Fractions Notes, Quizzes & Revision

What is a fraction?

A fraction shows a part of a whole. It is written as numerator / denominator. The numerator (top) shows how many parts we have. The denominator (bottom) shows how many equal parts make the whole.

Example: 3/5 means 3 parts out of 5 equal parts.

Types of fractions

• Proper fraction: numerator < denominator (e.g., 2/3).
• Improper fraction: numerator ≥ denominator (e.g., 7/4).
• Mixed number: whole number + proper fraction (e.g., 1 3/4).

Equivalent fractions & simplifying

Equivalent fractions look different but have the same value. Multiply or divide numerator and denominator by the same number.

Example: 2/3 = (2×2)/(3×2) = 4/6

Simplify: divide numerator and denominator by their highest common factor (HCF). 8/12 → HCF = 4 → (8÷4)/(12÷4) = 2/3

Convert mixed ↔ improper

To change a mixed number to an improper fraction: multiply the whole number by the denominator, add the numerator.

Example: 2 1/3 = (2×3 + 1)/3 = 7/3

To change an improper fraction to mixed: divide numerator by denominator. Quotient = whole, remainder = new numerator.

Example: 11/4 = 2 remainder 3 → 2 3/4

Comparing fractions

• If denominators are the same, larger numerator = larger fraction. e.g., 5/8 > 3/8.
• If numerators are same, smaller denominator = larger fraction. e.g., 3/4 > 3/6.
• Otherwise, make common denominators or convert to decimals. Example: Which is larger, 2/3 or 3/5? Common denominator 15 → 10/15 vs 9/15 → 2/3 is larger.

Addition and subtraction

Same denominator: add/subtract numerators, keep denominator.

Example: 3/7 + 2/7 = (3+2)/7 = 5/7

Different denominators: find common denominator (often LCM), convert, then add/subtract.

Example: 1/4 + 1/6 → LCM = 12 → 3/12 + 2/12 = 5/12

Multiplication and division

Multiply fractions: multiply numerators, multiply denominators. Simplify if possible.

Example: 2/3 × 4/5 = (2×4)/(3×5) = 8/15

Divide fractions: multiply by the reciprocal of the divisor (flip second fraction).

Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = (3×5)/(4×2) = 15/8 = 1 7/8

Real-life examples (Kenyan context)

• Sharing 8 mandazi between 5 children: each child gets 8/5 = 1 3/5 mandazi.
• A farmer uses 2/3 of a sack of seed for maize and 1/6 for vegetables: 2/3 + 1/6 = 4/6 + 1/6 = 5/6 of the sack used.
• Buying 3/4 kg of sugar and then using 1/2 of that amount: 3/4 × 1/2 = 3/8 kg used.

Practice questions

1. Write 7/4 as a mixed number.
2. Simplify 18/24.
3. Add: 5/12 + 1/3.
4. Compare: Which is larger 7/10 or 3/4?
5. Multiply: 3/5 × 10/9. Simplify your answer.

Tips for working with fractions

• Always simplify final answers when possible.
• Use fraction bars or drawings (pies, bars) to understand problems.
• Check work by converting to decimals if unsure.
• For LCM quickly find common multiples or multiply denominators then simplify.