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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 part of a whole.

## Adding two fractions with the same denominators: • Step 2: Keep the denominator the same.
• Step 3: Simplify the answer (if possible).

### Example:

Find $\frac{7}{12} + \frac{1}{12}$.

### Solution:

Step1:

Add numerators and keep the denominator the same

$\frac{7 + 1}{12}$

Step2:

$\frac{7 + 1}{12} = \frac{8}{12} = \frac{2}{3}$

Answer:$\frac{2}{3}$

### Adding 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: Add the fractions.
• Step 3: Simplify the answer (if possible).

### Example:

Find: $\frac{2}{3} + \frac{1}{5}$.

### Solution:

Step1:

Since the denominators are not alike, find a common denominator by multiplying them

3 x 5 = 15

Step2:

Rewrite each fraction using the common denominator (15)

$\frac{2 \times 5}{3 \times 5} = \frac{10}{15}$

$\frac{1 \times 3}{1 \times 3} = \frac{3}{15}$

Step3:

Add fractions by adding the numerators and keeping the denominator the same.

$\frac{10 + 3}{15} = \frac{13}{15}$

Answer: $\frac{2}{3} + \frac{1}{5} = \frac{13}{15}$