**Reducing the Equivalent Fractions:** In order to reduce the fraction to the lowest terms, we have to divide the numerator and denominator with the same number. Firstly, students must know what is meant by an equivalent fraction from here. Here we will discuss reducing the equivalent fractions to the lowest terms in which the numerator and denominator are as small as possible. If you learn the concept in-depth you will be able to recognize the equivalent fraction and reduce them into the lowest terms.

**Also, Refer:**

## What is meant by Equivalent Fraction?

Fractions that reduce to the same number and have an equal value is called an equivalent fraction. They are fractions that name the same amount in different ways like H.C.F. The equivalent fractions of \(\frac{4}{8}\), \(\frac{8}{16}\) is \(\frac{1}{2}\)

### How to Reduce Equivalent Fractions?

There are two methods to reduce the fractions to the lowest terms. Methods of Reducing Fractions to Lowest Terms are as follows.

**Method 1: Dividing out common primes.**

1. Write the numerator and denominator as the product of prime numbers.

2. Divide the numerator and denominator by each of the common prime factors which are known as canceling common factors.

3. The product of the remaining factors in the numerator and the product of the remaining factors of the denominator are relatively prime, and this fraction is reduced to the lowest terms.

**Method 2: Dividing out common factors**

1. Mentally divide the numerator and the denominator by a factor that is common to each.

2. Continue this process until the numerator and denominator are relatively prime factors.

**Example:**

Reduce the fraction \(\frac{2}{50}\) to its lowest terms?

**Solution:**

First, we have to find the H.C.F. of 2 and 50.

The factors of 50 are 50, 25, 10, 5, 2, 1.

The common factors of 2 and 50 are 2, 1, intersecting the two sets above.

In the intersection factors of 2 ∩ factors of 50, the greatest element is 2.

Therefore, the greatest common factor of 2 and 50 is 2.

So, divide the above fraction by 2.

\(\frac{2}{50}\) = \(\frac{1}{25}\)

The H.C.F of the numerator is 1 and denominator is 25.

So, the lowest term is \(\frac{1}{25}\).

Therefore the fraction \(\frac{2}{50}\) can be expressed in lowest terms as \(\frac{1}{25}\).

### Reducing the Equivalent Fractions Examples

**Example 1.**

Reduce the fraction \(\frac{6}{18}\) to its lowest terms?

**Solution:**

Given the fraction \(\frac{6}{18}\)

6 and 18 are the multiples of 6.

So, we have to multiply and divide by 6 with the numerator and denominator.

\(\frac{6}{18}\) × \(\frac{6}{6}\) = \(\frac{1}{3}\)

1 and 3 are the prime factors.

So, the equivalent fraction is \(\frac{1}{3}\).

Therefore the fraction \(\frac{6}{18}\) to its lowest terms is \(\frac{1}{3}\)

**Example 2.**

Reduce the fraction \(\frac{9}{18}\) to its lowest terms?

**Solution:**

Given the fraction \(\frac{6}{18}\)

9 and 18 are the multiples of 9.

So, we have to multiply and divide by 9 with the numerator and denominator.

\(\frac{9}{18}\) × \(\frac{9}{9}\) = \(\frac{1}{2}\)

1 and 2 are the prime factors.

So, the equivalent fraction is \(\frac{1}{2}\).

Therefore the fraction \(\frac{9}{18}\) to its lowest terms is \(\frac{1}{2}\)

**Example 3.**

Reduce the fraction \(\frac{17}{34}\) to its lowest terms?

**Solution:**

Given the fraction \(\frac{17}{34}\)

17 and 34 are the multiples of 17.

So, we have to multiply and divide by 17 with the numerator and denominator.

\(\frac{17}{34}\) × \(\frac{17}{17}\) = \(\frac{1}{2}\)

1 and 2 are the prime factors.

So, the equivalent fraction is \(\frac{1}{2}\).

Therefore the fraction \(\frac{17}{34}\) to its lowest terms is \(\frac{1}{2}\)

**Example 4.**

Reduce the fraction \(\frac{4}{16}\) to its lowest terms?

**Solution:**

Given the fraction \(\frac{4}{16}\)

4 and 16 are the multiples of 4.

So, we have to multiply and divide by 4 with the numerator and denominator.

\(\frac{4}{16}\) × \(\frac{4}{4}\) = \(\frac{1}{4}\)

1 and 4 are the least possible factors.

So, the equivalent fraction is \(\frac{1}{4}\).

Therefore the fraction \(\frac{4}{16}\) to its lowest terms is \(\frac{1}{4}\)

**Example 5.**

Reduce the fraction \(\frac{3}{15}\) to its lowest terms?

**Solution:**

Given the fraction \(\frac{3}{15}\)

3 and 15 are the multiples of 3.

So, we have to multiply and divide by 3 with the numerator and denominator.

\(\frac{3}{15}\) × \(\frac{3}{3}\) = \(\frac{1}{5}\)

1 and 5 are the prime factors.

So, the equivalent fraction is \(\frac{1}{5}\).

Therefore the fraction \(\frac{3}{15}\) to its lowest terms is \(\frac{1}{5}\)

### FAQs on Reducing the Equivalent Fractions

**1. How do you reduce equivalent fractions?**

You can divide the numerator and the denominator of the equivalent fractions by their H.C.F. to form its lowest terms.

**2. How do you change an equivalent fraction?**

Multiply both the numerator and denominator of a fraction by the same whole number. As long as you multiply both the top and bottom of the fraction by the same number, you won’t change the value of the fraction, and you will create an equivalent fraction.

**3.How do you reduce a fraction to a fraction in the lowest terms?**

Break down both the numerator and denominator into their prime factors. Cross out any common factors. Multiply the remaining numbers to get the reduced fraction.