths.

Explanation:
0.86 = 8 tenths 6 hundredths.

Question 36.
3.7 = ___________ tenths
Answer:
3.7 = 7 tenths.

Explanation:
3.7 = 7 tenths.

Question 37.
0.93 = __________ hundredths
Answer:
0.93 = 3 hundredths.

Explanation:
0.93 = 3 hundredths.

Write each sum as a decimal. (Lesson 7.2)
Question 38.
7 + 0.6 + 0.02 = ___
Answer:
7 + 0.6 + 0.02 = 7.62.

Explanation:
7 + 0.6 + 0.02 = 7.6 + 0.02
= 7.62.

Question 39.
10 + 0.4 + 0.04 = ___
Answer:
10 + 0.4 + 0.04 = 10.44.

Explanation:
10 + 0.4 + 0.04 =  10.4 + 0.04
= 10.44.

Question 40.
5 + \(\frac{1}{10}\) + \(\frac{8}{100}\) = ___
Answer:
5 + \(\frac{1}{10}\) + \(\frac{8}{100}\) = 5.09.

Explanation:
5 + \(\frac{1}{10}\) + \(\frac{8}{100}\) = 5 + (1 ÷ 100) + (8 ÷ 100)
= 5 + 0.1 + 0.08
= 5.1 + 0.08
= 5.18.

Question 41.
9 + \(\frac{3}{10}\) + \(\frac{7}{100}\) = ___
Answer:
9 + \(\frac{3}{10}\) + \(\frac{7}{100}\) = 9.37.

Explanation:
9 + \(\frac{3}{10}\) + \(\frac{7}{100}\) = 9 + (3 ÷ 10) + (7 ÷ 100)
= 9 + 0.3 + 0.07
= 9.3 + 0.07
= 9.37.

Fill in the blanks. (Lesson 7.2)
Question 42.
In 14.68, the digit 8 is in the ___ place. Its value is ___.
Answer:
In 14.68, the digit 8 is in the hundredths place. Its value is 8 hundredths.

Explanation:
In 14.68,
the digit 8 is in the hundredths place. Its value is 8 hundredths.

Fill in the blanks. (Lesson 7.2)
Question 43.
$0.75 = ___ cents
Answer:
$0.75 = 75 cents.

Explanation:
Conversion: 1 dollar = 100 cents.
$0.75 = 100 × 0.75
= 75 cents.

Question 44.
$12.25 = ___ cents
Answer:
$12.25 = 1225 cents.

Explanation:
Conversion: 1 dollar = 100 cents.
$12.25 = 100 × 12.25
= 1225 cents.

Question 45.
$8.05 = ___ cents
Answer:
$8.05 = 805 cents.

Explanation:
Conversion: 1 dollar = 100 cents.
$8.05 = 100 × 8.05
= 805 cents.

Write each amount of money in decimal form. (Lesson 7.2)
Question 46.
65 cents = $___
Answer:
65 cents = $___

Explanation:
Conversion: 1 dollar = 100 cents.
65 cents = 65 ÷ 100
= $ 0.65.

Question 47.
10 dollars and 90 cents = $___
Answer:
10 dollars and 90 cents = $10.90.

Explanation:
Conversion: 1 dollar = 100 cents.
10 dollars and 90 cents = 10 + (90 ÷ 100)
= 10 + 0.90
= $10.90.

Question 48.
2 dollars and 5 cents = $____
Answer:
2 dollars and 5 cents = $2.05.

Explanation:
Conversion: 1 dollar = 100 cents.
2 dollars and 5 cents = 2 + (5 ÷ 100)
= 2 + 0.05
= $2.05.

Fill in the blanks. (Lesson 7.3)
Question 49.
0.1 more than 1.1 is ____
Answer:
0.1 more than 1.1 =  1.2.

Explanation:
0.1 more than 1.1 =  0.1 + 1.1 = 1.2.

Question 50.
0.2 less than 2 is ____
Answer:
0.2 less than 2 = 0.8.

Explanation:
0.2 less than 2 =  2 – 0.2 = 0.8.

Question 51.
0.01 less than 0.1 is ___
Answer:
0.01 less than 0.1 = 0.09.

Explanation:
0.01 less than 0.1 =  0.1 – 0.01 = 0.09.

Question 52.
0.03 more than 0.07 is ___
Answer:
0.03 more than 0.07 = 0.10.

Explanation:
0.03 more than 0.07 =  0.07 + 0.03 = 0.10.

Mark ✗ to show where each decimal is located on the number line. Label its value. (Lesson 7.3)

Question 53.
0.16
Answer:
0.16 = 0 ones 1 tenths 6 hundredths.

Explanation:

Question 54.
0.24
Answer:
0.24 = 0 ones 1 tenths 6 hundredths.

Explanation:

Compare. Write > or <. (Lesson 7.3)
Question 55.
4.1 0.41
Answer:
4.1 > 0.41.

Explanation:
4.1 is greater than 0.41 as its ones place number is greater in comparison.

Question 56.
0.73 0.70
Answer:
0.73 < 0.70.

Explanation:
0.73  is lesser than 0.70 as its hundredths place number in comparison comes first in comparison.

