Primary 6 · Number & Algebra
P6 ratio
In P6, your child reads ratios of two or three whole numbers, finds equivalent ratios and the simplest form, and divides a quantity in a given ratio. Ratio also links to fractions and percentages.
- Taught in
- Term 1
- Syllabus
- 3 skills
- Usual slip
- Taking 4 as total
What your child learns in P6 ratio
Three skills, each with what it looks like on a worksheet.
See the syllabus wording
- notation, representations and interpretation of a:b and a:b:c, where a, b and c are whole numbers, excluding ratios involving fractions and decimals
- equivalent ratios
- dividing a quantity in a given ratio
- expressing a ratio in its simplest form
- finding the ratio of two or three given quantities
- finding the missing term in a pair of equivalent ratios
- relationship between fraction and ratio
Reading a ratio
a : b compares two amounts and a : b : c compares three. 4 apples to 3 pears is 4 : 3, so the apples are 4/7 of the fruit. The whole is all the terms added.
| Group | Detail |
|---|---|
| Apples | 4×apple |
| Pears | 3×pear |
Equivalent ratios and simplest form
Multiply or divide every term by the same number. 12 : 18 = 2 : 3 in its simplest form, dividing both by 6. For a missing term, find what the other term was multiplied by.
| × 1 | × 2 | × 6 |
|---|---|---|
| 2 : 3 | 4 : 6 | 12 : 18 |
Dividing a quantity in a ratio
Add the terms for the total units, find 1 unit, then count. To share 77 in the ratio 4 : 3, 7 units = 77, so 1 unit = 11 and the shares are 44 and 33.
Key facts and formulas
- Boys : girls = 3 : 5boys as a fraction of girls → boys as a fraction of all →
- Simplest form: ÷ every term by the same number
- Equivalent ratios: × or ÷ every term by the same number 3 : 4 = ? : 20 →
Words to know
- Ratio
- A comparison of amounts, such as 3 : 4. It says how a total is split.
- Unit
- One equal box of the bar model. Each term counts units.
- Equivalent ratio
- The same ratio with every term multiplied or divided by one number.
- Simplest form
- The ratio whose terms share no common factor, such as 2 : 3.
The sentence that costs the mark
A car park holds cars and motorcycles in the ratio 3 : 4. There are 28 vehicles in all. How many cars are there?
What the working usually does
3 out of4 parts=21 cars
Reads the second term as the whole, so takes three quarters of 28.
What the question asked
3 out of7 parts=12 cars
Adds the terms first, because 3 and 4 make 7 equal parts.
Neither column has a sum wrong, and both end on a whole number of cars. The mistake happens before any calculating starts, in deciding what the 3 is counted out of.
The same P6 ratio question, worked properly
Lah works through it the way she does every question in StudyLah: one step at a time, marking the picture as she goes.
At a shelter, cats, dogs and birds are in the ratio 3 : 8 : 2. There are 91 animals. Find how many more dogs there are than cats.
- The ratio counts units: cats are 3 units, dogs 8 units and birds 2 units, all the same size.
- The total is all three terms, not one of them: 3 + 8 + 2 = 13 units, and those 13 units are the 91 animals.
- Find 1 unit: 91 ÷ 13 = 7 animals.
- The bars show dogs with 5 units more than cats, so the difference is 5 × 7 = 35.
- So there are 35 more dogs than cats.
Every question in StudyLah comes with a walkthrough like this one.
Try it freeTwo quick P6 ratio questions
Try them together, then tap to check.
Question 1
Two stamp collections are in the ratio 5 : 8. The smaller collection has 21 fewer stamps than the larger collection. How many stamps are in the larger collection?
Show answer
Answer56. The difference is 8 − 5 = 3 units, so 3 units = 21 and 1 unit = 7. The larger has 8 × 7 = 56.
Question 2
What goes in the box to make the ratios equal? 9 : 15 = : 40
Show answer
Answer24. 9 : 15 is 3 : 5 in its simplest form. 5 × 8 = 40, so multiply the 3 by 8 too.
Helping at home
How to tell it has clicked
When a ratio comes up, ask one thing: out of how many? The answer you want adds the terms first: in 3 : 4, out of 7.
Answering "out of 4" means the second term has quietly become the total. That is the slip.
Try this tonight
In one row of the car park, count the cars and the motorcycles. Say the ratio, then ask how many vehicles that is in all.
Adding the two numbers before anything else is the habit worth building.
Before and after P6 ratio
Builds on
Primary 5 Fractions and DivisionTakes a fraction of what is left
You are here
Primary 6 Ratio
Splits a quantity into units
Leads to
Primary 6 PercentageFinds the whole and the percentage change
The methods your child will use here
In the PSLE's hardest questions
More in Primary 6
Struggling with the working rather than the topic itself? How to help your child with problem sums
See how your child is doing on this topic
StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.