Equivalent Fractions • Topic 3 of 3

Add and Subtract Fractions with Same Denominator

When two fractions have the same denominator, adding or subtracting them is easy: keep the denominator and just add (or subtract) the numerators.

$$\frac{a}{d}+\frac{b}{d}=\frac{a+b}{d}\qquad\qquad \frac{a}{d}-\frac{b}{d}=\frac{a-b}{d}$$

Why the bottom stays the same: the denominator tells the size of each piece. When we put pieces together or take some away, the size of a piece does not change — only how many we have changes. So only the numerators are added or subtracted.

Examples: $\tfrac15+\tfrac25=\tfrac35$ and $\tfrac45-\tfrac15=\tfrac35$.

Always simplify the answer when you can:

$$\frac26=\frac{2\div2}{6\div2}=\frac13$$

Improper fractions. If the top becomes bigger than the bottom, the answer is more than one whole. For example $\tfrac35+\tfrac45=\tfrac75$, which is the same as $1\tfrac25$.

Common mistake to avoid: do not add the denominators. $\tfrac15+\tfrac25$ is $\tfrac35$, never $\tfrac{3}{10}$.

ADD / SUBTRACT with the SAME denominator:

   keep the bottom, add (or subtract) the tops

     1     2     1 + 2     3
    --- + --- = ------- = ---
     5     5       5       5

     4     1     4 - 1     3
    --- - --- = ------- = ---
     5     5       5       5

Then SIMPLIFY if you can:   2/6 = 1/3

Solved Examples

Worked Example

Find $\tfrac15+\tfrac25$.

Solution

Same denominator, so add the tops: $1+2=3$.
Keep the bottom: $5$.
Answer: $\tfrac35$

Worked Example

Find $\tfrac45-\tfrac15$.

Solution

Subtract the tops: $4-1=3$.
Keep the bottom: $5$.
Answer: $\tfrac35$

Worked Example

Find $\tfrac16+\tfrac16$ and simplify.

Solution

$\tfrac16+\tfrac16=\tfrac26$
Simplify: $\tfrac26=\tfrac13$
Answer: $\tfrac13$

Worked Example

Find $\tfrac78-\tfrac38$ and simplify.

Solution

$\tfrac78-\tfrac38=\tfrac48$
Simplify: $\tfrac48=\tfrac12$
Answer: $\tfrac12$

Worked Example

Find $\tfrac35+\tfrac45$ and write the answer as a mixed number.

Solution

$\tfrac35+\tfrac45=\tfrac75$
$\tfrac75=1\tfrac25$ (since $7\div5=1$ remainder $2$)
Answer: $1\tfrac25$

Worked Example

Riya ate $\tfrac28$ of a pizza and her brother ate $\tfrac38$. How much did they eat together?

Solution

$\tfrac28+\tfrac38=\tfrac58$
Answer: $\tfrac58$ of the pizza

Key Points

Same denominator: add or subtract the numerators; keep the denominator.
$\tfrac{a}{d}\pm\tfrac{b}{d}=\tfrac{a\pm b}{d}$.
Never add the denominators — only the numerators change.
Always simplify the answer when possible (e.g. $\tfrac26=\tfrac13$).
If the top becomes bigger than the bottom, write it as a mixed number.
Word problems: "together/total" means add; "left/more than" often means subtract.

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.To add fractions with the same denominator, you add the:

Explanation: Add tops, keep bottom.

Q2.$\tfrac15+\tfrac25=$

Explanation: $\tfrac{1+2}{5}$.

Q3.$\tfrac45-\tfrac15=$

Explanation: $\tfrac{4-1}{5}$.

Q4.$\tfrac26$ simplifies to:

Explanation: Divide by $2$.

Practice more MCQs → 📝 Assignment · 35 marks