Circle the greatest decimal and underline the least. (Lesson 7.3)
Question 57.
3.04 3.4 0.34
Answer:

Explanation:
3.4 is comparatively greater than 3.04 and 0.34 as its tenths place number is greater.
0.34 is comparatively lesser than the 3.4 and 3.04 as its ones place number is less.

Question 58.
0.6 0.61 0.65
Answer:

Explanation:
0.6 is comparatively greater than 0.61 and 0.65 as its tenths place number comes first in number line.
0.65 is comparatively lesser than the 0.6 and 0.61 as its comes last in number line.

Fill in the blank. (Lesson 7.3)
Question 59.
Write a decimal that is greater than 0.9 but less than 1.0. ____
Answer:
A decimal that is greater than 0.9 but less than 1.0 is 0.987.

Explanation:
A decimal that is greater than 0.9 but less than 1.0 is 0.987.
The largest nearest number that can be approximated to 0.9 is 0.94999999999.
The lowest nearest number that can be approx. to 0.987 is 0.986500000000000000000
Hence, 0.987 is larger than 0.9.
Such problems are categorized under “ Number Theory”.

Round each decimal to the nearest whole number. (Lesson 7.4)
Question 60.
4.36 = ___
Answer:
4.36 = 4.0.

Explanation:
Rounding 4.36 to its nearest whole number = 4.0.

Question 61.
7.81 = ___
Answer:
7.81 = 8.0.

Explanation:
Rounding 7.81  to its nearest whole number = 8.0.

Question 62.
5.07 = ___
Answer:
5.07 = 5.0.

Explanation:
Rounding 5.07 to its nearest whole number = 5.0.

Round each decimal to the nearest tenth. (Lesson 7.4)
Question 63.
2.39 = ___
Answer:
2.39 = 2.50.

Explanation:
Rounding 2.39 to its nearest tenth = 2.50.

Question 64.
6.63 = ___
Answer:
6.63 = 7.0.

Explanation:
Rounding 6.63 to its nearest tenth = 7.0.

Question 65.
4.00 = ___
Answer:
4.00 = 4.0.

Explanation:
Rounding 4.00 to its nearest tenth = 4.0.

write each decimal as a fraction in simplest form. (Lesson 7.5)
Question 66.
0.6 =
Answer:
0.6 = 

Explanation:
simplest form of 0.6 = 6 ÷10.

Question 67.
0.55 =
Answer:
0.55 =

Explanation:
simplest form of  0.55 = 55 ÷ 100.

write each fraction or mixed number as a decimal. (Lesson 7.5)
Question 68.
\(\frac{1}{5}\) =
Answer:
\(\frac{1}{5}\) = 0.2.

Explanation:
\(\frac{1}{5}\) = 1 ÷ 5 = 0.2.

Question 69.
\(\frac{9}{20}\) =
Answer:
\(\frac{9}{20}\) = 0.45.

Explanation:
\(\frac{9}{20}\) = 9 ÷ 20 = 0.45.

Question 70.
\(\frac{5}{2}\) =
Answer:
\(\frac{5}{2}\) = 2.50.

Explanation:
\(\frac{5}{2}\) = 5 ÷ 2 = 2.50.

Question 71.
1\(\frac{3}{4}\) =
Answer:
1\(\frac{3}{4}\) = 1.75.

Explanation:
1\(\frac{3}{4}\) = 1 (3 ÷ 4)
= (4 + 3) ÷ 4
= 7 ÷ 4
= 1.75.

Question 72.
4\(\frac{2}{5}\) =
Answer:
4\(\frac{2}{5}\) = 4.4.

Explanation:
4\(\frac{2}{5}\) = 4 (2 ÷ 5)
= (20+2) ÷ 5
= 22 ÷ 5
= 4.4.

Question 73.
5\(\frac{1}{4}\) =
Answer:
5\(\frac{1}{4}\) = 5.25.

Explanation:
5\(\frac{1}{4}\) = 5 (1 ÷ 4)
= (20 + 1) ÷ 4
= 21 ÷ 4
= 5.25.

Find each sum or difference. (Lesson 8.1 and 8.2)

Question 74.

Answer:

Explanation:
6.74 + 2.17 = 8.91.

Question 75.

Answer:

Explanation:
3.28 + 0.91 = 4.19.

Question 76.

Answer:

Explanation:
5.76 + 4.26 = 10.02.

Question 77.

Answer:

Explanation:
7.05 – 1.33 = 5.72.

Question 78.

Answer:

Explanation:
8.72 – 3.43 = 5.29.

Question 79.

Answer:

Explanation:
6.36 – 5.79 = 0.57.

Problem Solving
Solve. Show your work. (Lesson 8.3)
Question 80.
Lina thinks of a number. When she adds 9.65 to it, she gets 20.7. What number is Lina thinking of?
Answer:
The number Lina thinks = 11.05.

Explanation:
When she adds 9.65 to it, she gets 20.7.
Let the number be X.
=> X + 9.65 = 20.7.
=> X = 20.7 – 9.65
=> X = 11.05.

Question 81.
Suri bought a skirt for $25.90 and a sweatshirt for $19.90. She paid the cashier $50. How much change did she receive?
Answer:
Amount of change she received = $4.2.

