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SATs practice · Year 6Chapter 3 · Ratio and proportion reasoning
Year 6 Maths reasoning (SATs) · Ratio and proportion reasoning · Lesson 3.1

Year 6 Maths reasoning (SATs): Ratio language and simplifying ratios

Part of the Year 6 Maths reasoning (SATs) ratio and proportion reasoning chapter. Chapter overview · whole chapter on one page

3.1

Ratio language and simplifying ratios

Year 6
Solve problems involving the relative sizes of two quantities where missing values can be found by integer multiplication or division (Year 5-6), Use the ratio language a:b and the link between ratio and fractions (Year 6)
Practice material. Do this without a calculator. This is practice in the style of the Year 6 maths reasoning test. It is not the official test, and no official test item is used. Marks and timings are a practice guide only.
Story. Lena is painting a wall. She mixes 3 tins of blue paint for every 5 tins of white paint, so that the shade is always the same.

Rule

A ratio compares two amounts. 3:5 means for every 3 of one thing there are 5 of the other.

Write a ratio in its simplest form by dividing both parts by the same number. 12:18 = 2:3.

To find a missing amount, find the value of one part first, then multiply.

Key ideas

  • Divide both parts of a ratio by the same number to simplify it.
  • In a ratio of 2:3 there are 5 parts altogether, so the first part is 2/5 of the total.
  • Find the value of one part, then multiply, to find a missing amount.
Worked example 3.1.1
Write the ratio 15:25 in its simplest form.

Method. Divide both parts of the ratio by the highest common factor.

  1. Find the highest common factor of both numbers. The biggest number that divides 15 and 25 is 5.
    HCF = 5
  2. Divide both parts by it. 15 / 5 = 3 and 25 / 5 = 5.
    3:5
  3. Write the answer.
    3:5

Check. 3 and 5 have no common factor except 1. ✓

Watch out. Both parts must be divided by the same number, just as with a fraction.

Worked example 3.1.2
The ratio of red to blue is 3:5. There are 18 red. How many blue are there?

Method. Find the value of one part, then multiply.

  1. Find the value of one part. 18 is 3 parts, so one part is 18 / 3.
    1 part = 6
  2. Multiply to find the other amount. There are 5 parts of blue.
    5 x 6 = 30
  3. Write the answer.
    30

Check. 30 : 18 = 3:5. ✓

Watch out. Do not add the ratio numbers to the amount. Find one part first.

Worked example 3.1.3
The ratio of cats to dogs is 2:7. There are 21 dogs. How many cats are there?

Method. Find the value of one part, then multiply.

  1. Find the value of one part. 21 is 7 parts, so one part is 21 / 7.
    1 part = 3
  2. Multiply to find the other amount. There are 2 parts of cats.
    2 x 3 = 6
  3. Write the answer.
    6

Check. 6 : 21 = 2:7. ✓

Watch out. Do not add the ratio numbers to the amount. Find one part first.

Watch out

Watch out. A ratio is not a fraction of the whole. In 2:3 there are 5 parts altogether, so the first part is 2/5 of the total.

Exam tip

Practice guide. Write the ratio above the amounts in a table, then fill in the missing value.

Exercise 3A  Practice: ratio language and simplifying

Non-calculator
1
FWrite the ratio 12:20 in its simplest form.
2
FWrite the ratio 45:30 in its simplest form.
3
FThe ratio of boys to girls is 2:3. There are 12 boys. How many girls are there?
4
FThe ratio of apples to pears is 4:5. There are 35 pears. How many apples are there?
5
FThe ratio of blue to green is 3:7. There are 49 green. How many blue are there?
6
FThe ratio of miles to laps is 5:2. There are 25 miles. How many laps are there?
7
FThe ratio of cats to dogs at a shelter is 2:5. Choose one: For every 2 cats there are 5 dogs, For every 5 cats there are 2 dogs or For every 7 cats there are 2 dogs.
8
FTick the ratios that are equivalent to 2:3. Options: 4:6 | 3:2 | 6:9 | 5:6 | 8:10. Write the options you would tick, in the order given.
9
PSThe ratio of sugar to flour is 1:4. There are 240 flour. How many sugar are there?
10
PSThe ratio of girls to boys in a class is 3:4. There are 28 pupils altogether. How many girls are there?
11
RAli says the ratio 3:6 is the same as 1:2. Is he right? Explain.
12
PSA pack of crisps has salt and vinegar flavours in the ratio 5:3. There are 40 bags altogether. How many bags are salt and vinegar? Write the number of salt and vinegar bags, in that order, separated by a comma.
13
RMaya says that in the ratio 2:5, the first part is 2/5 of the total, and the second part is 3/5 of the total. Is she right?
14
PSThe ratio of red to blue beads is 4:9. There are 36 blue beads. How many red beads are there?
15
RBen says: "A ratio of 6:9 means the same as 2:3, so I can use 2:3 for any problem about 6:9." Is he right? Write yes or no.
16
PSA bag has 20 counters in the ratio 3:2 for red and blue. What is the number of blue counters? Write one number.

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