# Simplifying a Fraction: Advanced

A fraction is said to be in simplest form if the highest common factor of its numerator and denominator is 1. Simplifying a fraction is dividing its numerator and denominator with common factors till further division cannot be done and the only common factor they have is 1. A given fraction may be or may not be in the simplest form.

To simplify a fraction or to reduce it to its simplest form, we find the highest common factor (hcf) of both its numerator and denominator. The fraction is reduced to its simplest form by dividing its numerator and denominator by hcf found.

Write the fraction 9/54 in simplest form.

### Solution

**Step 1:**

We need to find the greatest number that divides both 9 and 54 without a remainder. This number is 9 and we do the following.

9/54 = (9 ÷ 9) / (54 ÷ 9) = 1/6

**Step 2:**

The given fraction in simplest form is therefore 1/6.

9/54 and 1/6 are equivalent fractions and have the same value.

Write the fraction 28/20 in the simplest form.

### Solution

**Step 1:**

We need to find the greatest number that divides both 28 and 20 without a remainder. This number is 4 and we do the following.

28/20 = (28 ÷ 4) / (20 ÷ 4) = 7/5

**Step 2:**

The given fraction in simplest form is therefore 7/5.

28/20 and 7/5 are equivalent fractions and have the same value.

Write the fraction 21/49 in simplest form.

### Solution

**Step 1:**

We need to find the greatest number that divides both 21 and 49 without a remainder. This number is 7 and we do the following.

21/49 = (21 ÷ 7) / (49 ÷ 7) = 3/7

**Step 2:**

The given fraction in simplest form is therefore 3/7.

21/49 and 3/7 are equivalent fractions and have the same value.