Fractions as Divisors: Worded problems

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

$\frac{3}{7}\times28$

Let's multiply the numerator by 28:

$\frac{3\times28}{7}$

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

$\frac{3\times7\times4}{7}=$

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

$3\times4=12$

First multiply the fraction by the number of flowers:

$\frac{1}{9}\times36$

Then multiply the numerator by 36:

$\frac{1\times36}{9}=\frac{36}{9}$

Next, divide both the numerator and denominator by 9:

$\frac{36:9}{9:9}$

Therefore:

$\frac{4}{1}=4$

Let's split 28 into two fractions:

One that represents the girls

$\frac{3}{7}$

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

$1-\frac{3}{7}=\frac{7}{7}-\frac{3}{7}=\frac{4}{7}$

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

$28\times\frac{4}{7}$

Let's multiply the numerator by 28:

$\frac{4\times28}{7}$

Let's divide both the numerator and denominator by 7

$\frac{4\times28:7}{7:7}=$

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

$\frac{4\times4}{1}=4\times4=16$

Let's split 36 into two fractions:

One that represents the white flowers

$\frac{1}{9}$

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

$1-\frac{1}{9}=\frac{9}{9}-\frac{1}{9}=\frac{8}{9}$

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

$\frac{8}{9}\times36$

Let's multiply the numerator by 36:

$\frac{8\times36}{9}$

We'll divide both the numerator and denominator by 9

$\frac{8\times36:9}{9:9}=$

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

$\frac{8\times4}{1}=8\times4=32$

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

$45\times\frac{1}{3}=\frac{45\times1}{3}=\frac{45}{3}$

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

$\frac{45:3}{3:3}=\frac{15}{1}=15$

Let's split 36 into three fractions:

The first one represents the chocolate cakes

$\frac{1}{3}$

The second one represents the cheesecakes

$\frac{1}{3}$

And the third one representing the strawberry cakes remains unknown for now.

Let's find the unknown in the following way.

1 is the whole that represents the whole, so we'll subtract from it the two fractions we already know:

$1-\frac{1}{3}-\frac{1}{3}=$

$1=\frac{3}{3}$

We'll write the exercise like this:

$\frac{3}{3}-\frac{1}{3}-\frac{1}{3}=\frac{3-1-1}{3}=\frac{1}{3}$

We found the fraction that represents the strawberry cakes.

Now let's find the number representing each fraction:

We'll multiply the number of cakes by the fraction representing the chocolate/cheese/strawberry cakes:

$\frac{1}{3}\times45=$

Let's multiply the numerator by 45:

$\frac{1\times45}{3}=$

Let's divide both the numerator and denominator by 3

$\frac{45:3}{3:3}=\frac{15}{1}=15$

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

$\frac{3}{5}\times15=$

We'll multiply the numerator by 15:

$\frac{3\times15}{5}=$

We'll divide both the numerator and denominator by 5

$\frac{3\times15:5}{5:5}=$

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

$\frac{3\times3}{1}=\frac{9}{1}=9$