What is Ratio?

A ratio is a way to compare two or more quantities. It tells us how much of one thing there is compared to another.

Example of a Ratio

If there are 2 apples and 3 oranges, we can say the ratio of apples to oranges is 2:3. This means for every 2 apples, there are 3 oranges.

What is Proportion?

Proportion relates to ratios. It shows that two ratios are equal. For example, if we say the ratio of apples to oranges is the same in two different baskets, we are talking about proportion.

Example of Proportion

If Basket A has 2 apples and 3 oranges (2:3) and Basket B has 4 apples and 6 oranges (4:6), these two ratios are in proportion because they represent the same relationship.

Key Rules for Working with Ratios and Proportions

  1. Simplifying Ratios: Always try to simplify ratios. For example, 4:8 can be simplified to 1:2 by dividing both parts by 4.
  2. Equivalent Ratios: Ratios can be multiplied or divided by the same number to find equivalent ratios. For example, multiplying 2:3 by 2 gives you 4:6.
  3. Finding Missing Values: In a proportion, if you know three values, you can find the missing value. For example, if you know that 2:3 = x:6, you can find x by cross-multiplying.

Tips and Tricks

  • Visualising Ratios: Drawing pictures or using objects can help you understand ratios better. For example, using blocks to represent different quantities.
  • Using Tables: Create a table to list different ratios to see patterns.
  • Practice, Practice, Practice: The more you work with ratios and proportions, the easier they will become!

Questions to Practice

Easy Level

  1. What is the ratio of 1 cat to 2 dogs?
  2. If there are 5 red balls and 10 blue balls, what is the ratio of red to blue?
  3. Simplify the ratio 6:12.
  4. If there are 4 boys and 8 girls, what is the ratio of boys to girls?
  5. What is the ratio of 3 apples to 2 oranges?
  6. If a recipe calls for 2 cups of flour to 1 cup of sugar, what is the ratio of flour to sugar?
  7. How would you write the ratio of 7 cats to 3 dogs?
  8. What is the ratio of 10 pencils to 5 erasers?
  9. Simplify the ratio 8:24.
  10. If there are 15 marbles and 5 are red, what is the ratio of red marbles to total marbles?

Medium Level

  1. If the ratio of boys to girls in a class is 3:5 and there are 15 boys, how many girls are there?
  2. Simplify the ratio 18:24.
  3. If the ratio of cats to dogs is 2:1 and there are 10 cats, how many dogs are there?
  4. Find the missing value in the proportion 4:5 = x:25.
  5. If a recipe uses 3 parts sugar to 2 parts butter, how much sugar is needed for 10 parts of the mixture?
  6. The ratio of apples to oranges in a basket is 1:4. If there are 8 oranges, how many apples are there?
  7. If a car travels 60 miles in 1 hour, how far will it travel in 3 hours at the same speed?
  8. The ratio of boys to girls in a team is 2:3. If there are 20 girls, how many boys are there?
  9. If the ratio of red to blue marbles is 3:2 and there are 15 red marbles, how many blue marbles are there?
  10. If you buy 5 oranges for £2, how much would 10 oranges cost?

Hard Level

  1. In a recipe, the ratio of flour to sugar is 4:1. If you use 500g of flour, how much sugar do you need?
  2. If the ratio of cats to dogs is 5:3 and there are 30 animals, how many are cats?
  3. In a class, the ratio of boys to girls is 4:5. If there are 36 students, how many are girls?
  4. Solve for x in the proportion 12:x = 3:4.
  5. If 3 books cost £12, how much will 5 books cost?
  6. The ratio of red to green apples is 7:5. If there are 84 red apples, how many green apples are there?
  7. A car travels 150 miles in 3 hours. How far does it travel in 5 hours at the same speed?
  8. If the ratio of chocolate to vanilla ice cream is 2:3 and you have 30 scoops of vanilla, how many scoops of chocolate do you have?
  9. If the ratio of boys to girls in a school is 5:6 and there are 55 boys, how many girls are there?
  10. In a fruit basket, the ratio of bananas to apples is 2:1. If there are 14 bananas, how many apples are there?

Answers and Explanations

Easy Level Answers

  1. 1:2
  2. 1:2
  3. 1:2
  4. 1:2
  5. 3:2
  6. 2:1
  7. 7:3
  8. 2:1
  9. 1:3
  10. 1:3

Medium Level Answers

  1. 25 girls (3:5 means for every 3 boys, there are 5 girls; so, 15 boys = 5 groups of 3, hence 5 groups of 5 = 25 girls).
  2. 3:4
  3. 5 dogs (2:1 means for every 2 cats, there is 1 dog; 10 cats = 5 dogs).
  4. 20 (cross-multiply: 4 * 25 = 5 * x).
  5. 6 parts sugar (3 of sugar to 2 of butter, 10 parts = 3/5 of 10 = 6).
  6. 2 apples (1:4 means for every 4 oranges, there is 1 apple; thus, 8 oranges = 2 apples).
  7. 180 miles (60 miles/hour * 3 hours = 180).
  8. 12 boys (2:3 means for every 2 boys, there are 3 girls; if there are 20 girls, that means there are 12 boys).
  9. 10 blue marbles (3:2 means for every 3 red, 2 blue; 15 red = 10 blue).
  10. £4 (if 5 oranges are £2, then 10 oranges are double that).

Hard Level Answers

  1. 125g (4:1 means 4 parts flour to 1 part sugar; 500g flour = 125g sugar).
  2. 18 cats (5:3 means total parts = 8; if 30 animals = 8 parts, then 5 parts = 30/8 * 5 = 18).
  3. 20 girls (4:5, total parts = 9; 36 students = 36/9 * 5 = 20 girls).
  4. x = 16 (cross-multiply).
  5. £20 (if 3 books are £12, then 5 books cost 5/3 of £12).
  6. 60 green apples (7:5 means total parts = 12; if 84 red = 84/7 * 5 = 60).
  7. 250 miles (150 miles/3 hours = 50 miles/hour, 50 * 5 = 250).
  8. 20 scoops of chocolate (2:3 means 2 parts chocolate for every 3 parts vanilla; 30 vanilla = 20 chocolate).
  9. 66 girls (5:6 means total parts = 11; 55 boys = 55/5 * 6 = 66).
  10. 7 apples (2:1 means for every 2 bananas, there is 1 apple; thus, 14 bananas = 7 apples).

By practicing these questions, you’ll become a whiz at ratios and proportions! Keep working hard and you’ll get the hang of it!