Fractions that have the same value though they look different are called equivalent fractions. Equivalent fractions have same value, because when we multiply or divide both the numerator and denominator by the same number, the fractions have the same value only.

**Points to remember: **- The Numerator and the denominator must contain a whole number.
- To check whether the fractions are equivalent or not, we need to multiply or divide the numerator and denominator by the same number.
- Do not add or subtract numbers from the numerator and the denominator to make the fraction equivalent.

### Examples on Recognizing Equivalent Fractions

Given below are some of the examples for recognition and reasoning of equivalent fractions:

**Example 1: **

Find the missing number that makes the fraction equivalent?

$\frac{1}{3}$ = $\frac{5}{?}$

**Solution: **

**Step 1:** Since the given fractions are equivalent, we can multiply and divide both the numerator and denominator by the same number.

**Step 2:** As 1(first fraction numerator) times 5 $\rightarrow$ 5(second fraction numerator)

So, multiply both the numerator and the denominator of the first fraction by 5.

**Step 3:** $\frac{1 \times 5}{3 \times 5}$ = $\frac{5}{15}$

**Step 4:** So, the missing number = 15.

**Example 2:**

Find the missing number that makes the fraction equivalent?

$\frac{?}{9}$ = $\frac{2}{3}$

**Solution: **

**Step 1:** Since the given fractions are equivalent, we can multiply and divide both the numerator and denominator by same number.

**Step 2:** As 3(second fraction denominator) times 3 $\rightarrow$ 9(first fraction denominator)

So, multiply both the numerator and the denominator of the second fraction by 3.

**Step 3:** $\frac{2 \times 3}{3 \times 3}$ = $\frac{6}{9}$

**Step 4:** The missing number = 6.

**Example 3:**

Which of the following fraction is equivalent to $\frac{4}{5}$?

a) $\frac{6}{8}$

b) $\frac{5}{6}$

c) $\frac{8}{10}$

d) $\frac{2}{3}$

**Solution: **

**Step 1: **Given fraction: $\frac{4}{5}$

Multiply the numerator and denominator by 2

**Step 2:** $\frac{4 \times 2}{5 \times 2}$ = $\frac{8}{10}$

**Step 3:** Option C is the correct answer.

**Example 4: **

Find the missing number to complete the pattern of equivalent fractions.

$\frac{1}{3} = \frac{2}{6} = \frac{3}{?} = \frac{4}{12}$

**Solution: **

**Step 1:** Let’s equate first fraction and the third fraction $\frac{1}{3} = \frac{3}{?}$

**Step 2:** As 1(first fraction numerator) times 3 $\rightarrow$ 3(third fraction numerator)

So, multiply both the numerator and the denominator of the first fraction by 3

**Step 3:** $\frac{1 \times 3}{3 \times 3}$ = $\frac{3}{9}$

**Step 4:** So, the missing number = 9.

**Example 5:**

Find the missing number to complete the pattern of equivalent fractions.

$\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{?}$

**Solution:**

**Step 1:** Let’s equate first fraction and the fourth fraction