Explanation:
Cost of a skirt Suri bought = $25.90.
Cost of a sweatshirt Suri bought = $19.90.
Amount of money she paid to the cashier = $50.
Amount of change she received = Amount of money she paid to the cashier – (Cost of a skirt Suri bought + Cost of a sweatshirt Suri bought)
= $50 – ($25.90 + $19.90)
= $50 – $45.8
= $4.2.

Practice the problems of Math in Focus Grade 4 Workbook Answer Key Chapter 9 Practice 3 Turns and Right Angles to score better marks in the exam.

Math in Focus Grade 4 Chapter 9 Practice 3 Answer Key Turns and Right Angles

Find the measure of each angle.

Question 1.

A \(\frac{1}{2}\)-turn is ____.
Answer:
180°.

Explanation:
Here, a \(\frac{1}{2}\)-turn is 180°.

Question 2.

A \(\frac{3}{4}\)-turn is ____.
Answer:
270°.

Explanation:
Here, a \(\frac{3}{4}\)-turn is 270°.

Fill in the blanks.

Question 3.

A ___ -turn is 90°
Answer:
\(\frac{1}{4}\).

Explanation:
Here, a \(\frac{1}{4}\)-turn is 90°.

Question 4.

A ___ -turn is 360°
Answer:
1 -turn.

Explanation:
Here, a 1 -turn is 360°.

Look at the three pairs of angle strips shown.

Which pair of angle strips shows

Question 5.
\(\frac{1}{2}\) turn? ___________
Answer:
∠c.

Explanation:
In the above images, ∠c is a \(\frac{1}{2}\) turn which is 180°.

Question 6.
a straight angle? ____
Answer:
∠c.

Explanation:
In the above images, ∠c is a \(\frac{1}{2}\) turn which is 180°.

Question 7.
a turn between \(\frac{1}{2}\)-turn and \(\frac{3}{4}\)-turn? ____
Answer:
225°.

Explanation:
a turn between \(\frac{1}{2}\)-turn and \(\frac{3}{4}\)-turn is 225°.

Look at the three pairs of angle strips shown.

Which pair of angle strips shows

Question 8.
360°? _________
Answer:
1 turn.

Explanation:
In the above images, ∠D is a 1 turn which is 360°.

Question 9.
an angle between 180° and 360°? ___________
Answer:
\(\frac{3}{4}\).

Explanation:
In the above images, ∠F is a \(\frac{3}{4}\) turn which is 270°.

Complete.

Question 10.
180° makes up ___ of a full turn.
Answer:
180° makes up half of a full turn.

Explanation:
Here, 180° makes up half of a full turn. As 360° makes a full turn.

Question 11.
Three right angles make up a __ -turn
Answer:
Three right angles make up a \(\frac{3}{4}\) -turn.

Explanation:
Here, three right angles make up a \(\frac{3}{4}\) -turn which is 270°.

Question 12.
105° is between a ___-turn and a ___-turn.
Answer:
105° is between a \(\frac{1}{4}\)-turn and a \(\frac{1}{2}\)-turn.

Explanation:
105° angle lies between a \(\frac{1}{4}\)-turn and a \(\frac{1}{2}\)-turn.

Practice the problems of Math in Focus Grade 4 Workbook Answer Key Chapter 8 Adding and Subtracting Decimals to score better marks in the exam.

Math in Focus Grade 4 Chapter 8 Answer Key Adding and Subtracting Decimals

Put On Your Thinking Cap!

Challenging Practice

Question 1.
Miguel subtracts two numbers and gets the answer 4.95. The lesser of the two numbers is 3.4. What is the other number?
Answer:
The other number = 8.35.

Explanation:
Miguel subtracts two numbers and gets the answer 4.95.
Let the two number s be X and Y.
=> X – Y = 4.95.
The lesser of the two numbers is 3.4.
=> X – 3.4 = 4.95
=> X = 4.95 + 3.4
=> X = 8.35.

Question 2.
Julia subtracts two numbers and gets the answer 6.8. The greater of the two numbers is 10.55. What is the other number?
Answer:
The other number = 3.75.

Explanation:
Julia subtracts two numbers and gets the answer 6.8.
Let the two number s be X and Y.
=> X – Y = 6.8.
The greater of the two numbers is 10.55.
=> 10.55 – Y = 6.8
=> 10.55 = 6.8 + Y
=> 10.55 – 6.8 = Y
=> 3.75 = Y

Put On Your Thinking Cap!
Problem Solving
Question 1.
The number in each rectangle is the sum of the numbers in the two circles next to it. Find the numbers in the circles.

Answer:
A = 0.3.
B = 1.1
C = 0.6

Explanation:
The number in each rectangle is the sum of the numbers in the two circles next to it.
=> Equation 1: A + B = 1.4
=> Equation 2: A + C = 0.9
=> Equation 3: B + C = 1.7.
Equation 1 – Equation 2
=> (A + B) – (A + C ) = 1.4 – 0.9
=> A + B – A – C = 0.5
=> B – C = 0.5.
=> B = 0.5 + C.
Equation 3 – Equation 2:
(B + C) – (A + C ) =  1.7 – 0.9
=> B + C – A – C = 0.8
=> B – A = 0.8.
=> A = B – 0.8.
Substitute A and B in Equation:1.
=> A + B = 1.4
=> B – 0.8 + B = 1.4
=> 2B – 0.8 = 1.4
=> 2B = 1.4 + 0.8
=> 2B = 2.2
=> B = 2.2 ÷ 2
=> B = 1.1.
A = 1.1 – 0.8
=> A = 0.3.
Substitute A = 0.3 in Equation 2:
=> A + C = 0.9
=> 0.3 + C = 0.9
=> C = 0.9 – 0.3
=> C = 0.6.

