Australian Curriculum v9 / ACiQ Year 7 Mathematics - Unit 0 - Fraction, decimal and percentage equivalence

Fraction, decimal and percentage equivalence

Convert, compare and choose among equivalent fraction, decimal and percentage representations.

Updated 2026-07-24 - 5 min read

Convert, compare and choose among equivalent fraction, decimal and percentage representations. This draft teaching resource is aligned to the cited Year 7 content descriptions and still requires named human curriculum approval.

Track the value represented at every step: an efficient method is valid only when it preserves the number, comparison or required accuracy.

1. Move between equivalent forms

A fraction bar means division. A decimal multiplied by 100 gives a percentage, while a percentage divided by 100 gives a decimal.

Decision check: Apply this lesson's rule to the worked example: Convert through a decimal when comparing several different forms. Identify the exact value, label or property that satisfies the rule.

2. Compare and choose representations

Equivalent forms are useful for different jobs: quarters make 25% calculations quick, while decimals often make ordering clear.

Decision check: Apply this lesson's rule to the worked example: Choose one common form before comparing; restore the original forms in the answer. Identify the exact value, label or property that satisfies the rule.

Worked examples with complete reasoning

Worked example 1

Question: Write 1/2 as a decimal.

  1. Divide the numerator by the denominator: 1 ÷ 2.
  2. The decimal is 0.5.

Answer: 0.5

Check: A fraction bar means division.

Worked example 2

Question: Order 0.45, 2/5, 50% from least to greatest. Use the original forms in your answer.

  1. Convert all three values to decimals.
  2. Compare the decimals, then restore the original forms: 2/5, 0.45, 50%.

Answer: 2/5, 0.45, 50%

Check: Convert first; order second.

Worked example 3

Question: Find 25% of 80.

  1. Use the equivalent decimal 0.25.
  2. 0.25 × 80 = 20.

Answer: 20

Check: Choose the form that makes the multiplication easiest.

Method map for this topic

  1. Move between equivalent forms: Convert through a decimal when comparing several different forms.
  2. Compare and choose representations: Choose one common form before comparing; restore the original forms in the answer.

Common mistakes and how to correct them

  • fraction decimal: Not yet. A fraction bar means division. Recheck the fraction decimal step, then try again.
  • decimal fraction: Not yet. Use tenths, hundredths or thousandths, then simplify. Recheck the decimal fraction step, then try again.
  • decimal percentage: Not yet. Percent means out of 100. Recheck the decimal percentage step, then try again.
  • equivalent form: Not yet. Move through the decimal representation to compare forms. Recheck the equivalent form step, then try again.
  • rational order: Not yet. Convert first; order second. Recheck the rational order step, then try again.
  • representation choice: Not yet. Choose the form that makes the multiplication easiest. Recheck the representation choice step, then try again.

Practice

  1. Write 1/2 as a decimal.
  2. Write 3/4 as a decimal.
  3. Order 0.45, 2/5, 50% from least to greatest. Use the original forms in your answer.
  4. Order 3/4, 0.7, 80% from least to greatest. Use the original forms in your answer.
  5. Find 25% of 80.
  6. Find 3/8 of 64.

<details> <summary>Answers and reasoning</summary>

  1. 0.5 — Divide the numerator by the denominator: 1 ÷ 2. The decimal is 0.5.
  2. 0.75 — Divide the numerator by the denominator: 3 ÷ 4. The decimal is 0.75.
  3. 2/5, 0.45, 50% — Convert all three values to decimals. Compare the decimals, then restore the original forms: 2/5, 0.45, 50%.
  4. 0.7, 3/4, 80% — Convert all three values to decimals. Compare the decimals, then restore the original forms: 0.7, 3/4, 80%.
  5. 20 — Use the equivalent decimal 0.25. 0.25 × 80 = 20.
  6. 24 — Use the equivalent decimal 0.375. 0.375 × 64 = 24.

</details>

Checklist and vocabulary

| Skill | Observable evidence | | --- | --- | | convert fractions decimals percentages | Convert accurately between fractions, decimals and percentages. | | represent rational numbers number line | Compare and place equivalent rational-number forms on a number line. | | choose useful equivalent form | Choose an equivalent form that makes a calculation or comparison efficient. |

Retrieval prompts

  • State the defining relationship for each method above without looking.
  • Give one example where two visually similar representations mean different things.
  • Diagnose one misconception from the list and explain the first corrective step.
  • Name a check that is independent of simply repeating the same calculation.

Teach-back and self-check

Close the worked examples and explain fraction, decimal and percentage equivalence as if you were helping another Year 7 student. Begin by naming the clue that tells you which relationship, representation or operation is needed. Then show one complete example with labels and units where they matter. At each line, explain what stayed equivalent and why the next step is allowed.

Use this four-part check before calling the method secure:

  1. Identify: What information is given, and what must be found or justified?
  2. Represent: Which number line, diagram, table, expression, graph or organised list makes the relationship visible?
  3. Reason: Which rule connects the representation to the required answer?
  4. Verify: Can you check by estimation, substitution, an inverse operation, a second representation or the original context?

If the explanation depends on “I just knew”, return to the method map and name the missing decision. A durable method is one you can explain, check and use in a changed context after a delay.

Transfer task

Create a fraction, decimal and percentage equivalence decision from a shopping, recipe, travel or measurement context. State the quantities and required accuracy, solve it, then explain why your representation and rounding are suitable.

Sources