Operations Fractions

Operations on Fractions

How to add and subtract fractions with like and unlike denominators.
How to multiply fractions (numerator × numerator, denominator × denominator).
How to divide a whole number by a fraction and a fraction by a whole number.
To simplify answers to lowest terms and check reasonableness with estimation.

Verbal: Fractions with the same denominator are parts of the same-sized whole — add or subtract the numerators only.

Symbolic: 3/7 + 2/7 = 5/7; 5/6 − 1/6 = 4/6 = 2/3 (simplified).

Visual: A pizza cut into 8 equal slices — eating 3 slices then 2 more means 5/8 eaten.

Lowest terms: Divide numerator and denominator by their HCF. 12/18 → divide by 6 → 2/3.

Unlike denominators: Find LCM of denominators, convert to equivalent fractions, then add/subtract.

Example: 1/3 + 1/4 → LCM(3,4) = 12 → 4/12 + 3/12 = 7/12.

Mixed numbers: Convert to improper fraction first: 2½ = 5/2.

Evaluate: 2/3 + 1/4 − 1/6

Step 1 — LCM of 3, 4, 6 = 12
Step 2 — Convert: 8/12 + 3/12 − 2/12
Step 3 — Combine: (8 + 3 − 2)/12 = 9/12
Step 4 — Simplify: 9/12 = 3/4

Multiply: 3/5 × 10/9 = 30/45 = 2/3 (cancel 3 and 5 before multiplying for speed).

Mistake	Why it happens	Fix
Adding denominators: 1/2 + 1/3 = 2/5	Treating fractions like whole numbers	Add numerators only when denominators match
Forgetting to simplify	Stopping at 6/8	Always reduce to lowest terms
Dividing by multiplying wrong way	Confusion with reciprocal	a/b ÷ c = a/(b×c); a/b ÷ c/d = a/b × d/c
Skipping LCM for unlike denominators	Rushing	Equivalent fractions need common denominator

Open the Practice tab for graded questions on Operations on Fractions.