Math in Focus

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 7 Algebraic Expressions to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Chapter 7 Answer Key Algebraic Expressions

Math in Focus Grade 6 Chapter 7 Quick Check Answer Key

Draw a bar model to show each operation.

Question 1.
15 + 4
Answer:
19
Explanation:

Question 2.
17 – 9
Answer:
8
Explanation:

Question 3.
6 × 5
Answer:
30
Explanation:

Question 4.
28 ÷ 4
Answer:
7
Explanation:

Find the common factors and greatest common factor of each pair of numbers.

Question 5.
6 and 9
Answer:
Common Factor 1,3
Greatest Common Factor 3
Explanation:
To find the greatest common factor (GCF) between numbers,
take each number and write it’s prime factorization.
6 factors 1, 2, 3, 6
9 factors 1, 3,
Then, identify the factors common to each number and multiply those common factors together.

Question 6.
4 and 12
Answer:
Common Factor 1, 2, 4
Greatest Common Factor 4
Explanation:
To find the greatest common factor (GCF) between numbers,
take each number and write it’s prime factorization.
4 factors 1, 2, 4
12 factors 1, 2, 3, 4, 6
Then, identify the factors common to each number and multiply those common factors together.

Question 7.
5 and 15
Answer:
Common Factor 1, 5
Greatest Common Factor 5
Explanation:
To find the greatest common factor (GCF) between numbers,
take each number and write it’s prime factorization.
5 factors 1, 5
15 factors 1, 3, 5
Then, identify the factors common to each number and multiply those common factors together.

Question 8.
8 and 28
Answer:
Common Factor 1, 2, 4
Greatest Common Factor 4
Explanation:
To find the greatest common factor (GCF) between numbers,
take each number and write it’s prime factorization.
8 factors 1, 2, 4, 8
28 factors 1, 2, 4, 7, 14, 28
Then, identify the factors common to each number and multiply those common factors together.

Complete with quotient, sum, difference, product, dividend, or divisor.

Question 9.
The “5 less than 7” is 7 – 5.
Answer:
Difference
Explanation:
“5 less than 7” is 7 – 5.
the difference of 7 – 5 = 2

Question 10.
The of 5 and 7 is \(\frac{5}{7}\). 7 is the and 5 is the .
Answer:
The fraction of 5 and 7 is \(\frac{5}{7}\). 7 is the divisor and 5 is the dividend.
Explanation:
The fractions are defined as the parts of a whole.
The dividend is the number that is being divided in the division process.
The number by which dividend is being divided by is called divisor.

Question 11.
The of 5 and 7 is 7× 5.
Answer:
Product
Explanation:
The product of 5 and 7 is 7× 5.
When we multiply 2 numbers we call as product.

Question 12.
The of 5 and 7 is 5 + 7.
Answer:
Sum
Explanation:
The sum of 5 and 7 is 5 + 7.
sum can be defined as the result or answer we get on adding two or more numbers.

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 6 Lesson 6.5 Percent of Change to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Chapter 6 Lesson 6.5 Answer Key Percent of Change

Math in Focus Grade 6 Chapter 6 Lesson 6.5 Guided Practice Answer Key

Solve.

Question 1.
At a post office, the weight of the mail at 10:00 A.M. was 80 pounds. Two hours later, the weight of the mail had increased by 30%. Find the weight of the mail at noon.

Method 1
30% of 80 = \(\frac{?}{?}\) ×
=
The weight of the mail had increased by pounds.
80 + =
The weight of the mail at noon was pounds.

Method 2
100% → 80 lb
1% → 80 ÷ 100 = lb
% → × = lb
The weight of the mail had increased by pounds.
80 + =
The weight of the mail at noon was pounds.
Answer:
104 pounds.
Explanation:
At a post office, the weight of the mail at 10:00 A.M. was 80 pounds.
Two hours later, the weight of the mail had increased by 30%.
the weight of the mail at noon,
Method 1
30% of 80 = \(\frac{30}{100}\) × 80
= 24
The weight of the mail had increased by 24 pounds.
80 + 24 = 104
The weight of the mail at noon was 104pounds.

Method 2
100% → 80 lb
1% → 80 ÷ 100 =  0.8lb
10% → 8 × 3 = 24lb
The weight of the mail had increased by 24pounds.
80 + 24 = 104
The weight of the mail at noon was 104 pounds.

Question 2.
The price of a new car was $22,800 in April. However, the price of the car was reduced by 5% in May. Find the price in May.
In May, the price of the car was % as compared to the price of the car in April.

100% → $
1% → $ ÷ 100 = $
% → × $ = $
The price of the car in May was $.
Answer:
$21,660
Explanation:
The price of a new car ,was $22,800 in April,
the price of the car was reduced by 5% in May.
100% → $22,800
1% → $ 22,800 ÷ 100 = $22,80
5% → 100 × $ 22,800 = $1140
22,800 – 1140 = 21,660
The price of the car in May was $ 21,660.

Question 3.
One Friday, a restaurant received enough orange juice for a week. After the weekend, the restaurant’s orange juice supply had decreased by 24% to 76 quarts. After Monday, the supply had further decreased by 20%.
a) What was the original amount of orange juice received?

The original amount of orange juice received was quarts.
Answer:
100qt
Explanation:
One Friday, a restaurant received enough orange juice for a week.
After the weekend, the restaurant’s orange juice supply had decreased by 24% to 76 quarts.
100% – 24% = 76%
24% = 76qt
1% = 76 ÷ 1 = 76qt
100% = 100 x 76 = 7600qt
the original amount of orange juice received
7600 ÷ 76 = 100qt

b) How much orange juice was left after Monday?

quarts of orange juice was left after Monday.
Answer:
\(\frac{?}{?}\) quarts of orange juice was left after Monday.
Explanation:
One Friday, a restaurant received enough orange juice for a week.
After the weekend, the restaurant’s orange juice supply had decreased by 24% to 76 quarts.
After Monday, the supply had further decreased by 20%.
100% – 20 = 80%
100% x 76 = (76 ÷ 1) x (80 ÷  100)
76(4÷ 5) = 304 ÷ 5
= 60\(\frac{4}{5}\)

Question 4.
Dennis bought an antique model train for $64. Two years later, he sold it for $72. What was the percent increase in the price of the model train?

