What is a Ratio?

A ratio is a way to compare two or more quantities. It shows how much of one thing there is compared to another. We can write a ratio in different ways: as a fraction, with a colon, or in words.

For example, if we have 2 apples and 3 oranges, we can express the ratio of apples to oranges as:

  • 2:3 (read as “2 to 3”)
  • $\frac{2}{3}$ (as a fraction)
  • “There are 2 apples for every 3 oranges.”

Key Rules for Ratios

  1. Same Units: Make sure the items you are comparing are in the same units. For instance, you can’t compare apples and oranges directly.
  2. Simplifying Ratios: Just like fractions, ratios can be simplified. For example, the ratio 4:8 can be simplified to 1:2.
  3. Equivalent Ratios: These are ratios that express the same relationship. For example, 1:2, 2:4, and 3:6 are all equivalent ratios.

Tips and Tricks

  • Visual Aids: Drawing pictures or using objects can help you see ratios more clearly.
  • Use of Tables: Sometimes, making a table can help you organise and compare different ratios.
  • Practice: The more you work with ratios, the easier they become!

Examples

  1. Example 1: If there are 4 cats and 6 dogs, the ratio of cats to dogs is:
    • 4:6
    • Simplified: 2:3
  2. Example 2: In a class, there are 10 girls and 5 boys. The ratio of girls to boys is:
    • 10:5
    • Simplified: 2:1
  3. Example 3: If a recipe calls for 3 cups of flour and 2 cups of sugar, the ratio of flour to sugar is:
    • 3:2

Practice Questions

Easy Level Questions

  1. What is the ratio of 2 apples to 4 oranges?
  2. If there are 5 cats and 3 dogs, what is the ratio of cats to dogs?
  3. There are 12 boys and 8 girls in a class. What is the ratio of boys to girls?
  4. If a jug has 4 litres of water and 2 litres of juice, what is the ratio of water to juice?
  5. The ratio of red marbles to blue marbles is 1 to 2. If there are 2 red marbles, how many blue marbles are there?
  6. What is the ratio of 10 pencils to 5 erasers?
  7. There are 3 footballs and 6 basketballs. Write the ratio of footballs to basketballs.
  8. If a fruit basket has 2 bananas and 6 apples, what is the ratio of bananas to apples?
  9. The ratio of 1 dog to 3 cats is given. If there is 1 dog, how many cats are there?
  10. A student has 4 red pens and 1 blue pen. What is the ratio of red pens to blue pens?

Medium Level Questions

  1. If there are 8 green balls and 4 yellow balls, what is the simplified ratio of green balls to yellow balls?
  2. The ratio of books to magazines in a library is 3:1. If there are 12 books, how many magazines are there?
  3. A recipe requires 2 cups of rice for every 5 cups of water. What is the ratio of rice to water?
  4. If a car travels 60 km in 1 hour and 120 km in 2 hours, what is the ratio of distance traveled in the two hours to the distance traveled in the first hour?
  5. The ratio of girls to boys in a school is 7:5. If there are 35 girls, how many boys are there?
  6. A box contains 10 chocolates and 5 mints. What is the ratio of chocolates to mints?
  7. If a farmer has 15 cows and 10 sheep, what is the ratio of cows to sheep?
  8. A fruit seller has 20 apples and 30 oranges. What is the ratio of apples to total fruits?
  9. If the ratio of cats to dogs is 4:3 and there are 12 cats, how many dogs are there?
  10. There are 10 students in a class who like maths and 15 students who like science. What is the ratio of students who like maths to those who like science?

Hard Level Questions

  1. A bag contains 24 red balls, 36 green balls, and 12 blue balls. What is the ratio of red balls to green balls?
  2. In a class, the ratio of boys to girls is 3:4. If there are 21 boys, how many girls are there?
  3. The ratio of the ages of two siblings is 5:7. If the elder sibling is 14 years old, how old is the younger sibling?
  4. A recipe for cookies requires chocolate chips in the ratio of 3:2 to flour. If there are 9 cups of flour, how many cups of chocolate chips are needed?
  5. The ratio of the number of students in Year 5 to Year 6 is 4:5. If there are 40 students in Year 5, how many students are in Year 6?
  6. A school has a ratio of teachers to students of 1:15. If there are 120 students, how many teachers are there?
  7. If a car travels in the ratio of 2:3 for two different routes, and it travels 100 km on the first route, how far does it travel on the second?
  8. The ratio of red to blue to green marbles is 2:3:4. If there are 18 green marbles, how many red marbles are there?
  9. If the ratio of cats to dogs is 1:1 and there are 15 animals, how many cats and how many dogs are there?
  10. In a fruit basket, the ratio of apples to bananas is 5:3. If there are 40 apples, how many bananas are there?

Answers

Easy Level Answers

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

Medium Level Answers

  1. 2:1
  2. 4 magazines
  3. 2:5
  4. 120 km to 60 km or 2:1
  5. 25 boys
  6. 2:1
  7. 3:2
  8. 2:3
  9. 9 dogs
  10. 2:3

Hard Level Answers

  1. 2:3
  2. 28 girls
  3. 10 years old
  4. 6 cups of chocolate chips
  5. 50 students in Year 6
  6. 8 teachers
  7. 150 km
  8. 12 red marbles
  9. 7 cats and 8 dogs
  10. 24 bananas

Feel free to ask any questions or for further explanations! Happy learning!