Ratio meaning

• A ratio is a way of comparing two or more quantities.
• It tells us how much of one thing there is compared to another thing.
• For example, we could have a ratio which tells us how many apples there are compared to how many oranges there are.
• Importantly, they don’t tell us the actual amounts of each thing, just how their amounts compare to each other.

Writing ratios

• If we know that we have n apples and m oranges, we can write the ratio of apples to oranges as n:m.
• For example, if we have 3 apples and 5 oranges, we can write the ratio of apples to oranges as 3:5.
• This could also be written in any equivalent form. For example, the 3:5 apples to oranges ratio could also be written as 6:10 or 9:15, for example.
• To find equivalent ratios, we can multiply or divide both sides of the ratio by the same number - see simplifying ratios for more details.

Examples

A fruit bowl contains pears and bananas in the ratio 2:3. If there are 8 pears, how many bananas are there?

• The ratio of pears to bananas is 2:3.
• We can see that each part pear is equal to 4 actual pears, because:
  • 8 \div 2 = 4
• To keep the ratio the same, we need to multiply the number of bananas by 4 as well:
• 3 \times 4 = 12
• Answer: there are 12 bananas.

A classroom has boys and girls in the ratio 5:4. If there are 20 boys, how many girls are there?

• The ratio of boys to girls is 5:4.
• We can see that each part boy is equal to 4 actual boys, because:
  • 20 \div 5 = 4
• To keep the ratio the same, we need to multiply the number of part girls by 4 as well:
  • 4 \times 4 = 16
• Answer: there are 16 girls.

This was probably the most awkwardly worded example I’ve ever written.