The percent increase in the price of the model train was %.
Answer:
12.5%
Explanation:
Dennis bought an antique model train for $64.
Two years later, he sold it for $72.
the percent increase in the price of the model train

Question 5.
The original length of a spring was 28 millimeters. It was stretched to a length of 35 millimeters. Find the percent increase in its length.

mm –  mm = mm
The increase in length was millimeters.
\(\frac{?}{?}\) × 100% = %
The percent increase in its length was %.
Answer:
80%
Explanation:

35 mm – 28 mm = 7 mm
The increase in length was 7 millimeters.
\(\frac{7}{28}\) × 100% = 25 %
The percent increase in its length was 25 %.

Question 6.
The amount of the water in a dispenser was 50 liters at first. After 10 minutes, it decreased to 45 liters. Another 15 minutes later, the amount of water had decreased to 40 liters.
a) Find the percent decrease in the amount of water after the first 10 minutes.

Decrease in amount of water = 50 L – 45 L
= L
\(\frac{?}{?}\) × 100% = %
The percent decrease in the amount of water after the first 10 minutes was %.
Answer:
10%
Explanation:

Decrease in amount of water = 50 L – 45 L
= 5 L
\(\frac{5}{50}\) × 100% = 10 %
The percent decrease in the amount of water after the first 10 minutes was 10 %.

b) What was the percent decrease in the amount of water from 45 liters to 40 liters?
Answer:
11.11%
Explanation:
Decrease in amount of water = 45 L – 40 L
= 5 L
\(\frac{5}{45}\) × 100% = 11.11 %
The percent decrease in the amount of water from 45 liters to 40 liters was 11.11 %.

Question 7.
On Monday, Camille scored 120 points in a video game and Emily scored \(\frac{5}{4}\) as many points as Camille. On Tuesday, Emily scored 30% more points than what she scored on Monday. Find the increase in the number of points Emily scored on Tuesday.

The increase in the number of points Emily scored on Tuesday was .
Answer:
45 points
Explanation:

Math in Focus Course 1A Practice 6.5 Answer Key

Solve. Show your work.

Question 1.
Tom earned $600 last summer delivering newspapers. This summer, he earned 20% more. How much did he earn this summer?
Answer:
$720
Explanation:
Tom earned $600 last summer delivering newspapers.
This summer, he earned 20% more.
20% of 600 = (20 ÷ 100) x 600 = $120
This summer he earned = $600 + $120 = $720

Question 2.
A gift shop buys greeting cards at $3.50 each, and sells them at an 80% markup. At what price does the gift shop sell each greeting card?
Answer:
$6.30
Explanation:
A gift shop buys greeting cards at $3.50 each,
he sells them at an 80% markup.
80% of 3.50 = (80 ÷ 100) x 3.50 = 2.8
price each greeting card,
3.50 + 2.8 = 6.30

Question 3.
Ms. Kendrick earned $3,600 each month last year. This year, she is given a pay raise of 15%. How much more money does she earn each month this year than she earned each month last year?
Answer:
$540
Explanation:
Ms. Kendrick earned $3,600 each month last year.
This year, she is given a pay raise of 15%
more money does she earn each month this year than she earned each month last year
3600 x (15 ÷ 100) = 540

Question 4.
The original price of a computer was $1,250. At a year-end sale, the selling price of the computer was $900. Find the percent discount.
Answer:
28%
Explanation:
The original price of a computer was $1,250.
At a year-end sale, the selling price of the computer was $900.
(n ÷ 100) x 1250 = 900
1250n = 900 x 100
1250n = 90000
n = 90000 ÷ 1250
n = 72
the percent of discount = 100 – 72 = 28%

Question 5.
Last year, Alex earned a monthly salary of $250, and Ben earned a monthly salary of $180. This year, each of them received a pay increase of 25%. This year, how much more did Alex earn in one month than Ben?
Answer:
$17.5
Explanation:
Last year, Alex earned a monthly salary of $250,
This year, each of them received a pay increase of 25%.
(25 ÷ 100) x 250 = 62.5
Ben earned a monthly salary of $180,
This year, each of them received a pay increase of 25%.
(25 ÷ 100) x 180 = 45
This year, how much more did Alex earn in one month than Ben
62.5 – 45 = 17.5

Question 6.
Alan deposited $300 into a savings account. At the end of the first year, the amount of money in the account had increased to $336. At the end of the second year, he had $420.
a) Find the percent increase in the amount of money in his savings account at the end of the first year.
Answer:
12%
Explanation:
Alan deposited $300 into a savings account.
At the end of the first year, the amount of money in the account had increased to $336.
Simple interest = (principal amount x Rate of interest x time) ÷ 100
principal amount = 300
Amount increased = 336
S.I = 336 – 300 = 36
Time = 1 year
36 = (300 x R x 1) ÷ 100
R = (36 x 100) ÷ 300 = 12%

b) Find the percent increase in the amount of money in his savings account from the end of the first year to the end of the second year.
Answer:
25%
Explanation:
From the above explanation in the difference amount is
420 – 336 = 84$
(84/336) x 100 =25%

Question 7.
Linda had an orange ribbon and a blue ribbon. The orange ribbon was 2 meters long. The blue ribbon was \(\frac{4}{5}\) as long as the orange ribbon. Linda cut off a piece of blue ribbon. The length of the piece was 25% of the length of the blue ribbon.
a) What was the length of the blue ribbon before it was cut?
Answer:
1.6 m
Explanation:
The orange ribbon was 2 meters long
The blue ribbon was = 2x\(\frac{4}{5}\) = 1.6m
piece was 25% of the length of the blue ribbon.
2x\(\frac{4}{5}\) x \(\frac{25}{100}\)
= \(\frac{40}{100}\)
= 40%

b) Find the length of the piece of blue ribbon that Linda cut off.
Answer:
0.4 m
Explanation:
piece was 25% of the length of the blue ribbon.
2x\(\frac{4}{5}\) x \(\frac{25}{100}\)
= \(\frac{40}{100}\)
= 0.4

