Australian Curriculum v9 / ACiQ Year 7 Mathematics - Unit 0 - Fraction and decimal operations

Fraction and decimal operations

Use all four operations with positive fractions and decimals, round results to an accuracy suited to the context, and check reasonableness.

Updated 2026-07-24 - 7 min read

Use all four operations with positive fractions and decimals, round results to an accuracy suited to the context, and check reasonableness. 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. Add and subtract fractions

Fractions can be added or subtracted only when their parts are the same size. Equivalent fractions create a shared denominator.

Decision check: Apply this lesson's rule to the worked example: Change the denominators, not the values: scale numerator and denominator together. Identify the exact value, label or property that satisfies the rule.

2. Multiply and divide fractions

Multiplication finds a part of a quantity; division asks how many groups fit. Simplifying before multiplying can make the calculation smaller.

Decision check: Apply this lesson's rule to the worked example: Treat whole numbers as fractions over 1 and simplify common factors. Identify the exact value, label or property that satisfies the rule.

3. Operate and report accurately with decimals

Decimal addition needs aligned place values. Decimal division can be changed to an equivalent whole-number divisor by scaling both numbers. After calculating, identify the required place value and inspect the digit immediately to its right. Context can override nearest-value rounding: 6.12 litres of paint sold in whole litres requires 7 litres, not 6.

Text-equivalent representation: Rounding place-value strip: ones | tenths | hundredths | thousandths. Underline the requested place; the next digit decides whether it changes.

Decision check: Apply this lesson's rule to the worked example: Estimate first, calculate with aligned place values, then state the requested accuracy and check that the rounded result still serves the context. Identify the exact value, label or property that satisfies the rule.

Worked examples with complete reasoning

Worked example 1

Question: Calculate 3/4 × 2. Give the answer as a decimal.

  1. Treat 2 as 2/1.
  2. Multiply and simplify: (3 × 2)/4 = 6/4.
  3. As a decimal this is 1.5.

Answer: 1.5

Check: Multiply the numerator, then simplify before converting.

Worked example 2

Question: Calculate 3.6 + 1.45.

  1. Align the decimal points so equal place values are in the same column.
  2. Calculate to get 5.05.

Answer: 5.05

Check: Write trailing zeros if they help align place values.

Worked example 3

Question: A calculation gives 8.476 litres. Round this result to the nearest tenth of a litre.

  1. The tenths digit is 4 and the next digit is 7.
  2. Because 7 is at least 5, increase the tenths digit: 8.476 rounds to 8.5 litres.

Answer: 8.5

Check: Underline the requested place, then inspect only the digit immediately to its right.

Method map for this topic

  1. Add and subtract fractions: Change the denominators, not the values: scale numerator and denominator together.
  2. Multiply and divide fractions: Treat whole numbers as fractions over 1 and simplify common factors.
  3. Operate and report accurately with decimals: Estimate first, calculate with aligned place values, then state the requested accuracy and check that the rounded result still serves the context.

Common mistakes and how to correct them

  • decimal place value: Not yet. Write trailing zeros if they help align place values. Recheck the decimal place value step, then try again.
  • fraction multiplication: Not yet. Multiply the numerator, then simplify before converting. Recheck the fraction multiplication step, then try again.
  • common denominator: Not yet. Only add fractions after making the denominator the same. Recheck the common denominator step, then try again.
  • decimal division: Not yet. Make the divisor a whole number by scaling both dividend and divisor equally. Recheck the decimal division step, then try again.
  • operation choice: Not yet. Multiply the part of one by the whole amount. Recheck the operation choice step, then try again.
  • rounding accuracy: Not yet. Underline the requested place, then inspect only the digit immediately to its right. Recheck the rounding accuracy step, then try again.
  • rounding context: Not yet. When a context requires enough complete units, round up even if the decimal part is below 0.5. Recheck the rounding context step, then try again.

Practice

  1. Calculate 3/4 × 2. Give the answer as a decimal.
  2. Calculate 5/6 × 3. Give the answer as a decimal.
  3. Calculate 3.6 + 1.45.
  4. Calculate 7.2 - 2.85.
  5. A calculation gives 8.476 litres. Round this result to the nearest tenth of a litre.
  6. A race time is 12.684 seconds. Report it correct to two decimal places.

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

  1. 1.5 — Treat 2 as 2/1. Multiply and simplify: (3 × 2)/4 = 6/4. As a decimal this is 1.5.
  2. 2.5 — Treat 3 as 3/1. Multiply and simplify: (5 × 3)/6 = 15/6. As a decimal this is 2.5.
  3. 5.05 — Align the decimal points so equal place values are in the same column. Calculate to get 5.05.
  4. 4.35 — Align the decimal points so equal place values are in the same column. Calculate to get 4.35.
  5. 8.5 — The tenths digit is 4 and the next digit is 7. Because 7 is at least 5, increase the tenths digit: 8.476 rounds to 8.5 litres.
  6. 12.68 — The hundredths digit is 8 and the next digit is 4. Because 4 is below 5, keep the hundredths digit: 12.68 seconds.

</details>

Checklist and vocabulary

| Skill | Observable evidence | | --- | --- | | calculate fraction operations | Calculate with positive fractions using equivalent fractions and simplification. | | calculate decimal operations | Calculate with decimals while preserving place value. | | choose efficient rational strategy | Choose an efficient representation, round decimal results to a stated or context-appropriate accuracy, and check reasonableness by estimation. |

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 and decimal operations 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 and decimal operations 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