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NSW SelectiveYear 7 entry

Fractions, decimals and percentages for the Selective maths test

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Fractions, decimals and percentages are three ways to write the same amount. In the Selective maths test, your child switches every number to the easiest form, often a simple fraction, before comparing or calculating.

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The full lesson is in the SelectiveReady app. A free account opens How and Why Authors Write; this lesson needs a paid plan.

Updated 16 October 2026 · Facts checked 12 October 2026

Fractions, Decimals & Percentages (lesson preview)

A short preview from the SelectiveReady lesson “Fractions, Decimals & Percentages”, on fractions, decimals and percentages for the NSW Selective test.

Published:

Read the video transcript

Okay, here is a classic exam question. A shop is having a 20% off sale. A jacket you want costs $85. The question is, how much money do you save? Let's break it down together. So, let's use our toolkit. Step one, we see 20%, and a light bulb should go off in our head. We know that's the same thing as the fraction 1/5. So, step two, the question basically just becomes, what is 1/5 of $85? See how much easier that sounds? And that makes step three super simple. All we have to do is divide 85 by 5. And just like that, there's our answer. 85 divided by 5 is 17. You save $17. See? By swapping that tricky percentage for a simple fraction, a problem that could have been complicated becomes a total piece of cake. That's the power of your toolkit.

Fractions, Decimals & Percentages is a full lesson in the SelectiveReady app. A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan1SelectiveReady · 13 October 2026 · Published. The preview plays here with English and Chinese captions.

2

What will your child learn in this lesson?

Your child learns the big secret of this topic: a fraction, a decimal and a percentage can be three languages for one value. They'll be able to translate between the three, remember the common pairs, compare awkward fractions and find a percentage of an amount in their head.

The clip works out a saving in a sale by swapping the percentage for a simple fraction. The full lesson adds the conversion toolkit, three traps and a cheat sheet.

3

How do fractions and percentages show up in the Selective maths test?

They turn up across the Mathematical Reasoning section, often inside money, sport, measurement or graph questions. The Department lists no topics, only a range of maths content areas2NSW Education · 13 October 2026 · Published.

PartThe Department's rule
Questions and time352NSW Education · 12 October 2026 · Published questions in 402NSW Education · 12 October 2026 · Published minutes
Options per question52NSW Education · 12 October 2026 · Published
CalculatorNo calculator2NSW Education · 12 October 2026 · Published
Maths neededconcepts your child already learns at school2NSW Education · 12 October 2026 · Published
Wrong answersThe practice papers say there are no marks lost for incorrect answers3NSW Education · 13 October 2026 · Published

With no calculator, the fastest route is often a fraction your child knows by heart. Long decimal sums take time that other questions need.

4

How do fractions, decimals and percentages connect?

They are the same amount written three ways. One half, 0.5 and 50% all mean the same share of something, so a question can mix them and your child can choose the easiest form.

One amount, three ways: 1/2 becomes 0.5 by dividing top by bottom, 50% by multiplying by 100, and 1/2 again over 100.
To changeDo thisExample
Fraction to decimalDivide the top by the bottom3/4 = 3 ÷ 4 = 0.75
Decimal to percentageMultiply by 1000.75 × 100 = 75%
Percentage to fractionPut it over 100, then simplify75% = 75/100 = 3/4

Which pairs should my child know by heart?

The lesson says the fastest students memorise the common ones. Start with these six.

FractionDecimalPercentage
1/20.550%
1/40.2525%
3/40.7575%
1/50.220%
1/100.110%
1/80.12512.5%
5

What is the method for these questions?

Pick one form, convert everything to it, then calculate. The lesson's three tools make each step quick.

  1. Spot every form in the question

    Find each fraction, decimal and percentage. Mixed forms are a sign to convert before doing anything else.

  2. Choose the easiest form

    To find a percentage of an amount, use a fraction: 20% is one fifth, so divide by five. To compare, percentages often work best.

  3. Convert, then calculate

    Use the pairs you know. For two awkward fractions, cross-multiply: the side with the bigger product is the bigger fraction.

  4. Check which part is asked

    The question may give the part that won and ask for the part that lost. Reread the last line before choosing.

6

What does a worked example look like?

We wrote this question to show converting to one form.