Question 8.
One year, the number of subscribers for Newspaper A was 7,600, and the number of subscribers for Newspaper B was \(\frac{3}{4}\) of the number of subscribers for Newspaper A. The next year, the number of subscribers for Newspaper B increased by 25%. Find the total number of subscribers for Newspaper B the next year.
Answer:
7125 subscribers
Explanation:
subscribers for Newspaper A was 7,600
subscribers for Newspaper B was \(\frac{3}{4}\) x 7,600 = 5,700
\(\frac{25}{100}\) x 5,700 = 1,425
subscribers for Newspaper B increased by 25% = 1,425
the total number of subscribers for Newspaper B the next year.
5,700 + 1,425 = 7,125

Question 9.
Ryan had 240 CDs. Sharon had \(\frac{9}{2}\) of the number of CDs Ryan had. Sharon gave 75 CDs to her friends. Find the percent decrease in the number of CDs Sharon had. Round your answer to 2 decimal places.
Answer:
6.95%
Explanation:
Ryan had 240 CDs.
Sharon had \(\frac{9}{2}\) of the number of CDs Ryan had.
240 x \(\frac{9}{2}\) = 1080
Sharon gave 75 CDs to her friends.
1080 – 75 = 1005
The percent decrease in the number of CDs Sharon had
(1005 ÷ 1080) x 100 = 93.05
100% – 93.05% = 6.95

Question 10.
Shaun collected $925 on the first day of a charity fundraiser. On the second day, he collected $728. By the third day, he had collected a total of $2,538.
a) What was the percent decrease in the amount of money collected from the first day to the second day? Round your answer to 1 decimal place.
Answer:
21.3%
Explanation:
Shaun collected $925 on the first day of a charity fundraiser.
On the second day, he collected $728.
925 – 728 = 197
the percent decrease in the amount of money collected from the first day to the second day
(197 ÷ 925) x 100 = 21.29 = 21.3

b) Find the percent increase or decrease in the amount collected from the second day to the third day. Round your answer to 1 decimal place.
Answer:
21.6%
Explanation:
On the second day, he collected $728.
By the third day, he had collected a total of $2,538.
925 + 728 = 1653
2,538 – 1653 = 885
the percent decrease in the amount of money collected from the second day to the third day
(728 ÷ 885) x 100 = 21.29 = 21.3

Question 11.
Math Journal Jason and Robert each solved the following problem: In a science experiment, Mark had to record the change in the height of a candle when it is lighted. The height of the candle was 25 centimeters at first. After burning for 10 minutes, the height of the candle decreased to 20 centimeters. Another 20 minutes later, the height of the candle decreased to 15 centimeters. Find the percent decrease in its height from 20 centimeters to 15 centimeters.

Whose answer is incorrect? Explain why.
Answer:
Robert’s answer is correct
Explanation:
The question is to find the percent decrease in its height from 20 centimeters to 15 centimeters.

Brain @ Work

Question 1.
A shopping club is having a sale. Members and nonmembers of the club receive different discounts, as shown below.

a) Sally is not a member of the shopping club. She wants to purchase a camcorder that is selling at $580. How much does Sally have to pay for the camcorder?
Answer:
$502
Explanation:
Sally is not a member of the shopping club,
So she will get 10% discount and $20 off with a minimum purchase of $500
She wants to purchase a camcorder that is selling at $580.
Total amount she has to pay for the camcorder
580 x (10 ÷ 100) = 58
580 – 58 = 522
522 – 20 = $502

b) Tabitha is a member of the shopping club. She wants to purchase a computer laptop that is selling at $990. How much does Tabitha have to pay for the computer laptop?
Answer:
$722.5
Explanation:
Tabitha is a member of the shopping club.
She wants to purchase a computer laptop that is selling at $990.
She will get a discount of 25% and $20 off with  minimum purchase of $500
Total amount Tabitha have to pay for the computer laptop
990 x (25 ÷ 100) = 247.5
990 – 247.5 = 742.5
742.5 – 20 = $722.5

Question 2.
The figure- the area of the shaded part is 40% of the area of Square P. It is also 20% of the area of Square Q. What percent of the figure is shaded? Round your answer to 2 decimal places. (Hint: Find the ratio of the area of the shaded part to the unshaded part.)

Answer:
16.66 sq mt
Explanation:
P:Q
60 : 40 = 20 : 80
6 : 4 = 2 : 8
3 : 2 = 1 : 4
\(\frac{2}{12}\)
\(\frac{1}{6}\) = 16.66

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 6 Lesson 6.1 Understanding Percent to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Chapter 6 Lesson 6.1 Answer Key Understanding Percent

Math in Focus Grade 6 Chapter 6 Lesson 6.1 Guided Practice Answer Key

Solve.

Question 1.
Out of 25 chairs, 14 are brown. What percent of the chairs are brown?

% of the chairs are brown.
Answer:
56% of the chairs are brown.
Explanation:
Out of 25 chairs, 14 are brown.

Question 2.
Of the 400 animals in a zoo, 32 were monkeys.
a) What percent of the animals were monkeys?

% of the animals were monkeys.
Answer:
8% of the animals were monkeys.
Explanation:

b) What percent of the animals were not monkeys?
% – % = %
% of the animals were not monkeys.
Answer:
92 % of the animals were not monkeys.
Explanation:
8% of the animals were monkeys.
100 % – 8% = 92 %

Express each percent as a fraction or a mixed number in simplest form.

Question 3.
48% = \(\frac{48}{?}\)
= \(\frac{?}{?}\)
Answer:
\(\frac{12}{25}\)
Explanation:
48% = \(\frac{48}{100}\)
= \(\frac{12 . 4}{25 . 4}\)
= \(\frac{12}{25}\)

Question 4.
55%
Answer:
\(\frac{11}{20}\)
Explanation:
55% = \(\frac{55}{100}\)
= \(\frac{11 . 5}{20 . 5}\)
= \(\frac{11}{20}\)

Question 5.
108%
Answer:
\(\frac{108}{100}\)
Explanation:
108% = \(\frac{108}{100}\)
= \(\frac{52 . 4}{25 . 4}\)
= 2\(\frac{2}{25}\)

Express each percent as a decimal.

