Fractions and Decimals Cheat Sheet

Fractions and Decimals Cheat Sheet

Quick Revision

A fraction writes a part of a whole as numerator / denominator. A decimal writes the same value with a decimal point. Both convert easily to a percentage, and exams reward anyone who can switch between the three instantly.

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1. Types of Fractions

2. Converting Between Forms

Fraction → Decimal :  divide numerator by denominator
Decimal → Percentage : multiply by 100
Fraction → Percentage : (fraction × 100)%
Percentage → Fraction : percentage / 100, then simplify

Example

3/4 = 0.75 = 75%

3. Operations on Fractions

• Add / subtract — make the denominators the same (take the LCM), then add or subtract the numerators.
• Multiply — multiply the numerators and the denominators straight across.
• Divide — multiply by the reciprocal of the second fraction.

Example

2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

4. Comparing Fractions

• Make the denominators equal, then compare numerators; or
• Cross-multiply: for a/b and c/d, compare a×d with b×c.

Example

Compare 3/5 and 4/7: 3×7 = 21 and 5×4 = 20, so 3/5 > 4/7.

5. Fraction–Percentage Values to Memorise

6. Exam Quick Tips

• To divide by a fraction, multiply by its reciprocal.
• Compare fractions fast by cross-multiplication.
• Memorise the fraction-to-percentage table — it turns long sums into instant answers.
• For a recurring decimal like 0.333…, recall it as the fraction 1/3.

Keep revising with the rest of the Maths section:

• All Maths topics
• Percentage Formula Cheat Sheet
• Simplification Cheat Sheet

How this was made: Drafted with AI assistance; spot-checked by the editor on 31 October 2026.