Our practice question
Mia scored 17/20 on a spelling test. Leo scored 82%. Sam got 0.8 of the marks. Who scored highest?
StepWhat your child does
Spot the formsA fraction, a percentage and a decimal
Choose one formPercentages, because one score is already a percentage
Convert Mia's score17/20 = 85/100 = 85% (multiply top and bottom by 5)
Convert Sam's score0.8 × 100 = 80%
Compare and check85% is more than 82% and 80%, so Mia scored highest

Sam's 0.8 looks small next to 82 and 17. Converting first stops the eye being fooled by the size of the digits.

7

Which mistakes catch most children?

The most common trap is answering with the part the question gave, not the part it asked for. If 35% of a class walk to school, the question may ask about everyone else: 100% − 35% = 65%.

TrapWhat it looks likeThe fix
The leftover partGiving 35% when the question asks who didn't walkFind 100% minus the part given
"Of" or "increased by"30% of 50 is 15, but 50 increased by 30% is 65Ask whether to add the part back on
Bigger digits, bigger fractionThinking 5/11 is bigger than 3/7 because of its digitsCross-multiply: 5 × 7 = 35 and 3 × 11 = 33, so 5/11 is bigger
8

Can my child try one on their own?

Here is a question from our free maths set that mixes a percentage and a fraction. Your child answers it, then checks the steps below.

Practice question · SEL-MA-TST-04

Zara's netball team played 20 games this season. They won 45% of the games and drew 1/4 of them. They lost the rest.

How many games did they lose?

  1. A

    6

  2. B

    9

  3. C

    11

  4. D

    14

  5. E

    15

Show answer and explanation

Answer: A

Answer: A (6)

  1. Won: 10% of 20 is 2, and 5% is 1, so 45% of 20 is 4 × 2 + 1 = 9 games.
  2. Drew: 1/4 of 20 = 5 games.
  3. Lost: 20 − 9 − 5 = 6 games.

Why the other options are wrong

  • B (9): This is the number of games won, not lost.
  • C (11): This takes away only the wins (20 − 9) and forgets the draws.
  • D (14): This is the number of games won or drawn (9 + 5), which are the games they did not lose.
  • E (15): This takes away only the draws (20 − 5) and forgets the wins.

  1. Games won: a percentage

    10% of 20 games is 2, and 5% is 1. So 45% is four lots of 2, plus 1: 9 games.

  2. Games drawn: a fraction

    A quarter of 20 games is 5 games.

  3. Answer what's asked

    The question asks about games lost: 20 − 9 − 5 = 6. The answer is A. Option D, 14, is the games they didn't lose.

9

How can my child practise fractions and percentages?

A little every day beats a long weekend session. Mental maths matters most, because there's no calculator in the test.

Learn the pairs

Quiz the table above in the car: say a fraction and your child says the decimal and the percentage.

Sale signs

In shops, work out 10%, 20%, 25% or 50% off a price in your head, then check at the register.

Recipes

Halve or quarter a recipe together. Three quarters of 200 g is a real fraction problem.

Sport scores

Compare two players: 7 goals from 10 shots, or 12 from 20? Turn both into percentages.

10

Questions parents ask about fractions and percentages for Selective

How do you find a percentage of a number without a calculator?

Turn the percentage into a fraction you know. For 25% of 48, find a quarter: 48 ÷ 4 = 12.

How do you compare two fractions quickly?

Cross-multiply. Multiply each top by the other bottom, and the bigger product shows the bigger fraction.

Does my child need to know recurring decimals?

Thirds are worth knowing: one third is about 0.33, or about 33%. Learn the pairs in the table above first.

Is the full lesson free?

A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan1SelectiveReady · 13 October 2026 · Published.

Next questions

Selective Mathematical Reasoning →Lesson: Ratio & Rate →Lesson: Measurement & Unit Conversions →Lesson: Reading Charts and Graphs →Free Selective practice test →

Sources and checks

  1. SelectiveReady

    SelectiveReady · Checked 13 October 2026

  2. Selective high school practice tests

    NSW Department of Education · Checked 12 October 2026 · Practice materials: personal or non-commercial use only; CC BY 4.0 does not apply (page notice). Page text: CC BY 4.0.

  3. Selective High School Placement Test, Thinking Skills Question Paper, Practice Test 1 (2026 entry practice tests, PDF)

    NSW Department of Education · Checked 13 October 2026 · Practice materials: personal or non-commercial use only; CC BY 4.0 does not apply (page notice). Quoted briefly with credit. Saved text: the cover-page instructions only; the question pages are not stored (W§3.22).

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