Question 2.
Each week, Rena saves $5. Her brother saves $2.50 less each week, but he started saving 4 weeks earlier. After how many weeks will Rena’s savings be equal to her brother’s?
Answer:
Number of weeks Rena’s savings be equal to her brother’s = 2.

Explanation:
Amount of money Rena saves each week = $5.
Her brother saves $2.50 less each week, but he started saving 4 weeks earlier.
Amount of money her brother saves each week = Amount of money Rena saves each week – $2.50.
= $5 – $2.50
= $2.50.
Total amount of money her brother saves for 4 weeks =  4 × Amount of money her brother saves each week
= 4 × $2.50
= $10.
Number of weeks Rena’s savings be equal to her brother’s =  Total amount of money her brother saves for 4 weeks ÷ Amount of money Rena saves each week
= $10 ÷ $5
= 2.

Practice the problems of Math in Focus Grade 4 Workbook Answer Key Chapter 9 Angles to score better marks in the exam.

Math in Focus Grade 4 Chapter 9 Answer Key Angles

Math Journal

Question 1.
Which statements are wrong? Explain your answer.

a. Two right angles form a \(\frac{1}{2}\)-turn.
Answer:
Yes.

Explanation:
Yes, two right angles form a \(\frac{1}{2}\)-turn.

b. The measure of an angle is a fraction of a \(\frac{3}{4}\)-turn.
Answer:

c. An acute angle has a measure greater than 90°.
Answer:
Wrong.

Explanation:
No, because the acute angle will be less than 90°. So the statement is wrong.

d. A \(\frac{1}{4}\)-turn is 90°.
Answer:
Yes.

Explanation:
Yes, a \(\frac{1}{4}\)-turn is 90°.

e. A straight angle has a measure of 180°.
Answer:
Yes.

Explanation:
Yes, a straight angle has a measure of 180°.

f. 150° is between a \(\frac{1}{4}\) -turn and a \(\frac{1}{2}\)-turn.
Answer:
Yes.

Explanation:
Yes, 150° is between a \(\frac{1}{4}\) -turn and a \(\frac{1}{2}\)-turn.

Complete.

Question 2.
Conrad named the angle as shown. Is he correct? Explain your answer.

The names of the angle are ∠EFG, ∠FGE, and ∠F.
Answer:
Wrong.

Explanation:
The names of the angle ∠FGE, and ∠F are wrong because the middle point must be a vertex.

Put On Your Thinking cap!

Challenging Practice

Look at the clock. The hour hand and minute hand were at the position as shown in figure A. Figure B shows the position of the hour hand and minute hand after some time.

What fraction of a turn did the minute hand move? Explain your answer.

Answer:
The fraction will be \(\frac{1}{4}\).

Explanation:
Here, the fraction of a turn did the minute hand move is \(\frac{1}{4}\).

Put on Your Thinking Cap!

Problem Solving

Look at the diagram.
Tom walks from J to K and at that point makes a \(\frac{1}{4}\)-turn to his right.
Then, he walks to H and at that point, makes a \(\frac{1}{2}\)-turn before walking on to the end of that line.
Where will he be?

Answer:
Tom will be on G.

Explanation:
Here, Tom walks from J to K and at that point makes a \(\frac{1}{4}\)-turn to his right which is 90°, and then he walks to H, and at that point, makes a \(\frac{1}{2}\)-turn which is 180° before walking on to the end of that line. So he will be at point G.

This handy Math in Focus Grade 4 Workbook Answer Key Chapter 12 Practice 5 Using Formulas for Area and Perimeter detailed solutions for the textbook questions.

Math in Focus Grade 4 Chapter 12 Practice 5 Answer Key Using Formulas for Area and Perimeter

Solve. Show your work.

Example

The floor of a patio measuring 8 feet by 7 feet is tiled with 1 -foot square tiles. The shaded area in the figure is tiled in black, and the unshaded area is tiled in white. What is the area tiled in white?

Area of patio = 8 × 7
= 56 ft²
Shaded area = 6 × 4
= 24 ft²
Area of patio – shaded area
= 56 – 24
= 32 ft²
The area tiled in white is 32 square feet.

Question 1.
The floor of Mr. Jones’ living room is in the shape shown below.

a. Estimate, in square yards, the area of his living room.
Answer:
We can calculate the living rom by making the room into two shapes where area of them can be easily find.
Area of the living room = area of the triangle + area of the rectangle
= 1/2 × 3 × 2 + 4 × 3
= 3 + 12
= 15
The estimated area of Mr. Jones’ living room is 15 square yards.

b. Mr. Jones wants to carpet his living room. If a roll of carpet is 3 yards wide, what is the smallest length of carpet Mr. Jones should buy?
Answer:
Area of the carpet required is 15 square yards.
As carpet will be in rectangular shape, so length x width = 15
As given, width is 3 yards. So 3 × 5 = 15
The smallest length of carpet Mr. Jones should buy is 5 yards.

Solve. Show your work.

