Practice the problems of Math in Focus Grade 4 Workbook Answer Key Chapter 6 Practice 8 Real-World Problems: Fractions to score better marks in the exam.

## Math in Focus Grade 4 Chapter 6 Practice 8 Answer Key Real-World Problems: Fractions

**Solve. Show your work.**

Example

Ali bought three pockets of dried fruit.

What is the total weight of all three packets of dried fruit?

The total weight of aB three packets of dried fruit is \(\frac{5}{6}\) pound.

**Solve. Show your work.**

Question 1.

Jim had three waffles.

He ate \(\frac{1}{6}\) of one waffle, and \(\frac{2}{3}\) of another waffle.

How many waffles were left?

Answer:

Amount of waffles were left = 13 ÷ 6 or \(\frac{13}{6}\)

Explanation:

Amount of waffles he ate = \(\frac{1}{6}\) of one waffle + \(\frac{2}{3}\) of another waffle.

Amount of waffles were left = (1 – \(\frac{1}{6}\) ) + (1 – \(\frac{2}{3}\)) + 1

= [(6-1) ÷ 6] + [(3-2) ÷ 3] + 1

= \(\frac{5}{6}\) + \(\frac{1}{3}\) + 1

= [(5 + 2) ÷ 6] + 1

= \(\frac{7}{6}\) + 1

= (7 + 6) ÷ 6

= 13 ÷ 6 or \(\frac{13}{6}\)

Question 2.

A grocery store has 5 pounds of granola. One customer buys \(\frac{2}{3}\) pound of granola and another buys \(\frac{5}{6}\) pound. After these purchases, how much granola is left?

Answer:

Number of pounds left over = 5 ÷ 3 or \(\frac{5}{3}\)

Explanation:

Number of pounds one customer buys = \(\frac{2}{3}\) of granola

=> \(\frac{2}{3}\) × 5

=> \(\frac{10}{3}\)

Number of pounds another customer buys = \(\frac{5}{6}\)

Total number of pounds granola grocery store has = 5.

Total number of pounds granola grocery store has = Number of pounds one customer buys + Number of pounds another customer buys + Number of pounds left over

=> 5 = \(\frac{10}{3}\) + \(\frac{5}{6}\) + Number of pounds left over

=> 5 = [(20 + 5) ÷ 6] + Number of pounds left over

=> 5 = \(\frac{10}{3}\) + Number of pounds left over

=> 5 – \(\frac{10}{3}\) = Number of pounds left over

=> (15 – 10) ÷ 3 = Number of pounds left over

=> \(\frac{5}{3}\) or 5 ÷ 3 = Number of pounds left over

Question 3.

Karen jogs \(\frac{1}{2}\) mile. Selma jogs \(\frac{1}{4}\) mile more than Karen. Lena jogs \(\frac{3}{4}\) mile more than Selma. How far does Lena jog?

Answer:

Number of miles Lena jogs = \(\frac{3}{2}\)

Explanation:

Number of miles Karen jogs = \(\frac{1}{2}\)

Selma jogs \(\frac{1}{4}\) mile more than Karen.

=> Number of miles Selma jogs = Number of miles Karen jogs + \(\frac{1}{4}\)

= \(\frac{1}{2}\) + \(\frac{1}{4}\)

= (2 + 1) ÷ 4

= \(\frac{3}{4}\)

Lena jogs \(\frac{3}{4}\) mile more than Selma.

=> Number of miles Lena jogs = Number of miles Selma jogs + \(\frac{3}{4}\)

= \(\frac{3}{4}\) + \(\frac{3}{4}\)

= \(\frac{6}{4}\)

= \(\frac{3}{2}\)

Question 4.

Jeremy has 18 marbles. He loses 6 of them.

a. What fraction of the marbles does he lose?

Answer:

Fraction of the marbles he lost = 1 ÷ 3 or \(\frac{1}{3}\) or 0.33.

Explanation:

Total number of marbles Jeremy has = 18.

Number of marbles he loses = 6.

Fraction of the marbles he lost = Number of marbles he loses ÷ Total number of marbles Jeremy has

= 6 ÷ 18

= 1 ÷ 3 or \(\frac{1}{3}\) or 0.33.

b. What fraction of the marbles does he have left?

