Examples with solutions for Fractions as Divisors: Worded problems

Exercise #1

In a garden there are 36 flowers, 19 \frac{1}{9} of which are white, while the rest are red.

How many white flowers are there in the garden?

Video Solution

Step-by-Step Solution

Let's write the following exercise, we'll multiply the fraction by the number of flowers:

19×36 \frac{1}{9}\times36

We'll multiply the numerator by 36:

1×369=369 \frac{1\times36}{9}=\frac{36}{9}

We'll divide both the numerator and denominator by 9:

36:99:9 \frac{36:9}{9:9}

We get:

41=4 \frac{4}{1}=4

Answer

4 4

Exercise #2

In a ninth grade class, there are 28 students, 37 \frac{3}{7} of whom are female.

How many females are in the class?

Video Solution

Step-by-Step Solution

Let's write the following exercise, we'll multiply the fraction by the number of students:

37×28 \frac{3}{7}\times28

Let's multiply the numerator by 28:

3×287 \frac{3\times28}{7}

Let's solve the exercise in the numerator, we'll break down 28 into a smaller multiplication exercise:

3×7×47= \frac{3\times7\times4}{7}=

Let's reduce the 7 in the numerator and denominator of the fraction and we'll get:

3×4=12 3\times4=12

Answer

12 12

Exercise #3

In a garden there are 36 flowers, 19 \frac{1}{9} of which are white, while the rest are red.

How many red flowers are there in the garden?

Video Solution

Step-by-Step Solution

Let's split 36 into two fractions:

One that represents the white flowers

19 \frac{1}{9}

Now let's find the fraction that represents the red flowers:

119=9919=89 1-\frac{1}{9}=\frac{9}{9}-\frac{1}{9}=\frac{8}{9}

Now let's multiply the number of flowers by the fraction that represents the red flowers:

89×36 \frac{8}{9}\times36

Let's multiply the numerator by 36:

8×369 \frac{8\times36}{9}

We'll divide both the numerator and denominator by 9

8×36:99:9= \frac{8\times36:9}{9:9}=

Let's first solve the division problems in the numerator and denominator and we get:

8×41=8×4=32 \frac{8\times4}{1}=8\times4=32

Answer

32 32

Exercise #4

There are 28 students in a 9th grade class. 37 \frac{3}{7} of the students are female.

How many male students are there in the class?

Video Solution

Step-by-Step Solution

Let's split 28 into two fractions:

One that represents the girls

37 \frac{3}{7}

Now let's find the fraction that represents the boys:

137=7737=47 1-\frac{3}{7}=\frac{7}{7}-\frac{3}{7}=\frac{4}{7}

Now let's multiply the number of students by the fraction that represents the boys:

28×47 28\times\frac{4}{7}

Let's multiply the numerator by 28:

4×287 \frac{4\times28}{7}

Let's divide both the numerator and denominator by 7

4×28:77:7= \frac{4\times28:7}{7:7}=

Let's first solve the division exercises in the numerator and denominator and we'll get:

4×41=4×4=16 \frac{4\times4}{1}=4\times4=16

Answer

16 16

Exercise #5

45 cakes are baked each morning in a bakery.


13 \frac{1}{3} of the cakes are chocolate, 13 \frac{1}{3} are vanilla, while the rest are strawberry.

How many chocolate cakes are baked each day?

Video Solution

Step-by-Step Solution

Let's begin by multiplying the total number of cakes by the fraction representing the number of chocolate cakes:

45×13=45×13=453 45\times\frac{1}{3}=\frac{45\times1}{3}=\frac{45}{3}

We then proceed to divide both the numerator and denominator by 3 as follows:

45:33:3=151=15 \frac{45:3}{3:3}=\frac{15}{1}=15

Answer

15 15

Exercise #6

Graciela bought 15 apples and distributed them to give to her mother 35 \frac{3}{5} , to her sister15 \frac{1}{5} and the rest for herself.

How many apples did Graciela's mother receive?

Video Solution

Step-by-Step Solution

Let's multiply the number of apples by the fraction representing the number of apples she gave to her mother:

35×15= \frac{3}{5}\times15=

We'll multiply the numerator by 15:

3×155= \frac{3\times15}{5}=

We'll divide both the numerator and denominator by 5

3×15:55:5= \frac{3\times15:5}{5:5}=

Let's first solve the division operations in the numerator and denominator, and we'll get:

3×31=91=9 \frac{3\times3}{1}=\frac{9}{1}=9

Answer

9 9

Exercise #7

In the bakery, they bake 45 cakes in the morning, 13 \frac{1}{3} of which are chocolate 13 \frac{1}{3} are cheese, while the rest with strawberry jam.

How many cakes with strawberry jam are baked every morning?

Video Solution

Answer

15 15