Question 2.
The figure shows a small rectangle and a large rectangle. Find the area of the shaded part of the figure.

Area of large rectangle = ___________ × ___________
= ______________ ft²
Area of small rectangle = ___________ × ___________
= ________ ft²
Area of shaded part area of large rectangle – area of small rectangle
= ________ ft²
The area of the shaded part is __________ square feet.
Answer:
Area of large rectangle = 18ft × 16ft
= 288 ft²
Area of small rectangle = 9ft × 6ft
= 54 ft²
Area of shaded part area of large rectangle – area of small rectangle
= 288 ft² – 54 ft²
= 234 ft²
The area of the shaded part is 234 square feet.

Solve. Show your work.

Question 3.
The figure shows a small rectangle and a large rectangle. Find the area of the shaded part of the figure.

Area of large rectangle = ___________ × ___________
= ______________ in.²
Area of small rectangle = ___________ × ___________
= ________ in.²
Area of shaded part area of large rectangle – area of small rectangle
= ________ in.²
The area of the shaded part is __________ square inches.
Answer:
Area of large rectangle = 15 in × 11 in
= 165 in.²
Area of small rectangle = 4 in × 3 in
= 12 in.²
Area of shaded part area of large rectangle – area of small rectangle
= 165 – 12
=153 in.²
The area of the shaded part is 153 square inches.

Example

A rug is centered on a rectangular floor as shown in the diagram. Find the area of the rug.

Length of rug = 9 – 1 – 1
= 7 m
Width of rug = 6 – 1 – 1
= 4 m
Area of rug = 7 × 4
= 28 m²
The area of the rug is 28 square meters.

Solve. Show your work.

Question 4.
A rectangular pool is surrounded by a 2-yard-wide deck as shown in the diagram. Find the area of the deck.

Answer:
Total area = 22yd × 12yd
= 264 yd²
Area of the pool = 18yd × 8yd
= 144 yd²
Area of the deck = Total area – area of the pool
= 264 – 144
= 120 yd²
The area of the deck is 120 square yards.

Question 5.
A rectangular picture frame measures 25 centimeters by 1 5 centimeters. It has a wooden border 3 centimeters wide. To fit the picture frame, how large should a picture be?

Answer:
Length of picture  = 25 – 3 – 3
= 19 cm
Width of picture = 15 – 3 – 3
= 9 m
Area of picture = 19 × 9
= 171 cm²
The area of the picture is 171 square centimeters.

Solve. Show your work.

Question 6.
Renee has a piece of rectangular cardboard measuring 90 centimeters by 80 centimeters. She cuts out a small rectangular piece measuring 15 centimeters by 20 centimeters.

a. Find the area of the remaining piece of cardboard.
Answer:
Area of larger rectangular cardboard = 90 cm × 80 cm  = 7,200 cm²
Area of smaller rectangular cardboard = 20 cm × 15 cm  = 300 cm²
Area of the remaining piece of cardboard = Area of larger rectangular cardboard – area of smaller rectangular cardboard
= 7,200 – 300
= 6,900 cm²
Area of remaining piece of cardboard is 6,900 square centimeters.

b. Find the perimeter of the remaining piece of cardboard.
Answer:
Even if we remove a rectangular piece of cardboard at the edge of larger cardboard, the perimeter remains same.
Perimeter of larger rectangular cardboard = 90 cm + 80 cm + 90 cm+ 80 cm  = 340 cm
Perimeter of remaining piece of cardboard is 340 centimeters.

c. Compare the perimeter of the remaining piece of cardboard with that of the original piece of cardboard. Which one is greater?
Answer:
Perimeter of remaining piece of cardboard is 340 centimeters.
Perimeter of original piece of cardboard is 340 centimeters.
Perimeter of original piece of cardboard is equal to perimeter of remaining piece of cardboard.

Solve. Show your work.

Question 7.
Melanie makes a path 1 yard wide around her rectangular patch of land as shown in the diagram. Find the perimeter and area of the patch of land.

Answer:
Length of patch of land  = 20 – 1 – 1
= 18 yards
Width of patch of land = 12 – 1 – 1
= 10 yards
Area of patch of land = 18 × 10
= 180 yd²
The area of the patch of land is 180 square yards.
Perimeter of the patch of land = 18 + 10 + 18 + 10
= 56 yards

Question 8.
A rectangular piece of paper measuring 15 centimeters by 7 centimeters is folded along the dotted lines to form the figure shown.

Find the area of the figure formed.
Answer:
Area of the triangle = 1/2 × b × h
= 1/2 × 7 × 7
= 49/2 square centimeters
Area of the rectangle = length × width
= 7 cm × 1 cm
= 7 square centimeters
Area of the triangle = 1/2 × b × h
= 1/2 × 7 × 7
= 49/2 square centimeters
Area of the figure = Area of the triangle + Area of the rectangle + Area of the triangle
= 49/2 + 7 + 49/2
= 56 square centimeters
Area of the figure formed is 56 square centimeters

This handy Math in Focus Grade 4 Workbook Answer Key Chapter 12 Practice 3 Rectangles and Squares detailed solutions for the textbook questions.

Math in Focus Grade 4 Chapter 12 Practice 3 Answer Key Rectangles and Squares

Find the area of each figure.

