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SATs practice · Year 6Chapter 5 · Ratio and proportion
Year 6 Arithmetic (SATs) · Ratio and proportion · Lesson 5.2

Year 6 Arithmetic (SATs): Missing values in equivalent ratios

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

5.2

Missing values in equivalent ratios

Year 6
Solve problems involving the relative sizes of two quantities, finding missing values by integer multiplication or division (Year 5-6)
Story. Paint is mixed by using 1 part blue to 4 parts white. Ruby knows she has 5 litres of blue paint, and she needs to find how much white she must use to keep the same mix.

Rule

In an equivalent ratio, both parts are multiplied or divided by the same whole number.

To find a missing value, work out what one unit (or one part) is worth, then multiply by the number of units you need.

Key ideas

  • Multiply or divide both parts by the same whole number.
  • Find the value of one part, then multiply by the number of parts.
  • Check that the new ratio simplifies to the original one.
Worked example 5.2.1
The ratio of red to blue sweets is 3 : 5. There are 15 blue sweets. How many red sweets are there?

Method. Find the value of one part from the blue sweets, then multiply by the red parts.

  1. Find the value of one unit. The blue sweets is 5 units, so one unit is 15 ÷ 5.
    15 ÷ 5 = 3
  2. Multiply by the number of units you need. The other amount has 3 units.
    3 × 3 = 9
  3. Write the answer.
    9

Check. 9 red and 15 blue: 9 : 15 = 3 : 5. ✓

Worked example 5.2.2
Fill in the missing number: 4 : 7 = ☐ : 21.

Method. Find what 7 is multiplied by to make 21, then do the same to 4.

  1. Find the scale factor. 7 × 3 = 21, so multiply by 3.
    7 × 3 = 21
  2. Multiply the first part. 4 × 3 = 12.
    4 × 3 = 12
  3. Check the ratio. 12 : 21 simplifies to 4 : 7.
    12 : 21 = 4 : 7
  4. Write the answer.
    12

Check. 12 : 21 = 4 : 7. ✓

Worked example 5.2.3
A cake recipe uses flour : sugar = 2 : 1. There are 300 g of flour. How much sugar is needed?

Method. Find one part from the flour, then take one part for sugar.

  1. Find the value of one unit. The flour is 2 units, so one unit is 300 ÷ 2.
    300 ÷ 2 = 150
  2. Multiply by the number of units you need. The other amount has 1 units.
    150 × 1 = 150
  3. Write the answer.
    150 g

Check. 300 g of flour is 2 parts, so 1 part is 150 g. ✓

Exercise 5B  Practice: missing values in equivalent ratios

Non-calculator
1
FFill in the missing number: 3 : 4 = ☐ : 20.
2
FFill in the missing number: 5 : 8 = ☐ : 40.
3
FFill in the missing number: 2 : 9 = ☐ : 36.
4
FFill in the missing number: 4 : 9 = ☐ : 45.
5
FThe ratio of apples to bananas is 4 : 3. There are 28 apples. How many bananas are there?
6
FWrite 5 : 2 with the first number 25.
7
PSPaint is mixed in the ratio 1 blue : 4 white. Ruby uses 5 litres of blue. How many litres of white paint does she need?
8
PSIn a club, boys : girls = 3 : 2. There are 30 girls. How many boys are there?
9
PSA recipe uses sugar : flour = 1 : 8. There is 1200 g of flour. How many grams of sugar are needed?
10
PSThe ratio of red to green beads is 6 : 5. There are 360 red beads. How many green beads are there?
11
RExplain how you know that 6 : 9 is the same as 2 : 3.
12
RWhich ratio is equivalent to 2 : 3? Choose one: 4 : 9, 6 : 9, 3 : 2 or 5 : 6.

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