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NSW SelectiveYear 7 entry

Ratio and rate for the Selective maths test

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A ratio compares amounts, and a rate compares a quantity with one unit of something else, like kilometres per hour. For Selective maths, the key is finding what one part or one unit is worth, then scaling up.

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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

Ratio & Rate (lesson preview)

A short preview from the SelectiveReady lesson “Ratio & Rate”, on ratio and rate for the NSW Selective test.

Published:

Read the video transcript

On to step two. Now that we know there are eight total parts, we can figure out what each individual part is worth. To do that, we take the whole amount of money, the $120, and we divide it by our eight parts. So, $120 divided by eight parts is $15. This right here, this $15 is the magic key that unlocks the whole problem. Once you find the value of one part, you're basically on the home stretch. We are so close. For step three, we just go back to our original ratio. Remember, Ollie gets three parts and Ben gets five. And since we know each of those parts is worth 15 bucks, now we can find their final shares. So for Ollie, we multiply his three parts by $15, and he gets $45. For Ben, we multiply his five parts by that same $15, which gives him $75, and there we have it.

Ratio & Rate 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. This preview has English and Chinese captions.

2

What will your child learn in this lesson?

Your child learns to crack ratio and rate questions with one move: find the value of one part. They'll be able to share an amount in a ratio, simplify a ratio, and use the speed triangle for distance, speed and time.

The clip picks up at step two of sharing $120 between two boys in the ratio 3 : 5. The full lesson adds what ratios and rates are, simplifying, the triangle, two traps and a cheat sheet.

3

What is the difference between a ratio and a rate?

A ratio compares two amounts. The lesson uses a recipe: 3 cups of flour for every 2 cups of sugar is the ratio 3 : 2. A rate compares a quantity with one unit of something else, like 60 kilometres per hour or $3 per kilogram.

RatioRate
ComparesAny two amountsA quantity with one unit of another
Looks like3 : 260 km per hour
The key moveFind one partFind per one
Simplify byDividing both sides by the same number: 12 : 8 is 3 : 2Dividing down to one unit

Simplifying a ratio works like simplifying a fraction. Divide both sides by the biggest number that goes into both.

What is the speed triangle?

It links distance, speed and time. The lesson says to cover the one you need with a finger, and the triangle shows the calculation.

You needCover it, and you seeOur example
DistanceSpeed × time15 km per hour for 2 hours is 30 km
SpeedDistance ÷ time30 km in 2 hours is 15 km per hour
TimeDistance ÷ speed30 km at 15 km per hour takes 2 hours
4

How do ratio and rate questions show up in the Selective test?

The Department describes the section as applying the maths your child knows to new problems2NSW Education · 13 October 2026 · Published, and ratio questions fit that well: a familiar idea in a new setting. It publishes no list of topics, so how many ratio questions appear isn't known. 2NSW Education · 13 October 2026 · Published

The Department's ruleWhat it means for ratio and rate
Questions use concepts your child already learns at school2NSW Education · 12 October 2026 · PublishedSharing, scales and speed are school maths
No calculator2NSW Education · 12 October 2026 · Published in any sectionFinding one part first keeps the numbers small
352NSW Education · 12 October 2026 · Published questions in 402NSW Education · 12 October 2026 · Published minutesA three-step method saves time
52NSW Education · 12 October 2026 · Published options per questionIn our practice sets, one option is often a single share, not what was asked
5

What is the method for sharing in a ratio?

The lesson's three magic words are add, divide, multiply. Then a fourth step checks the answer.

Add, divide, multiply: add the parts, divide to find one part, multiply for each share, then check the total.

  1. Add the parts

    For 3 : 5, there are 3 + 5 = 8 parts. The lesson says this is the step most people forget.

  2. Divide to find one part

    Share the total by the number of parts: $120 ÷ 8 = $15 for one part.

  3. Multiply for each share

    3 × $15 = $45 and 5 × $15 = $75. The first name gets the first number.

  4. Check the total

    $45 + $75 = $120. The shares must add back to the amount you started with.