Example

Area of the rectangle = 12 × 6
= 72 ft²
The area of the rectangle is 72 square feet.

Question 1.

Area of the square = _________ × __________
= __________ cm²
The area of the square is _____________ square centimeters.
Answer:
Area of the square = 9 cm × 9 cm
= 81 cm²
The area of the square is 81 square centimeters.

Solve. Show your work.

Example

The area of a rectangular hall is 78 square yards. Its width is 6 yards. Find the length.

Length × width = area
Length × 6 = 78 yd²
Length = 78 ÷ 6
= 13 yd
The length of the hall is 13 yards.

Question 2.
A rectangle has an area of 56 square centimeters. Its length is 8 centimeters. Find the width.

The width of the rectangle is ___________ centimeters.
Answer:
Length = 8 cm
width = ?
Area of the rectangle = 56 cm²
Area of the rectangle = length × width
56 cm² = 8 cm x width
56 cm²  ÷ 8 cm = width
7 cm = width 
The width of the rectangle is 7 centimeters.

Solve. Show your work.

Question 3.
The area of a rectangular carpet is 84 square meters. Its width is 7 meters.

a. Find the length.
Answer:
Length = ?
width = 7 m
Area of the rectangular carpet = 84 m²
Area of the rectangular carpet = length × width
84 m² = length x 7 m
84 m²  ÷ 7 m = length
12 m = length
The length of the rectangular carpet is 12 meters.

b. Find the perimeter of the carpet.
Answer:
Perimeter of the carpet = 7 m + 12 m + 7 m + 12 m
= 38 m
Perimeter of the carpet is 38 meters.

Question 4.
The area of a square is 64 square inches. Find the length of one side of the square.
(Hint: What number multiplied by itself is equal to 64?)

Answer:
Area = side × side = s²
Where $s$ is the length of the side of the square.
Area of a square is 64 square inches.
64 in²$\mathrm{=\; s2}$(8 in)$2$= $\mathrm{s2}$8 inches = s
The length of one side of the square is 8 inches.

Question 5.
The area of a square garden is 100 square meters.
a. Find the length of each side of the garden.

Answer:
A square is a regular polygon with four sides.
Area = width × height
But since the width and height are by definition the same, the formula is usually written as
Area = side × side = s²
where s is the length of one side.
To find the length of each side of the garden we know that the area is 100  applying the area formula and solving for s, the length of one side, we get that
100 m²= s²
(10 m)² = s²
10 m = s
The length of each side of the garden is 10 m.

b. Find the perimeter of the garden.
Answer:
In the case of a square, all four sides are the same length, so the perimeter is four times the length of a side.
We find that the length of each side is 10 m. Therefore, the perimeter is
Perimeter = 4 × s
= 4 x 10 m
= 40 m
where s is the length of any one side.
The perimeter of the garden is 40 m.

Solve. Show your work.

Question 6.
The area of a rectangular recreation area is 45 square miles. Its width is 5 miles.

a. Find the length.
Answer:
Length = ?
width = 5 mi
Area of the rectangular recreation = 45 mi²
Area of the rectangular recreation = length × width
45 mi² = length x 5 mi
45 mi²  ÷ 5 mi = length
9 mi = length
The length of the rectangular recreation is 9 miles.

b. Find the perimeter.
Answer:
Perimeter of the rectangular recreation = 9 mi + 5 mi + 9 mi + 5 mi
= 28 miles
Perimeter of the rectangular recreation is 28 miles.

Question 7.
The perimeter of a rectangular poster is 156 inches. Its width is 36 inches.

a. Find the length.
Answer:
Length = ?
width = 36 in
perimeter  of a rectangular poster = 156 in
Perimeter of the rectangular poster = length + width + length + width
156 in = l + 36 in + l + 36 in
156 in = 2l + 72 in
156 in – 72 in = 2l
84 in = 2l
42 in = l
The length of the rectangular poster is 42 inches.

b. Find the area.
Answer:
Length = 42 inches
width = 36 inches
Area of the rectangular poster = length x width
= 42 inches x 36 inches
= 1,512 in² 
Area of the rectangular poster is 1,512 square inches.

This handy Math in Focus Grade 4 Workbook Answer Key Chapter 12 Practice 4 Composite Figures detailed solutions for the textbook questions.

Math in Focus Grade 4 Chapter 12 Practice 4 Answer Key Composite Figures

Find the lengths of the unknown sides of each figure. Then find the perimeter of each figure.

Example

Length of first unknown side = 16 – 4 = 12 in.
Length of second unknown side = 13 + 4 = 17 in.
Perimeter of figure = 16 + 13 + 12 + 4 + 4 + 17 = 66 in.
Perimeter = 66 in.

Question 1.

Perimeter = ____________ yd
Answer:

Length of first unknown side = 6 yards
Length of second unknown side = 24 yards – 8 yards – 5 yards = 11 yards
Perimeter of figure = 5 yd + 6 yd + 8 yd + 3 yd + 24 yd + 3 yd + 11 yd +6 yd
= 66 yd
Perimeter = 66 yd.

Solve. Show your work.

Question 2.
Tom wants to fence in the piece of land shown in the diagram. Find the perimeter of the piece of land to find the length of fencing material he needs.

