Equivalent fraction of a fraction means a fraction, which on simplification becomes equal to the main fraction. That is, they have the same value.

Those fractions, which on simplification (when the numerator and denominator cannot be divided any further by their greatest common factor), gives the same resulting fraction as the original one, are known as equivalent fractions.

**Word Problems on Equivalent Fractions:**

Given below are some of the word problems on equivalent fractions.

**Example 1:**

Peter has 39 dollars. He wants to save one-third of his money for a trip. How many dollars should he set aside? (Use 39 as the denominator and find an equivalent fraction to one-third.)

**Solution:**

We can write this as $\frac{1}{3}= \frac{x}{39}$

3x = 39

Dividing each side by 3, we get

x = 13 dollars.

**Example 2: **

Emily has 48 dollars. She wants to spend one-fourth of his money in the gaming zone. How many dollars should she spend? (Use 48 as the denominator and find an equivalent fraction to $\frac{1}{4}$.)

**Solution: **

We can write this as $\frac{1}{4} = \frac{x}{48}$

4x = 48

Dividing each side by 4, we get

x = 12 dollars.

Emily can spend 12 dollars in the gaming zone.

**Example 3: **

Kelly has 100 dollars. She wants to give one-tenth of her money for a social cause. How many dollars should she give?

**Solution: **

We can write this as $\frac{1}{10} = \frac{x}{100}$.

10x = 100.

Dividing each side by 10, we get

x = 10 dollars.

Kelly gives 10 dollars.

Those fractions, which on simplification (when the numerator and denominator cannot be divided any further by their greatest common factor), gives the same resulting fraction as the original one, are known as equivalent fractions.

The process to make equivalent fractions of a fraction is to
multiply the denominator and then the numerator with the same multiples, like starting from 2, 3, 4 and so on. We can multiply the denominator and numerator both with the same multiple, to get the resulting equivalent fraction.

Equivalent fractions word problems are very important to solve in our day to day
real life problems. Because, if at any time, we need to know, out of a total of say 400, we want to have one fourth of our money to spend on the donation for a social cause. Here, we will use 400 as a denominator and will find an equivalent fraction of one fourth, giving the result as 100. Similarly, we can use division instead of
multiplication to find out the equivalent fractions, which also follows the same process and concept as explained above.

Given below are some of the word problems on equivalent fractions.

Peter has 39 dollars. He wants to save one-third of his money for a trip. How many dollars should he set aside? (Use 39 as the denominator and find an equivalent fraction to one-third.)

We can write this as $\frac{1}{3}= \frac{x}{39}$

3x = 39

Dividing each side by 3, we get

x = 13 dollars.

Emily has 48 dollars. She wants to spend one-fourth of his money in the gaming zone. How many dollars should she spend? (Use 48 as the denominator and find an equivalent fraction to $\frac{1}{4}$.)

We can write this as $\frac{1}{4} = \frac{x}{48}$

4x = 48

Dividing each side by 4, we get

x = 12 dollars.

Emily can spend 12 dollars in the gaming zone.

Kelly has 100 dollars. She wants to give one-tenth of her money for a social cause. How many dollars should she give?

We can write this as $\frac{1}{10} = \frac{x}{100}$.

10x = 100.

Dividing each side by 10, we get

x = 10 dollars.

Kelly gives 10 dollars.

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