Answer:

Fraction of the marbles does he have left = 2 ÷ 3 or \(\frac{2}{3}\) or 0.67.

Explanation:

Total number of marbles Jeremy has = 18.

Number of marbles he loses = 6.

Number of the marbles he have left = Total number of marbles Jeremy has – Number of marbles he loses

= 18 – 6

= 12.

Fraction of the marbles does he have left = Number of the marbles he have left ÷ Total number of marbles Jeremy has

= 12 ÷ 18

= 2 ÷ 3 or \(\frac{2}{3}\) or 0.67.

Question 5.

Mrs. Yan buys 4 red tulips and 5 yellow tulips.

a. What fraction of the tulips are red?

Answer:

Fraction of the tulips are red = 4 ÷ 9 or \(\frac{4}{9}\)

Explanation:

Number of red tulips Mrs. Yan buys = 4.

Number of yellow tulips Mrs. Yan buys = 5.

Total number of tulips Mrs. Yan buys = Number of red tulips Mrs. Yan buys + Number of yellow tulips Mrs. Yan buys

= 4 + 5

= 9.

Fraction of the tulips are red = Number of red tulips Mrs. Yan buys ÷ Total number of tulips Mrs. Yan buys

= 4 ÷ 9 or \(\frac{4}{9}\)

b. What fraction of the tulips are yellow?

Answer:

Fraction of the tulips are yellow = 5 ÷ 9 or \(\frac{5}{9}\)

Explanation:

Number of red tulips Mrs. Yan buys = 4.

Number of yellow tulips Mrs. Yan buys = 5.

Total number of tulips Mrs. Yan buys = Number of red tulips Mrs. Yan buys + Number of yellow tulips Mrs. Yan buys

= 4 + 5

= 9.

Fraction of the tulips are yellow = Number of yellow tulips Mrs. Yan buys ÷ Total number of tulips Mrs. Yan buys

= 5 ÷ 9 or \(\frac{5}{9}\)

Question 6.

Charles owns 3 cats, 4 goldfish, and some parakeets. Altogether, he has 10 pets.

a. What fraction of his pets are goldfish?

Answer:

Fraction of his pets are goldfish = 2 ÷ 5 or \(\frac{2}{5}\)

Explanation:

Number of cats Charles owns = 3.

Number of goldfish Charles owns = 4.

Total number of pets Charles owns = 10.

Fraction of his pets are goldfish = Number of goldfish Charles owns ÷ Total number of pets Charles owns

= 4 ÷ 10

= 2 ÷ 5 or \(\frac{2}{5}\)

b. What fraction of his pets are parakeets?

Answer:

Fraction of his pets are parakeets = 3 ÷ 10 or \(\frac{3}{10}\)

Explanation:

Number of cats Charles owns = 3.

Number of goldfish Charles owns = 4.

Total number of pets Charles owns = 10.

=> Total number of pets Charles owns = Number of parakeets Charles owns + Number of cats Charles owns + Number of goldfish Charles owns

=> 10 = ?? + 3 + 4

=> 10 = ?? + 7

=> 10 – 7 = ??

=> 3 = ??.

Fraction of his pets are parakeets = Number of parakeets Charles owns ÷ Total number of pets Charles owns

= 3 ÷ 10 or \(\frac{3}{10}\)

Question 7.

Rick had $20. He spent $10 on food, $6 on a movie ticket and saved the rest.

a. How much money did he save?

Answer:

Amount of money he saved = $4.

Explanation:

Total amount of money Rick had = $20.

Amount of money Rick had spent on food = $10.

Amount of money Rick had spent on a movie ticket = $6.

Amount of money he saved = Total amount of money Rick had – (Amount of money Rick had spent on food + Amount of money Rick had spent on a movie ticket)

= $20 – ($10 + $6)

= $20 – $16

= $4.

b. What fraction of the total amount did he save?

Answer:

Fraction of the total amount did he save = 1 ÷ 5 or \(\frac{1}{5}\)

Explanation:

Total amount of money Rick had = $20.

Amount of money he saved = $4.