Question 6.
13% = \(\frac{?}{?}\)
=
Answer:
0.13
Explanation:
13% = \(\frac{13}{100}\)
= 0.13

Question 7.
8%
Answer:
0.08
Explanation:
8% = \(\frac{8}{100}\)
= 0.08

Question 8.
126%
Answer:
1.26
Explanation:
126% = \(\frac{126}{100}\)
=1.26

Math in Focus Course 1A Practice 6.1 Answer Key

Solve. Show your work.

Question 1.
Out of a total of 500 flowers, 65 are roses. What percent of the flowers are roses?
Answer:
13%
Explanation:

Question 2.
Of the 200 packages of bagels sold, 15 of them are sesame seed bagels. What percent of the bagel packages sold are sesame seed bagels?
Answer:
7.5%
Explanation:
15 out of 200 = \(\frac{15}{200}\)
= \(\frac{15}{2 X 100}\)
= \(\frac{7.5}{100}\)

Question 3.
In a survey of music preferences, 81 out of 450 students said that they preferred country music. What percent of the students preferred country music?

Answer:
18%
Explanation:

Question 4.
There are 750 spectators in the stadium, of which 420 are women and the rest are men.
a) What percent of the spectators are women?
Answer:
56%
Explanation:
420 out of 750 =
= \(\frac{420}{750}\)
= \(\frac{42}{75}\)
= 0.56 x 100 = 56%

b) What percent of the spectators are men?
Answer:
44%
Explanation:
420 out of 750 =
= \(\frac{420}{750}\)
= \(\frac{42}{75}\)
= 0.56 x 100
percent of women spectators = 56%
percent of men spectators = 100 – 57 = 44%

Express each percent as a fraction or a mixed number in simplest form.

Question 5.
65%
Answer:
\(\frac{13}{20}\)
Explanation:

Question 6.
78%
Answer:
\(\frac{39}{50}\)
Explanation:
78% = \(\frac{78}{100}\)
Divided numerator and denominator with 2
= \(\frac{39}{50}\)

Question 7.
92%
Answer:
\(\frac{23}{25}\)
Explanation:
92% = \(\frac{92}{100}\)
Divided both the numerator and denominator with 4
= \(\frac{23}{25}\)

Question 8.
125%
Answer:
\(\frac{5}{4}\)
Explanation:
125% = \(\frac{125}{100}\)
Divided numerator and denominator with 5
= \(\frac{5}{4}\)

Question 9.
276%
Answer:
\(\frac{66}{25}\)
Explanation:
276% = \(\frac{276}{100}\)
Divided numerator and denominator with 4
= \(\frac{66}{25}\)

Question 10.
580%
Answer:
\(\frac{29}{5}\)
Explanation:
580% = \(\frac{580}{100}\)
Divided numerator and denominator with 2
= \(\frac{29}{5}\)

Express each percent as a decimal.

Question 11.
6%
Answer:
0.06
Explanation:
In order to convert percent to decimal number,
percentage should be divided by 100.
\(\frac{6}{100}\) = 0.06

Question 12.
43%
Answer:
0.43
Explanation:
In order to convert percent to decimal number,
percentage should be divided by 100.
\(\frac{43}{100}\) = 0.43

Question 13.
80%
Answer:
0.8
Explanation:
In order to convert percent to decimal number,
percentage should be divided by 100.
\(\frac{80}{100}\) = 0.8

Question 14.
367%
Answer:
3.67
Explanation:
In order to convert percent to decimal number,
percentage should be divided by 100.
\(\frac{367}{100}\) = 3.67

Question 15.
579%
Answer:
5.79
Explanation:
In order to convert percent to decimal number,
percentage should be divided by 100.
\(\frac{579}{100}\) = 5.79

Question 16.
779%
Answer:
7.79
Explanation:
In order to convert percent to decimal number,
percentage should be divided by 100.
\(\frac{779}{100}\) = 7.79

Solve. Show your work.

Question 17.
The music for Nadia’s dance routine lasts for exactly 4 minutes. When Nadia dances her routine, she starts with her music and finishes 12 seconds before the music ends. What percent of the time the music is playing is Nadia dancing?
Answer:
95%
Explanation:
4 minutes is 4 x 60 seconds = 240 seconds.
Nadia stops 12 seconds before the music ends so 240 – 12 = 228 seconds she dances.
= \(\frac{228}{240}\) = 0.95
0.95 x 100 = 95%

Question 18.
Math Journal In a game of darts, Annie hits the bull’s eye 4 times out of 25 times. Benjamin hits the bull’s eye 8 times out of 100 times.
a) Who hits the bull’s eye more times?
Answer:
Benjamin
Explanation:
Benjamin hits the bull’s eye 8 times out of 100 times.
\(\frac{8}{100}\) = 8%

b) Whose aim is more accurate? Justify your answer.
Answer:
Annie’s 16 % > Benjamin8%
Explanation:
Annie hits the bull’s eye 4 times out of 25 times.
= \(\frac{4}{25}\)
= \(\frac{4 X 4}{25 X 4}\)
\(\frac{16}{100}\) = 16%

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 5 Review Test to finish your assignments.

Math in Focus Grade 6 Course 1 A Chapter 5 Review Test Answer Key

Concepts and Skills

Solve.

Question 1.
A factory produces 300 video game disks in 15 minutes. How many video game disks can it produce in 1 minute?
Answer:
20 discs
Explanation:
Video game discs per unit = \(\frac{300}{15}\)
Multiply with common factor on both sides.
Thus, the factory produces 20 discs.

Question 2.
A printer can print 25 pages per minute. At this rate, how long will it take to print 2,000 pages?
Answer:
80 minutes
Explanation:
A printer can print 25 pages per minute = 25 X 4 = 100.
100 X 20 = 2,000, and 4 X 20 = 80.
each minute makes 25 pages, and 4 min = 100,
which means that 8 min = 2,000 (25 x 8 = 2,000)

Problem Solving

Solve. Show your work.

