# Subtracting fractions

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A fraction is made up of an integer numerator (the top number) and a non-zero integer denominator (the bottom number) and represents a portion of a whole.

## Subtracting two fractions with the same denominators:

• Step 1: Subtract numerators.
• Step 2: Keep the denominator the same.
• Step 3: Simplify the answer (if possible).

### Example:

Find: $\frac{7}{9} - \frac{2}{9}$

### Solution:

Step1:

Subtract numerators and keep the denominator the same

$\frac{7 - 2}{9}$

Step2:

$\frac{7 - 2}{9} = \frac{5}{9}$

Answer: $\frac{5}{9}$

## Subtracting two fractions with unlike denominators:

• Step 1: Write equivalent fractions with a common denominator. You can do it using one of these methods:
• multiply the numerator and the denominator of each fraction by the other fraction’s denominator, or
• use the least common denominator (LCD). The LCD is the least common multiple (LCM) of the denominators.
• Step 2: Subtract the fractions.
• Step 3: Simplify the answer (if possible).

### Example:

Find: $5\frac{3}{4} - 1\frac{7}{10}$

### Solution:

Step1:

Rewrite the problem as

$\frac{23}{4} - \frac{17}{10}$

Step2:

Evaluate the least common denominator. As the LCM of 4 and 10 is 20, the LCD is 20. Rewrite the difference using the LCD

$\frac{23}{4} - \frac{17}{10} = \frac{23 \cdot 5}{4 \cdot 5} - \frac{17 \cdot 2}{10 \cdot 2}$

Step3:

Multiply

$\frac{115}{20} - \frac{34}{20}$

Step4:

Simplify

$\frac{81}{20} = 4\frac{1}{20}$

Answer: $4\frac{1}{20}$