Fraction of the total amount did he save = Amount of money he saved ÷ Total amount of money Rick had

= 4 ÷ 20

= 1 ÷ 5 or \(\frac{1}{5}\)

Question 8.

There are 24 students in a class, and \(\frac{2}{3}\) of the students in the class are boys. How many students are girls?

Answer:

Number of girls in the class = 8.

Explanation:

Total number of students in the class = 24.

\(\frac{2}{3}\) of the students in the class are boys.

=> Number of boys in the class = Number of students in the class × \(\frac{2}{3}\)

= 24 × \(\frac{2}{3}\)

= 8 × 2

= 16.

Number of girls in the class = Total number of students in the class – Number of boys in the class

= 24 – 16

= 8.

Question 9.

One morning, The Shirt Shop sold 15 T-shirts.

Of the T-shirts sold, \(\frac{1}{5}\) were gray. The rest were white. How many white T-shirts were sold?

Answer:

Number of white T-shirts were sold = 12.

Explanation:

Number of T-shirts The Shirt Shop sold One morning = 15.

Of the T-shirts sold, \(\frac{1}{5}\) were gray.

=> Number of gray T-shirts sold = Number of T-shirts The Shirt Shop sold One morning × \(\frac{1}{5}\)

= 15 × \(\frac{1}{5}\)

= 3 × 1

= 3.

Number of white T-shirts were sold = Number of T-shirts The Shirt Shop sold One morning – Number of gray T-shirts sold

= 15 – 3

= 12.

Question 10.

A chef bought some green and red peppers. She bought 18 green peppers, which was \(\frac{3}{4}\) of the total number.

a. How many red peppers did she buy?

Answer:

Number of red peppers she buys = 6.

Explanation:

Number of green peppers She bought = 18.

She bought 18 green peppers, which was \(\frac{3}{4}\) of the total number.

Let the total number of peppers she buys be X.

Number of green peppers She bought = Total number of peppers she buys × \(\frac{3}{4}\)

= 18 = X × \(\frac{3}{4}\)

=> 18 × \(\frac{4}{3}\) = X

=> 6 × 4 = X

=> 24 = X.

Number of red peppers she buys = Total number of peppers she buys – Number of green peppers She bought

= 24 – 18

= 6.

b. How many peppers did she buy altogether?

Answer:

Total number of peppers she buys = 24.

Explanation:

Number of green peppers She bought = 18.

She bought 18 green peppers, which was \(\frac{3}{4}\) of the total number.

Let the total number of peppers she buys be X.

Number of green peppers She bought = Total number of peppers she buys × \(\frac{3}{4}\)

= 18 = X × \(\frac{3}{4}\)

=> 18 × \(\frac{4}{3}\) = X

=> 6 × 4 = X

=> 24 = X.

Question 11.

There were 25 melons in a box at the grocery store.

The store sold \(\frac{3}{5}\) of the melons.

How many melons were sold?

Answer:

Number of melons sold = 15.

Explanation:

Number of melons in a box at the grocery store = 25.

The store sold \(\frac{3}{5}\) of the melons.

=> Number of melons sold = Number of melons in a box at the grocery store × \(\frac{3}{5}\)

= 25 × \(\frac{3}{5}\)

= 5 × 3

= 15.

Question 12.

Ava read \(\frac{1}{4}\) of a book on Monday, and \(\frac{1}{5}\) of it on Tuesday. There are 80 pages in the book. How many pages did she read altogether on both days?

Answer:

Number of pages she read altogether on both days = 36.

Explanation:

Number of pages in the book = 80.

Ava read \(\frac{1}{4}\) of a book on Monday.

=> Number of pages Ava read on Monday = Number of pages in the book × \(\frac{1}{4}\)

= 80 × \(\frac{1}{4}\)

= 20 × 1

= 20.

Ava read \(\frac{1}{5}\) of it on Tuesday.

> Number of pages Ava read on Tuesday = Number of pages in the book × \(\frac{1}{5}\)

= 80 × \(\frac{1}{5}\)

= 16 × 1

= 16.

Number of pages she read altogether on both days = Number of pages Ava read on Monday + Number of pages Ava read on Tuesday

= 20 + 16

= 36.