Addition and subtraction of fractions of the same denominator

Rule: To add fractions with the same denominator, add the numerators (top numbers) together. Keep the denominator the same.

Steps:

1. Check that the denominators are the same.
2. Add the numerators.
3. Write the answer with the same denominator.

Worked Example

$\frac{3}{8} + \frac{4}{8} = ?$

Solution

Step 1: The denominators are both 8. ✓

Step 2: Add the numerators: 3 + 4 = 7

Step 3: Write the answer: $\frac{7}{8}$

So, $\frac{3}{8} + \frac{4}{8} = \frac{7}{8}$

Another Example from Real Life

Yona poured $\frac{2}{9}$ of water into a tank, and Halima poured $\frac{3}{9}$ of water into the same tank. What fraction of the tank is now filled?

$\frac{2}{9} + \frac{3}{9} = \frac{2+3}{9} = \frac{5}{9}$

Answer: $\frac{5}{9}$ of the tank is filled.

Rule: To subtract fractions with the same denominator, subtract the numerators. Keep the denominator the same.

Steps:

1. Check that the denominators are the same.
2. Subtract the numerators.
3. Write the answer with the same denominator.

Worked Example

$\frac{7}{10} - \frac{3}{10} = ?$

Solution

Step 1: The denominators are both 10. ✓

Step 2: Subtract the numerators: 7 - 3 = 4

Step 3: Write the answer: $\frac{4}{10}$

So, $\frac{7}{10} - \frac{3}{10} = \frac{4}{10}$

Another Example from Real Life

A farmer planted oranges on $\frac{5}{8}$ of his farm. The rest of the farm was left unused. What fraction of the farm was not used?

The whole farm = $\frac{8}{8}$

$\frac{8}{8} - \frac{5}{8} = \frac{8-5}{8} = \frac{3}{8}$

Answer: $\frac{3}{8}$ of the farm was not used.

Addition

1. $\frac{1}{4} + \frac{2}{4} =$
2. $\frac{2}{5} + \frac{2}{5} =$
3. $\frac{3}{6} + \frac{2}{6} =$

Subtraction

1. $\frac{5}{8} - \frac{2}{8} =$
2. $\frac{4}{5} - \frac{1}{5} =$
3. $\frac{6}{7} - \frac{3}{7} =$

• The denominator (bottom number) never changes when adding or subtracting fractions with the same denominator.
• Only add or subtract the numerators (top numbers).
• Always make sure the denominators are the same before you add or subtract.
• A fraction like $\frac{4}{4}$ means one whole (1).

In Tanzania, farmers and traders use fractions when selling crops or goods. For example, a market vendor at Mwanza or Dar es Salaam might sell $\frac{3}{5}$ of a bag of maize in the morning and $\frac{1}{5}$ in the afternoon. By adding these fractions ($\frac{3}{5} + \frac{1}{5} = \frac{4}{5}$), the vendor knows that $\frac{4}{5}$ of the bag has been sold and $\frac{1}{5}$ remains. This helps them keep track of their stock and plan what to sell next.