Fractions — worked examples (add, subtract, mixed)

Once equivalent and comparing are in place, the rest is short. Three operations make up the Year-4 toolkit: adding and subtracting with the same denominator, converting between mixed numbers and improper fractions, and taking a fraction of a set.

Adding fractions with the same denominator

Same bottoms — keep the bottom, add the tops.

$\frac{2}{7} + \frac{3}{7} = \frac{2 + 3}{7} = \frac{5}{7}$

$\frac{1}{8} + \frac{4}{8} = \frac{5}{8}$

If the answer turns out to be a fraction equal to 1 (top = bottom) or bigger than 1 (top > bottom), it's still correct — you can either leave it or rewrite it as a mixed number.

$\frac{3}{5} + \frac{4}{5} = \frac{7}{5}$ (which equals $1 \frac{2}{5}$ )

⚠️ Never add the bottoms. $\frac{1}{4} + \frac{2}{4}$ is not $\frac{3}{8}$ . The bottom tells you the size of one slice, and the slice size doesn't change just because you have more slices.

Subtracting fractions with the same denominator

Same idea, just minus.

$\frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$

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

After subtracting, check if the result can be simplified (divided top and bottom by the same number).

Mixed numbers and improper fractions

Mixed number	Improper fraction	Meaning
$1 \frac{1}{2}$	$\frac{3}{2}$	one whole and a half
$2 \frac{3}{4}$	$\frac{11}{4}$	two wholes and three quarters
$3 \frac{1}{5}$	$\frac{16}{5}$	three wholes and one fifth

Improper → mixed

Divide the top by the bottom. The quotient is the whole-number part; the remainder is the new top; the bottom stays.

$\frac{11}{4}$ : 11 ÷ 4 = 2 remainder 3. Answer: $2 \frac{3}{4}$ .

Mixed → improper

Multiply the whole-number part by the bottom, then add the top.

$2 \frac{3}{4}$ : $2 \times 4 + 3 = 11$ . Answer: $\frac{11}{4}$ .

$1 \frac{2}{5}$ : $1 \times 5 + 2 = 7$ . Answer: $\frac{7}{5}$ .

Fraction of a set

Treat the bottom as "how many equal groups" and the top as "how many groups we want".

$\frac{3}{4}$ of 20 sweets = ?

Divide 20 by 4 (the bottom): 20 ÷ 4 = 5. Each "quarter" of the bag is 5 sweets.
Multiply by 3 (the top): 3 × 5 = 15 sweets.

Short rule: divide by the bottom, multiply by the top.

$\frac{2}{3}$ of 12 apples = 12 ÷ 3 × 2 = 8 apples.

$\frac{5}{6}$ of 24 marbles = 24 ÷ 6 × 5 = 20 marbles.

Mixing it all together

Sara had a chocolate bar with 8 squares. She ate $\frac{3}{8}$ of it, and her brother ate $\frac{1}{4}$ of it. How much is left?

Step 1 — rewrite $\frac{1}{4}$ with denominator 8: $\frac{1}{4} = \frac{2}{8}$ .

Step 2 — add what they ate: $\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$ .

Step 3 — subtract from the whole: $\frac{8}{8} - \frac{5}{8} = \frac{3}{8}$ .

There's $\frac{3}{8}$ of the bar left — that's 3 squares.

What's next

Try it out

➕ Add fractions with the same denominator
➖ Subtract fractions with the same denominator
🔁 Convert between mixed and improper
🍕 Fraction of a set