Question 3.
An empty bathtub is filled with water at a rate of 2.5 liters per minute. How long will it take to fill the bathtub with 30 liters of water?
Answer:
12 min
Explanation:
Let x = number of minutes
( 2.5 liters/min )X (x) = 30 liters
x = (30 liters) / (2.5 liters/min)
x = 30/2.5 min
x = 12 min

Question 4.
\(\frac{2}{3}\) cup of oatmeal is needed to make 10 granola bars. How many such granola bars can be made with 20 cups of oatmeal?
Answer:
300 bars
Explanation:
10 granola bars can be made from \(\frac{2}{3}\) cups
now we know we have 20 cups of oatmeal,
write as equivalent ratio
2/3 cup oatmeal      20 cups of oatmeal
——————-  =  ———————
10 granola bars         ? granola bars
10 bars/(2/3 cups) = 15 bars/cup
15 bars/cup X (20cup) = 300 bars

Question 5.
150 grams of fertilizer is required for a land area of 6 square meters.
a) At this rate, how many grams of fertilizer are required for a land area of 13 square meters?
Answer:
13 sq m land area
Explanation:
If 150g of fertilizer can cover 6 sq m of land then,
25 g of fertilizer can cover 1 sq m of land;
For 13 sq m of land = \(\frac{150}{6}\)  ÷  \(\frac{25}{1}\)
= \(\frac{150}{150}\) = 1
1 gram  for 1 sq m land
So, 13 grams for 13 sq m land.

b) For what land area will 850 grams of fertilizer be sufficient?
Answer:
34 sq m land
Explanation:
25g of fertilizer covers 1 sq m of land
So, 850 g of fertilizer sufficient to
= \(\frac{850}{25}\) = 34

Question 6.
A machine can stamp 36 bottle caps in 10 seconds. Copy and complete the table.


a) At this rate, how many bottle caps can the machine stamp in 5 minutes?
Answer:
1,080 stamps
Explanation:
A machine can stamp 216 bottles per minute.
In 5 min, machine can stamp
= 216 x 5 = 1,080

b) At this rate, how many minutes will it take to stamp 24,408 bottle caps?
Answer:
406 bottles
Explanation:
1 min = 60 seconds
24,408 ÷ 60 = 406

Question 7.
The table below shows the charges for using an Internet service.

Nicholas used the Internet service for 16 hours and 40 minutes last month.
a) Under which plan would he have to pay less?
Answer:
Plan A

b) How much less?
Answer: $4
Explanation:
In Plan A
price for 10hrs = $6
price for subsequent half hour = $1
Total time used = 16 hours and 40 minutes
price for the fist 10 hours = $6
remaining time = 16-10hrs = 6hrs and 40minutes
No of half hours in 6 hours and 40 minutes = 6 x 2 + 2 = 12 + 2 = 14
price for the half hours = 14 x $1 = 14$
TOTAL PRICE = $6 + $14 = $20.00
Plan B
price for 12hrs = $4
price for subsequent half hour = $2
Total time used = 16 hours and 40 minutes
price for the fist 12 hours = $4
remaining time = 16-12hrs = 4hrs and 40minutes
No of half hours in 4 hours and 40 minutes = 4 x 2 + 2 = 8 + 2 = 10
price for the half hours = 10 x $2 = 20$
TOTAL PRICE = $4 + $20 = $24.00
There fore PLAN A is the best plan

Question 8.
Ashley took 3 minutes to run a distance of 540 meters from Point X to Point Y. Grace took 2 minutes to run a distance of 480 meters from Point Z to Point Y.
a) Find the speed of each girl.
Answer:
Ashley speed is 180m per min
Grace speed is 240m per min
Explanation:
Speed = \(\frac{Distance}{Time}\)
Speed = \(\frac{540}{3}\)
Speed =180m per minute
Ashley speed is 180m per min

Speed = \(\frac{Distance}{Time}\)
Speed = \(\frac{480}{2}\)
Speed = 240 m/minute
Grace speed is 240m per min

b) Which of the two girls ran faster?

Answer:
Grace speed is more.
Explanation:
From the above information given,
Speed = \(\frac{480}{2}\)
Speed = 240 m/minute
Grace speed is 240m per min

Question 9.
The distance between Town A and Town B is 45 kilometers.
a) If a train travels at a speed of 60 kilometers per hour, how long will it take to travel from Town A to Town B?
Answer:
45 minutes
Explanation:
If the train travels at 60km/hr,
it travels at 1 km/min.
1km = 1min
45 km = ?
So, it takes 45 min to go from A to B.

b) If a train takes 40 minutes to travel from Town A to Town B, what is its speed in kilometers per minute? Round your answer to 1 decimal place.
Answer:
1.1 km/min
Explanation:
We can find the rate by dividing the Distance by the Time
45km / 40 min  = 1.125 km/min
= 1.1 km/min  (rounded)

Question 10.
At 7:30 A.M., a bus left Town P for Town Q at a speed of 60 kilometers per hour. 15 minutes later, a car left Town Q and headed for Town P. The car reached Town P at 10:45 A.M. The bus reached Town Q at noon.
a) What is the distance between Town P and Town Q?
Answer:
270 km
Explanation:
The bus took 4.5 hrs, with speed 60kph town P to town Q
Distance = Speed x Time
= 60 x 4.5
=270 kilometers

b) What was the speed of the car?
Answer:
90 kph
Explanation:
a car started at 7:45 Town Q and headed for Town P. The car reached Town P at 10:45 A.M.
Time =3 hours
Distance= 270 KM
Speed = \(\frac{Distance}{Time}\)
Speed = \(\frac{270}{3}\)
Speed = 90 KMPH

Question 11.
Brian drove 120 miles at speed of 60 miles per hour. He drove the same distance back home at average speed of 40 miles per hour. Brian adds these speeds and divides by 2 to come up with an average speed of 50 miles per hour. What is wrong with his reasoning? Find his average speed.
Answer:
48mph
Explanation:
Time = distance/speed
Joe drives at two different speeds: 60 mph and 40 mph.
Time spent driving 60 mph = 120 miles/60 mph = 2 hours
Time spent driving 40 mph = 120 miles/40 mph = 3 hours
T = t1 + t2 = 5 hours
Average speed = Total Distance/T
= 240/5 = 48mph

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 2 Practice 8 Addition with Regrouping in Ones and Tens to finish your assignments.

