Fractions, Decimals and Percentages

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Use the language and notation of proper fractions, improper fractions, mixed numbers, decimals, and percentages in appropriate contexts
  2. Recognize equivalence and convert between these forms
  3. Write fractions in their simplest form
  4. [Extended] Use recurring decimal notation (e.g., 0.1̇7̇ = 0.171717...)
  5. [Extended] Convert between recurring decimals and fractions

1. Understanding Fractions

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What is a fraction?

A fraction is a way of representing part of a whole. It's written as one number over another, like this: ³⁄₄

  • The numerator (top number) tells you how many parts you have
  • The denominator (bottom number) tells you how many equal parts the whole is divided into

For example, ³⁄₄ means the whole is divided into 4 equal parts, and you have 3 of them.

Types of Fractions

Proper Fraction

  • A fraction where the numerator is smaller than the denominator
  • In other words: N < D
  • The value is always less than 1
  • Examples: ²⁄₅, ³⁄₈, ⁷⁄₁₀

Improper Fraction

  • A fraction where the numerator is greater than or equal to the denominator
  • In other words: N ≥ D
  • The value is equal to or greater than 1
  • Also called a "top-heavy fraction"
  • Examples: ⁵⁄₃, ⁹⁄₄, ¹¹⁄₇

Mixed Number

  • A combination of a whole number and a proper fraction
  • Examples: 2³⁄₄ (means "two and three-quarters"), 1½, 3²⁄₅

2. Converting Between Fractions

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Converting Mixed Numbers to Improper Fractions

Follow these steps:

Step 1: Multiply the whole number by the denominator
Step 2: Add the numerator to this result
Step 3: Write this total over the original denominator

Example: Convert 3²⁄₅ to an improper fraction

  • Step 1: 3 × 5 = 15
  • Step 2: 15 + 2 = 17
  • Step 3: ¹⁷⁄₅

Example: Convert 5³⁄₄ to an improper fraction

  • Step 1: 5 × 4 = 20
  • Step 2: 20 + 3 = 23
  • Step 3: ²³⁄₄

Converting Improper Fractions to Mixed Numbers

Follow these steps:

Step 1: Divide the numerator by the denominator
Step 2: The whole number part is your answer from the division
Step 3: The remainder becomes the numerator of the fraction part
Step 4: Keep the same denominator

Example: Convert ¹¹⁄₉ to a mixed number

  • Step 1: 11 ÷ 9 = 1 remainder 2
  • Step 2: Whole number = 1
  • Step 3: Remainder = 2
  • Step 4: Answer = 1²⁄₉

Example: Convert ²²⁄₃ to a mixed number

  • 22 ÷ 3 = 7 remainder 1
  • Answer = 7¹⁄₃

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