Ratio and rate · Usually met around P6
Ratios and fractions
Of the whole: the denominator is all the parts.
How to do it
Method
Of the whole: the denominator is all the parts
2 : 3 → A is 25 of the whole and 23 of B
Another way
Count the boxes
▭▭ / ▭▭▭ → 25
In full
A ratio can be written as fractions. A : B = 2 : 3 means 2 + 3 = 5 parts in all: A is 25 of the whole and B is 35. Comparing the two parts, A is 23 of B, and B is 32 times A. The other way round: if A is 25 of the whole, B is 1 − 25 = 35, so A : B = 2 : 3. Watch the denominator: compared with the whole, it is all the parts added; compared with the other part, it is that part's number. Counting the boxes of a bar model makes it clearest.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The bar model shows the numbers of ⚽ and 🌸, every box the same. What fraction of the total is ⚽?
Answer in simplest form
Show the answer and working
Answer: 34
⚽ takes 3 of the 3 + 1 = 4 boxes: 34.
Example 2
The ratio of red beads to blue beads is 4 : 1. What fraction of all the beads are blue?
Answer in simplest form
Show the answer and working
Answer: 15
4 + 1 = 5 parts in all, and blue is 1 of them: 15.
Example 3
The ratio of boys to girls is 3 : 8. Which sentence is true?
- A. Boys are 38 of everyone
- B. There are 38 as many girls as boys
- C. Boys are 311 of everyone
- D. Girls are 311 of everyone
Choose the right answer
Show the answer and working
Answer: C. Boys are 311 of everyone
Everyone is 3 + 8 = 11 parts; boys are 3 of them: 311.
Practise it in the game →Ratio and rate · Free to start, unlimited questions, no download