Ratio and proportion
Share a quantity in a given ratio, or scale one quantity against another.
What a ratio is
A ratio compares quantities. If red and blue counters are in the ratio 3 : 2, then for every 3 red there are 2 blue.
The technique that solves most of them: find one share
Add the parts of the ratio to get the total number of shares, then divide.
30 counters are shared in the ratio 3 : 2. How many are red?
3 + 2 = 5 shares. 30 ÷ 5 = 6 per share. Red gets 3 shares = 3 × 6 = 18.
That "find one share first" step turns nearly every ratio question into two easy divisions.
The classic mistake
Dividing by one side of the ratio instead of by the total. 30 ÷ 3 = 10 is a very tempting wrong answer, and it will usually be one of the options.
How to attack this question type
- 1
Add the ratio parts FIRST to get the number of shares. Almost every error here comes from dividing by the wrong number.
- 2
Find the value of one share, then multiply up. Do not try to jump straight to the answer.
- 3
Check your answer adds back to the total. If red is 18 and blue is 12, that is 30 — correct.
- 4
Watch for questions asking for the DIFFERENCE between shares rather than one share. Re-read what is actually wanted.
Practice · untimed
A box of 45 marbles holds red and blue marbles in the ratio 4 : 5. How many are red?