6

What does a worked ratio question look like?

We wrote this question to show the same idea when the total isn't given. One part is still the key.

Question: Mia and Sam share stickers in the ratio 2 : 5. Sam gets 18 more stickers than Mia. How many stickers are there altogether?

StepWhat your child does
Draw the partsMia has 2 boxes and Sam has 5 boxes, all the same size
Find what 18 stands forSam has 3 more boxes than Mia, so 3 parts = 18
Find one part18 ÷ 3 = 6 stickers
Find the total2 + 5 = 7 parts, and 7 × 6 = 42 stickers
CheckMia 12, Sam 30. The difference is 18

The tempting wrong answer treats 18 as the total and shares it in the ratio. Drawing the boxes shows that 18 is only the difference.

7

Which ratio and rate mistakes are most common?

The number one trap is dividing the total by one number of the ratio. In the clip's question, $120 ÷ 5 forgets Ollie's three parts completely.

TrapWhat it looks likeThe fix
Forgetting to add the parts$120 ÷ 5 for Ben's shareAdd 3 + 5 first: eight parts
Shares to the wrong personOllie given 5 parts and Ben given 3First name gets the first number
Treating 3 : 5 as a fractionOllie gets 3/5 of the moneyOllie gets 3 parts out of 8, which is 3/8
Mixing units in a rateA map distance in cm used as kmTurn every measure into the same unit first
8

Can my child try one on their own?

Here is a question from our free maths set: a map scale and a bike ride at a steady speed. Your child finds the real distance, then the time.

Practice question · SEL-MA-TST-08

On a map of a bike trail, 2 cm stands for 5 km. The trail is 14 cm long on the map. Ruby rides the whole trail at a steady 15 km per hour.

How long does Ruby's ride take?

  1. A

    56 min

  2. B

    2 h 5 min

  3. C

    2 h 20 min

  4. D

    2 h 33 min

  5. E

    4 h 40 min

Show answer and explanation

Answer: C

Answer: C (2 h 20 min)

  1. 14 cm is 7 lots of 2 cm, so the trail is 7 × 5 = 35 km.
  2. In 2 hours Ruby rides 2 × 15 = 30 km. That leaves 5 km.
  3. 5 km is 1/3 of 15 km, so it takes 1/3 of an hour = 20 minutes.
  4. Total time: 2 h 20 min.

Why the other options are wrong

  • A (56 min): This treats 1 cm on the map as 1 km, so the trail is only 14 km.
  • B (2 h 5 min): This writes 35 ÷ 15 = 2 remainder 5 as 2 h 5 min, but the 5 is kilometres still to ride, not minutes.
  • D (2 h 33 min): This turns 2.33 hours into 2 h 33 min, but a third of an hour is 20 minutes, not 33.
  • E (4 h 40 min): This uses 1 cm for 5 km, which doubles the trail to 70 km.

  1. Use the scale

    14 cm is 7 lots of 2 cm, so the trail is 7 × 5 = 35 km.

  2. Use the rate

    At 15 km per hour, 2 hours covers 30 km. That leaves 5 km.

  3. Turn the leftover into minutes

    5 km is a third of 15 km, so it takes a third of an hour: 20 minutes. The answer is C.

  4. Check the traps

    B reads the leftover 5 km as 5 minutes. D turns 2.33 hours into 2 h 33 min.

9

Questions parents ask about ratio and rate

What does the colon in 3 : 5 mean?

It reads "3 to 5": for every 3 of the first thing, there are 5 of the second.

Is a ratio the same as a fraction?

No. In 3 : 5 there are 8 parts, so the first share is 3/8 of the whole, not 3/5.

What is a unit rate?

A rate for one unit, like the price of one kilogram. It makes best-buy questions easy to compare.

How can my child practise at home?

Use recipes. Ask how much of each ingredient you'd need to make one and a half times as much, and check the shares add up.

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: Fractions, Decimals & Percentages →Lesson: Measurement and Units →Lesson: Time Calculations →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.

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