Math in Focus Grade 2 Chapter 2 Practice 8 Answer Key Addition with Regrouping in Ones and Tens

Solve.

Question 1.
On Wednesday, 487 people visit the zoo. On Thursday, 135 more people visit the zoo than on Wednesday. How many people visit the zoo on Thursday?
___ people visit the zoo on Thursday.
Answer:
616 people visit the zoo on Thursday.
Explanation:
On Wednesday, 487 people visit the zoo.
On Thursday, 135 more people visit the zoo than on Wednesday.
481 + 135 = 616 people visit the zoo on Thursday

Question 2.
After selling 694 books, Mr. Brown has 276 books left. How many books did he have at first?
He had ___ books at first.
Answer:
He had 970 books at first.
Explanation:
After selling 694 books,
Mr. Brown has 276 books left.
694 + 276 = 970 books that he have at first

Question 3.
A toy company gives away 111 toys in a contest There are 177 toys left. How many toys are there at first?

There are ___ toys at first.
Answer:
There are 288 toys at first.
Explanation:
A toy company gives away 111 toys in a contest
There are 177 toys left.
111 + 177 = 288 toys are there at first

Question 4.
There are 167 dolls in a toy store. The owner buys 533 more dolls. How many dolls are there now?

There are ___ dolls now.
Answer:
There are 700 dolls now.
Explanation:
There are 167 dolls in a toy store.
The owner buys 533 more dolls.
167 + 533 = 700 dolls are there now

Question 5.
Sunshine Camp has 324 boys.
There are 379 girls.
How many campers are at Sunshine Camp?
There are ___ campers at Sunshine Camp.
Answer:
There are 703 campers at Sunshine Camp.
Explanation:
Sunshine Camp has 324 boys.
There are 379 girls.
324 + 379 = 703 campers are at Sunshine Camp

Question 6.
Luke has 548 coins in his collection. Luke has 276 fewer coins than Sam. How many coins does Sam have?

Sam has ___ coins in his collection.
Answer:
Sam has 824 coins in his collection.
Explanation:
Luke has 548 coins in his collection.
Luke has 276 fewer coins than Sam.
548 + 276 = 824 coins that Sam have

Go through the Math in Focus Grade 4 Workbook Answer Key Chapter 3 Practice 2 Multiplying by a 2-Digit Number to finish your assignments.

Math in Focus Grade 4 Chapter 3 Practice 2 Answer Key Multiplying by a 2-Digit Number

Example

15 × 10 = 150 63 × 10 = 630

Question 1.
5 × 60 = 5 × ___ tens
= ____ tens
= ____
Answer:
5 × 60 = 30.

Explanation:
Given that 5 × 60 which is
5 × 60 = 5 ×6 tens
= 3 tens
= 300.

Question 2.
16 × 20 = 16 × ___ tens
= ___ tens
= ___
Answer:
16 × 20 = 320.

Explanation:
Given that 16 × 20 which is
16 × 20 = 16 × 2 tens
= 32 tens
= 320.

Question 3.
33 × 40 = 33 × ___ tens
= ___ tens
= ___
Answer:
33 × 40 = 1320.

Explanation:
Given that 33 × 40 which is
33 × 40 = 33 × 4 tens
= 132 tens
= 1,320.

Question 4.
29 × 30 = 29 × ___ tens
= ___ tens
= ___
Answer:
29 × 30 = 870.

Explanation:
Given that 29 × 30 which is
29 × 30 = 29 × 3 tens
= 87 tens
= 870.

Question 5.
41 × 60 = 41 × ___ × 10
= ___ × 10
= ___
Answer:
41 × 60 = 2,460.

Explanation:
Given that 41 × 60 which is
41 × 60 = 41 × 6 × 10
= 246 × 10
= 2,460.

Question 6.
96 × 40 = 96 × ___ × 4
= ___ × 4
= ___
Answer:
96 × 40 = 3,840.

Explanation:
Given that 96 × 40 which is
96 × 40 = 96 × 10 × 4
= 960 × 4
= 3,840.

Question 7.
618 × 50
= 618 × ___ × 10
= ___ × 10
= ___
Answer:
618 × 50 = 30,900.

Explanation:
Given that 618 × 50 which is
= 618 × 5 × 10
= 3,090 × 10
= 30,900.

Question 8.
752 × 70
= 752 × ___ × 7
= ___ × 7
= ___
Answer:
752 × 70 = 52,640.

Explanation:
Given that 752 × 70 which is
= 752 × 10 × 7
= 7,520 × 7
= 52,640.

What is the French word that has the same meaning as ‘hello’? Match the letters to the products below to find out.

Find each product.

Question 9.
42 × 1o = ________
Answer:
42 × 1o = 420.

Explanation:
The multiplication of 42 × 1o is 420.

Question 10.
786 × 1o = ____
Answer:
786 × 1o = 7,860.

Explanation:
The multiplication of 786 × 1o is 7,860.

Question 11.
16 × 5 = ____
16 × 50 = ___
Answer:
16 × 5 = 80,
16 × 50 = 800.

Explanation:
The multiplication of 16 × 5 is 80 and 16 × 50 is 800.

Question 12.
137 × 6 = ___
137 × 60 = ___
Answer:
137 × 6 = 822,
137 × 60 = 8,220.

Explanation:
The multiplication of 137 × 6 is 822 and 137 × 60 which is 8,220.

Question 13.
23 × 4 = _________
23 × 40 = ___
Answer:
23 × 4 = 92,
23 × 40 = 920.

Explanation:
The multiplication of 23 × 4 is 92 and 23 × 40 which is 920.

Question 14.
405 × 9 = ___
405 × 90 = ___
Answer:
405 × 9 = 3,645,
405 × 90 = 36,450.

Explanation:
The multiplication of 405 × 9 is 3,645 and 405 × 90 which is 36,6450.