Perimeter = __________ m
Answer:
Length of first unknown side = 8 m
Length of second unknown side = 9 m
Length of third unknown side = 3m
Perimeter of the piece of land = 3 m + 8 m + 12 m + 8 m + 9 m + 3 m + 3 m = 46 m
Perimeter = 46 m
He needs 46 m of fencing material.

Question 3.
Find the perimeter of this figure.

Perimeter = ___________ mi
Answer:

Length of first unknown side ST = 28 mi – 12 mi = 16 mi
Length of second unknown side TU = 24 mi – 6 mi = 18 mi
Perimeter of the figure = 28 mi + 6 mi + 16 mi + 18 mi + 12 mi + 24 mi = 104 mi
Perimeter = 104 mi

Solve. Show your work.

Question 4.
Find the perimeter of the figure.

Perimeter = ___________ cm
Answer:
Perimeter  of the figure = 42 cm + 18 cm + 34 cm + 42 cm + 16 cm = 152 cm
Perimeter = 152  cm

Find the area of each composite figure. Show your work.

Example

Break up the figure into two rectangles as shown. Then find the area of the whole figure.

Area of rectangle 1 = length × width
= 10 × 3
= 30 in.²
Area of rectangle 2 = length × width
= 7 × 6
= 42 in.²
Total area = area of rectangle 1 + area of rectangle 2
= 30 + 42
= 72 in.²
Area = 72 in.²

Find the area of each composite figure. Show your work.

Question 5.

Area = ____________ ft²
Answer:
For rectangle 1
length = 22 feet
Width = 18 feet
Area of rectangle 1 = length × width
= 22 feet × 18 feet
= 396 ft²
For rectangle 2
length = 14 feet
width = 9 feet
Area of rectangle 2 = length × width
= 14 feet × 9 feet
= 126 ft²
Total area = area of rectangle 1 + area of rectangle 2
= 396 ft²+ 126 ft²
= 522 ft²
Area =522 ft²

Question 6.

Area = __________ m²
Answer:

Explanation:
For rectangle 1
length = 12 m
Width = 5 m
Area of rectangle 1 = length × width
= 12 m × 5 m
= 60 m²
For rectangle 2
length = 8 m
width = 3 m
Area of rectangle 2 = length × width
= 8 m × 3 m
= 24 m²
Total area = area of rectangle 1 + area of rectangle 2
= 60 m²+ 24 m²
=84 m²
Area =84 m²

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

Math in Focus Grade 4 Chapter 14 Answer Key Tessellations

Put On Your Thinking Cap!

Challenging Practice

Question 1.
From the given triangle, make another shape that can also tessellate. Cut off a part of the triangle and attach it

Answer:

Question 2.
From the square on the left, the shaded part is cut out to form the shape shown on the right.

Use the grid below to find out if this shape tessellates. Then fill in the blank with can or cannot.

The shape ___________ tessellate.
Answer:

The shape cannot tessellate.

Question 3.
Each of these shapes is formed by attaching the part that was cut out from the square above to a different side of the square.

Answer:

Use the grid below to find out if the shapes tessellate. Then fill in the blanks with can or cannot.

a.

The shape ___________ tessellate.
Answer:

The shape can tessellate.

b.

The shape ___________ tessellate.
Answer:

The shape can tessellate.

Use the shape to make two different tessellations in the spaces provided.

Question 4.
Tessellation 1

Answer:

Question 5.
Tessellation 2

Answer:

Practice the problems of Math in Focus Grade 1 Workbook Answer Key Chapter 14 Mental Math Strategies to score better marks in the exam.

Math in Focus Grade 1 Chapter 14 Answer Key Mental Math Strategies

Put On Your Thinking cap!

Challenging Practice

You can use a telephone dial to find the value of a word.

Example
YES = 9 + 3 + 7 = 19

Question 1.
Name a three-letter word with a value of 14. _____
Answer: MAT=6+2+6=14 is  a three-letter word with a value of 14

Question 2.
Find a word that has the same value as BOAT. _____
Answer: GUN is a word that has the same value as BOAT
BOAT=2+6+2+8=18
GUN=4+8+6=18

Question 3.
Think of a four-letter word. Find its value. Ask your friend to guess the word.

Answer: KITE = 5+4+8+3 =20

Put on Your Thinking Cap!

Problem Solving

There are 6 bicycles and tricycles at Sunshine Day Care Center. There are 16 wheels in all. How many bicycles are there?

Chapter Review/Test
Vocabulary
Choose the correct word.

Question 1.
To help you subtract ____ think of addition.
Answer: To help you subtract a value think of addition.

Question 2.
4 + 4 = 8 is a ____
Answer: 4 + 4 = 8 is a addition

Concepts and Skills
Add mentally.

Question 3.
25 + 4 = ____
Answer: 25+4=29
adding 25 with 4 we get 29

Question 4.
33 + 4 = ____
Answer: 33+4=37
adding 33 with 4 we get 37

Question 5.
10 + 28 = ____
Answer: 10 + 28 = 38
adding 10 with 28we get 38

Question 6.
15 + 20 = ____
Answer: 15 + 20 = 35
adding 15 with 20 we get 35

Question 7.
6 + 7 = ___
Answer: 6+7=13
adding 6 with 7 we get 13

Question 8.
4 + 7 = ____
Answer: 4+7=11
adding 4 with 7 we get 11

Subtract mentally. Think of addition.

