VCE Vault

Year 7 Mathematics · Number and Algebra · 10m read

Fractions, Decimals and Percentages

Ever notice that a 50% discount, half price, and 0.5 off all mean the same thing? That's because fractions, decimals, and percentages are just three different ways of showing the same value—and knowing how to switch between them is genuinely the superpower behind most maths you'll do this year. You'll need this skill constantly in VCE, whether you're tackling finance, statistics, or algebra problems that depend on comparing values quickly.

Learning objective: Convert between fractions, decimals and percentages and compare them.

By the end of this lesson you can:

  • I convert a fraction to a decimal and percentage.
  • I order fractions and decimals on a number line.
  • I calculate simple percentages of quantities.

The conversion triangle

FRACTION → DECIMAL: divide the numerator by the denominator.
3/4 → 3 ÷ 4 = 0.75

DECIMAL → PERCENTAGE: multiply by 100 (move decimal right 2 places).
0.75 → 0.75 × 100 = 75%

PERCENTAGE → FRACTION: write over 100, then simplify.
75% = 75/100 = 3/4

FRACTION → PERCENTAGE (shortcut): convert to decimal first, then ×100.
7/20 → 7 ÷ 20 = 0.35 → 35%

KEY BENCHMARKS to memorise:
1/2 = 0.5 = 50%
1/4 = 0.25 = 25%
3/4 = 0.75 = 75%
1/5 = 0.2 = 20%
1/10 = 0.1 = 10%
1/3 ≈ 0.333... ≈ 33.3%

COMPARING FRACTIONS: convert all to decimals first, then compare.

Pizza slices analogy. Cutting a pizza into 4 slices and taking 3 is 3/4. As a decimal that's 0.75. As a percentage, 75% of the pizza is gone. Same amount, three ways to say it.

Percentage of a quantity

  • Method 1 — decimal: Write % as decimal, multiply. 30% of 80 → 0.30 × 80 = 24.
  • Method 2 — fraction: 30% of 80 → (30/100) × 80 = 2 400/100 = 24.
  • 10% shortcut: Move decimal one place left. 10% of 350 = 35. Then build: 20% = 2×35 = 70.

Conversions between forms

  • Fraction → decimal: a/b = a \div b
  • Decimal → percent: d \times 100\%
  • Percent of an amount: A \times \dfrac{p}{100}

Quick reference

| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
| 1/3 | 0.333… | 33.3% |

Worked example (Easy)

Convert 3/8 to a decimal and a percentage.

  1. Fraction to decimal. 3 ÷ 8 = 0.375
  2. Decimal to percentage. 0.375 × 100 = 37.5%

Answer: 0.375 and 37.5%

Worked example (Medium)

A jumper costs $60. Find 35% of $60.

  1. Write 35% as decimal. 35% = 0.35
  2. Multiply. 0.35 × 60 = $21

Answer: $21

Common mistakes

  • Comparing fractions by looking only at numerators or denominators Students think 3/8 > 2/5 because 3 > 2, ignoring that the denominators are different sizes. Fix: Convert all fractions to decimals first: 3/8 = 0.375 and 2/5 = 0.4. Now compare: 0.4 > 0.375, so 2/5 > 3/8.
  • Moving the decimal the wrong way when converting Students confuse which direction to shift: decimal → percentage (×100, right) vs percentage → decimal (÷100, left). Fix: Remember: decimal to percentage = BIGGER number (×100, move right). Percentage to decimal = SMALLER number (÷100, move left).
  • Not simplifying fractions from percentages Students write 75% = 75/100 and stop, forgetting to simplify. Fix: Always reduce: 75/100 → divide both by 25 → 3/4. Find the HCF (highest common factor) and divide.

Fractions, decimals and percentages in real life

These three representations appear everywhere in daily life, and knowing which to use — and when — is a practical superpower.

Percentages are used for comparison: "Your test score improved by 15%." They're easy to understand because they're always out of 100. Sales discounts ("30% off"), interest rates ("4.5% p.a.") and statistics ("72% of Australians...") all use percentages because they make comparison intuitive.

Decimals are used for precision: money ($4.99), measurements (1.75 m), and scientific data (pH 6.8). Calculators and computers use decimals internally because they're the most efficient form for arithmetic.

Fractions are used when exact proportions matter: recipes ("2/3 cup of flour"), music (a half note), and probability (1/6 chance). Fractions preserve exactness — 1/3 is precise, while 0.333... is an approximation.

The key insight is that these are three costumes for the same value. A confident mathematician switches between them depending on the context, just as a bilingual person switches languages depending on the audience.

Practice questions

  1. Convert 3/5 to a percentage.

    1. 30%
    2. 35%
    3. 60%
    4. 15%

    (1 marks)

  2. Find 15% of 240.

    (2 marks)

Summary

  • Convert a fraction to a decimal and percentage.
  • Order fractions and decimals on a number line.
  • Calculate simple percentages of quantities.

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