Find each product.

Question 15.
70 × 800
7 × 8 = ______
7 × 80 = ______
7 × 800 = _______
So, 700 × 800 = ___
Answer:
7 × 8 = 56,
7 × 80 = 560,
7 × 800 = 5,600,
70 × 800 = 56,000,
700 × 800 = 5,60,000.

Explanation:
The multiplication of 7 × 8 which is 56,so 70 × 800 is 56,000
7 × 80 = 560,
7 × 800 = 5,600,
700 × 800 = 5,60,000.

Question 16.
300 × 90
__________
__________
__________
__________
Answer:
3 × 9 = 27,
3 × 90 = 270,
3 × 900 = 2,700,
30 × 90 = 2,700,
300 × 90 = 27,000.

Explanation:
The multiplication of 300 × 90 which is 27,000. So
3 × 9 = 27,
3 × 90 = 270,
3 × 900 = 2,700,
30 × 90 = 2,700.

Multiply. Find the missing numbers.

Example

Question 17.

Answer:
61 × 86 = 5,246.

Explanation:
The multiplication of 61 × 86 is 5,246.

Question 18.

Answer:
872 × 62 = 54,064.

Explanation:
The multiplication of 872 × 62 is 54,064.

Question 19.

Answer:
709 × 49 = 34,741.

Explanation:
The multiplication of 709 × 49 is 34,741.

Estimate each product. Round each number to its greatest place value.

Example
67 × 35 is about 70 × 40.
70 × 40 = 2,800

Question 20.
61 × 86 is about _____ × ___.
__ × __ = ____
Answer:
Actual product is 61 × 86 = 5,246.
Estimated product is 60 × 90 = 5,400.

Explanation:
Given that 61 × 86 which is about 60 × 90,
60 × 90 = 5,400.

Question 21.
872 × 62 is about _____ × ____.
__ × __ = ___
Answer:
Actual product is 872 × 62 = 54,064.
Estimated product is 870 × 60 = 52,200.

Explanation:
Given that 872 × 62 which is about 870 × 60,
870 × 60 = 52,200.

Question 22.
709 × 49 is about ____ × ___.
__ × __ = ___
Answer:
Actual product is 709 × 49 = 34,741.
Estimated product is 710 × 50 = 35,500.

Explanation:
Given that 709 × 49 which is about 710 × 50,
710 × 50 = 35,500.

Multiply. Then estimate to check that your answers are reasonable. Round each number to its greatest place value.

Example

252 is close to 200, So, the answer is reasonable.

Question 23.
48 × 21 = ____
Answer:
Actual product is 48 × 21 = 1,008.
Esstimated product is 50 × 20 = 1,000.

Explanation:
Given that 48 × 21 which is about 50 × 20,
50 × 20 = 1,000.

Question 24.
196 × 34 = ___
Answer:
Actual product is 196 × 34 = 6,664.
Esstimated product is 200 × 30 = 6,000.

Explanation:
Given that 196 × 34 which is about 200 × 30,
200 × 30 = 6,000.

Question 25.
608 × 73 = ___
Answer:
Actual product is 608 × 73 = 44,384.
Esstimated product is 610 × 20 = 12,200.

Explanation:
Given that 608 × 73 which is about 610 × 20,
610 × 20 = 12,200.

Question 26.
721 × 54 = ___
Answer:
Actual product is 721 × 54 = 38,934.
Esstimated product is 720 × 50 = 36,000.

Explanation:
Given that 721 × 54 which is about 720 × 50,
720 × 50 = 36,000.

Go through the Math in Focus Grade 4 Workbook Answer Key Chapter 3 Practice 3 Modeling Division with Regrouping to finish your assignments.

Math in Focus Grade 4 Chapter 3 Practice 3 Answer Key Modeling Division with Regrouping

Lisa cannot remember the steps to divide.
Help her complete the steps.

Question 1.

Answer:

Question 2.

Answer:

Divide. Then use the quotients to complete the number puzzle.

Down

Question 3.

Answer:
798 ÷ 2 = 399.

Explanation:
The quotient of 798 ÷ 2 is 399.

Question 4.

Answer:
849 ÷ 3 = 283.

Explanation:
The quotient of 849 ÷ 3 is 283.

Question 5.

Answer:
696 ÷ 4 = 174.

Explanation:
The quotient of 696 ÷ 4 is 174.

Across

Question 6.

Answer:
695 ÷ 5 = 139.

Explanation:
The quotient of 695 ÷ 5 is 139.

Question 7.

Answer:
754 ÷ 2 = 377.

Explanation:
The quotient of 754 ÷ 2 is 377.

Question 8.

Answer:
372 ÷ 4 = 93.

Explanation:
The quotient of 372 ÷ 4 is 93.

Divide. Then solve the riddle.

Question 9.

Which pet makes the loudest noise?
Match the letters to the quotients below to find out.

Answer:
The pet that makes loudest noise is Trumpet.

Explanation:

Divide.

Question 10.
516 ÷ 10 = ____
Answer:
516 ÷ 10 = 51 R 16.

Explanation:
By dividing 516 ÷ 10 we will get quotient as 51 with remainder 6.

Question 11.
144 ÷ 3 = ____
Answer:
144 ÷ 3 = 48.

Explanation:
By dividing 144 ÷ 3 we will get quotient as 48.

Question 12.
396 ÷ 4 = ____
Answer:
396 ÷ 4 = 99.

Explanation:
By dividing 396 ÷ 4 we will get quotient as 99.

Question 13.
885 ÷ 5 = ____
Answer:
885 ÷ 5 = 177.

Explanation:
By dividing 885 ÷ 5 we will get quotient as 177.

Look at the steps for dividing a 3-digit number by a 1-digit number.

Example

This shows the steps in division.

Write a number for each instruction box to match the instruction with the correct step for division. The first one has been done for you.

Complete the division.

Question 14.

Then write the steps, using the exercise on page 53 as a guide.
Step 1
___________________
Step 2
___________________
Step 3
___________________
Step 4
___________________
Step 5
___________________
Answer:
752 ÷ 4 = 188.