Question 9.
8 – 6 = ____
Answer:8-6=2
By removing 6 from 8 we get 2

Question 10.
9 – 7 = ____
Answer:9 – 7 = 2
By removing 7 from 9 we get 2

Question 11.
16 – 7 = ____
Answer:16 – 7 =
By removing 7 from 16 we get 9

Question 12.
18 – 9 = ____
Answer:18 – 9 =
By removing 9 from 18 we get 9

Question 13.
15 – 8 = ____
Answer: 15 – 8 =7
By removing 8 from 15 we get 7

Question 14.
14 – 7 = ____
Answer:14 – 7 = 7
By removing 7 from 14 we get 7

Subtract mentally.

Question 15.
15 – 4 = ______
Answer: 15 – 4 = 11
By removing 4 from 15 we get 11

Question 16.
38 – 6 = ______
Answer:38 – 6 = 32
By removing 6 from 38 we get 32

Question 17.
21 – 10 = ___
Answer: 21 – 10 =
By removing 10 from 21 we get 11

Question 18.
37 – 20 = ___
Answer: 37 – 20 = 17
By removing 20 from 37 we get 17

Problem Solving

Fill in the blanks.

Question 19.

How many stamps are left? _____
Answer: 23 stamps are left
27-4=23
By removing 4 from 27 we get 23

Question 20.
13 children are on a school bus. 6 more children get on the bus. ____
Answer: Now there are a total of 19 children on a school bus
13+6=19
adding 13 with 6 we get 19

This handy Math in Focus Grade 1 Workbook Answer Key Chapter 3 Practice 1 Ways to Add detailed solutions for the textbook questions.

Math in Focus Grade 1 Chapter 3 Practice 1 Answer Key Ways to Add

Add. Count on from the greater number.

Example

Question 1.

Answer:

Explanation:
There are 3 muffins and the chef prepared 2 more muffins
6 + 2 = 8
The sum of 6 and 2 is 8

Question 2.

Answer:

Explanation:
In one pizza they made 5 pieces
and in the other pizza they made 3 pieces
5 + 3 = 8
The sum of 5 and 3 is 8

Question 3.

Answer:

Explanation:
In one page there are 7 stickers
and in the other page there are 3 stickers
7 + 3 = 10
The sum of 7 and 3 is 10

Question 4.

Answer:

Explanation:
A man ordered 8 burgers and then he added 2 more burgers
8 + 2 = 10
the sum of 8 and 2 is 10

Look at the pictures.

Add. Count on from the greater number.

Example

Question 5.

Answer:

Explanation:
A girl saws 4 stars and a boy saw another group of 4 stars
4 + 4 = 8
the sum 4 and 4 is 8

Question 6.

Answer:

Explanation:
In one basket there are 2 carrots and in the bag there are 3 carrots
2 + 3 = 5
The sum of 2 and 3 is 5

Question 7.

Answer:

Explanation:
There are 3 birds on the tree
7 birds on the ground
3 + 7 = 10
The sum of 3 and 7 is 10.

Question 8.

Answer:

Explanation:
In one plate there are 9 cookies and in other plate there is only one cookie
9 + 1 = 10
The sum of 9 and 1 is 10.

Count on to add.

Question 9.

Answer:

Explanation:
In a ten frame there are 6 colored counters
and 1 non colored counter
6 + 1 = 7
The sum of 6 and 1 is 7

Question 10.

Answer:

Explanation:
In a ten frame there are 4 colored counters
and 5 non colored counter
4 + 5 = 9
The sum of 4 and 5 is 9

Question 11.

Answer:

Explanation:
In a ten frame there are 5 colored counters
and 1 non colored counter
5 + 1 = 6
The sum of 5 and 1 is 6

Question 12.

Answer:

Explanation:
In a ten frame there are 6 colored counters
and 3 non colored counter
6 + 3 = 9
The sum of 6 and 3 is 9

Count on from the greater number to add.

Question 13.
4 + 1 = ___
Answer:
5
Explanation:
The sum of 4 and 1 is 5
4 + 1 = 5

Question 14.
6 + 2 = ______
Answer:
8
Explanation:
the sum of 6 and 2 is 8
6 + 2 = 8

Question 15.
9 + 1 = ___
Answer:
10
Explanation:
The sum of 9 and 1 is 10
9 + 1 = 10

Question 16.
3 + 4 = ______
Answer:
7
Explanation:
The sum of 3 and 4 is 7
3 + 4 = 7

Question 17.
3 + 7 = ______
Answer:
10
Explanation:
The sum of 3 and 7 is 10
3 + 7 = 10

Question 18.
4 + 5 = ______
Answer:
9
Explanation:
The sum of 4 and 5 is 9
4 + 5 = 9

Complete.
Write the answer in each

Example

Question 19.

Answer:

Explanation:
2 more than 6 is 8
so, we have to add 2 to 6
6 + 2 = 8

Question 20.

Answer:

Explanation:
4 more than 5 is 9
so, we have to add 4 to the 5
4 + 5 = 9

Question 21.

Answer:

Explanation:
3 more than 7 is 10
so, we have to add 3 to the number 7
3 + 7 = 10

Question 22.

Answer:

Explanation:
2 more than 8 is 10
so, we have to add 2 more to the number 8
2 + 8 = 10