Ratios
What is a ratio?
A ratio is a way to compare amounts of something. Recipes, for example, are sometimes given as ratios. A milkshake has two strawberries to every 100g of sugar. Therefore the ratio is 2:1
wHAT TYPES OF RATIO QUESTIONS ARE THERE?
Comparing Ratios
Which ratio is larger 2:16 or 15:45?
Divide by two both sides of the ratio 2:16
The answer will be 1:8
Divide by fifteen both sides of the ratio 15:45
The answer will be 1:3
Thus, 2:16 is larger than 15:45
Finding Quantities using ratios
Their grandfather gives them 140 sweets, which is to be divided between them in the ratio of their ages. How much does each of them get?
The ratio of their ages is 12:9.
We can simplify this. Dividing by 3 gives 4:3.
So Amit gets 4 parts, and Arun gets 3.
This means that the money has to be divided into 7 parts (4 + 3).
140 ÷ 7 = 20, so 1 part is 20.
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Amit gets 4 parts: 4 × 20 = 80 sweets.
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Arun gets 3 parts: 3 × 20 = 60 sweets.
Solving problems involving ratios
Anna has 75 cents.
Fiona has 1.20€.
What is the ratio of Anna's money to Fiona's money, in its simplest form?
One amount is in cents and the other one in euros.
We have to convert Fiona's amount into cents first:
€1.20 = 120 cents.
Now the ratio is 75:120. Both sides are divisible by 15.
Dividing both sides by 15 gives 5:8
So the ratio is 5:8.