Explanation:
By dividing 752 ÷ 4 we will get the remainder as 188.

Go through the Math in Focus Grade 4 Workbook Answer Key Chapter 3 Practice 5 Real-World Problems: Multiplication and Division to finish your assignments.

Math in Focus Grade 4 Chapter 3 Practice 5 Answer Key Real-World Problems: Multiplication and Division

Solve. Show your work.

Example
A company has 4,059 people. Their names are listed in alphabetical order and then divided into groups of 5.
How many groups of 5 names are there and how many names are left?
4,059 ÷ 5 = 811R 4
There are 811 groups of 5 names, and 4 names are left.
If the number of men in the company is 600 times the number of names left, how many men are there in the company?
600 × 4 = 2,400
There are 2,400 men in the company.

Question 1.
Factory A produces 326 sweaters in a day. Factory B produces 1 07 more sweaters a day than Factory A.

a. How many sweaters does Factory B produce in a day?
Answer:
433 sweaters.

Explanation:
Given that Factory A produces 326 sweaters in a day and Factory B produces 107 more sweaters a day than Factory A. So the number of sweaters Factory B produce in a day is 326+107 which is 433 sweaters.

b. How many sweaters do the two factories produce in 68 days?

Answer:
The number of sweaters does the two factories produce in 68 days is 51,612 sweaters.

Explanation:
Factory A produces 326 sweaters in a day and Factory B produces 433 sweaters in a day. So the total number of sweaters Factory A and Factory B produce in a day is 326+433 which is 759 sweaters. So the number of sweaters the factories produce in 68 days is 759×68 which is 51,612 sweaters.

Question 2.
In her shop, Lee had a piece of fabric measuring 150 meters. A customer asked her to sew 10 cushion covers, each requiring 3 meters of fabric. Another customer bought 21 meters of the same fabric. How much fabric does Lee have left?
Answer:
The remaining amount left is 99 m.

Explanation:
Given that Lee had a piece of fabric measuring 150 meters and a customer asked her to sew 10 cushion covers and each requiring 3 meters of fabric. So for 10 covers 10×3 which is 30 m. And the amount remaining is 150-30-21 which is 99 m.

Question 3.
A bakery produces 3,000 loaves of bread. The bread is delivered to 75 stores. Of the 75 stores, 67 receive 2,000 loaves of bread altogether. The remaining stores receive an equal number of loaves of bread. How many loaves does each of the remaining stores receive?
Answer:
The remaining stores will receive 125 loaves for 8 stores.

Explanation:
Given that a bakery produces 3,000 loaves of bread and the bread is delivered to 75 stores. Of the 75 stores, 67 receive 2,000 loaves of bread altogether and the remaining loaf is 3,000-2,000 which is 1,000. The remaining stores will be 75-67 which is 8 stores. So the remaining loaves does each of the remaining stores receive will be 1,000÷8 which is 125 loaves.

Question 4.
Before lunch, Cindy packed 850 oranges, and Glen packed 470 fewer oranges than Cindy. Glen went home after lunch, but Cindy went back to work. That afternoon, Cindy packed 3 times as many oranges as Glen had packed in the morning.

a. How many oranges did Glen pack?
Answer:
Glen packed 370 oranges.

Explanation:
Given that before lunch, Cindy packed 850 oranges, and Glen packed 470 fewer oranges than Cindy which is 850-470 which is 370 oranges.

b. How many oranges did Cindy pack altogether?
Answer:
Cindy pack altogether is 1,960 oranges.

Explanation:
In the morning, Cindy packed 850 oranges and in the afternoon Cindy packed 3 times as many oranges as Glen had packed in the morning which is 3×370 which is 1,110 oranges. So Cindy pack altogether is 850+1,110 which is 1,960 oranges.

c. Cindy packed the oranges in bags of 5. How many bags of oranges did Cindy pack?

Answer:
Cindy packed 392 bags.

Explanation:
As Cindy packed the oranges in bags of 5, so the number of bags of oranges did Cindy packed is 1,960÷5 which is 392 bags.

Question 5.
Ms. Edstrom had a budget of $1500 to spend on a table and 6 chairs. The total price was $249 under her budget amount. The table cost 3 times as much as a chair.
Answer:
The table will be $417.

Explanation:
Given that Ms. Edstrom had a budget of $1500 to spend on a table and 6 chairs and the total price was $249 under her budget amount. Let X be the tables and Y be chairs. Then,
X = 3Y as the chairs are 3 times as much as a chair. So
X+6Y = 1,251
3Y+6Y = 1,251
9Y = 1,251
Y = 1,251÷9
= $139.
So the table will be 3×$139 =  $417.

Question 6.
Kamala had 5,026 grams of flour in a canister. She bought a 4,157-gram bag of flour. She poured some flour from the bag to the canister. As a result, the mass of the flour in the canister is now twice the mass of the flour left in the bag. How much flour is in the bag now?
Answer:
The flour left in the bag is 4,157-1,096 which is 3,061 grams.

Explanation:
Given that Kamala had 5,026 grams of flour in a canister and she bought a 4,157-gram bag of flour.
Let X be the number of grams of flour, so
5,026+X = 2(4,157-X)
5,026+X = 8,314 – 2X
2X+X = 8,314 – 5,026
3X = 3,288
X = 3,288÷3
X = 1,096.
So the flour left in the bag is 4,157-1,096 which is 3,061 grams.

Question 7.
Mr. Shea saved $2,500 in April. His monthly salary is twice the amount he saved in April. In May, he saved a certain amount of money. He spent $4,200 more than the amount he saved. How much did he save in May?
Answer:
The savings in the May will be $400.

Explanation:
Given that Mr. Shea saved $2,500 in April and his monthly salary is twice the amount he saved in April which is $2,500×2 which is $5,000. And in May, he saved a certain amount of money and he spent $4,200 more than the amount he saved. Let the savings in May be X, so the expenses in May will be X+4,200. So the amount he saved in May will be
(X)+(X+4,200) = $5,000
2X+4,200 = $5,000
2X = $5,000 – 4,200
2X = 800
X = 800÷2
= $400.
The savings in the May will be $400.

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.