Introduction to Ratio and Scale

Hello Year 6! Today we are going to learn about ratio and scale. These are important concepts in maths that help us compare things and understand sizes.

What is a Ratio?

A ratio tells us how much of one thing there is compared to another. We can think of it as a way to show relationships between numbers.

Example of a Ratio:

If you have 2 apples and 3 oranges, the ratio of apples to oranges is written as 2:3. This means for every 2 apples, there are 3 oranges.

Key Rules for Ratios

  1. Write in simplest form: Always try to simplify the ratio. For example, if you have 4 red balls and 2 blue balls, you can simplify the ratio from 4:2 to 2:1.
  2. Equal parts: Ratios can also be equal. If you have 6 boys and 6 girls, the ratio is 6:6, which simplifies to 1:1.
  3. Order matters: The order of the numbers in a ratio is important. 2:3 is not the same as 3:2.

What is Scale?

Scale is used to create a representation of something that is bigger or smaller than the original. It’s often used in maps or models.

Example of Scale:

If a map has a scale of 1:100, it means that 1 cm on the map represents 100 cm in real life.

Key Rules for Scale

  1. Understanding the scale factor: If the scale is 1:50, then 1 unit on the model or drawing represents 50 units in real life.
  2. Using scale to find real sizes: If a room is 3 cm on a scale drawing with a scale of 1:20, the real size of the room is 3 cm × 20 = 60 cm.

Tips and Tricks

  • Always keep ratios as simple as possible.
  • Remember the order when writing ratios.
  • For scale, make sure to multiply or divide correctly to find real sizes.

Practice Questions

Easy Level Questions

  1. What is the ratio of 3 cats to 2 dogs?
  2. Simplify the ratio 10:5.
  3. If there are 4 red cars and 6 blue cars, what is the ratio of red to blue?
  4. Write the ratio of 5 apples to 10 oranges.
  5. If you have 3 pencils and 6 pens, what is the ratio of pencils to pens?
  6. Simplify the ratio 8:4.
  7. What is the ratio of 1 banana to 3 apples?
  8. If a box has 2 green balls and 1 yellow ball, what is the ratio of green to yellow?
  9. Write the ratio of 12 to 8 in simplest form.
  10. If there are 5 boys and 7 girls, what is the ratio of boys to girls?

Medium Level Questions

  1. If the ratio of cats to dogs is 3:4 and there are 12 cats, how many dogs are there?
  2. A recipe calls for 2 cups of flour and 3 cups of sugar. What is the ratio of flour to sugar?
  3. If 15 students out of 25 are girls, what is the ratio of girls to boys?
  4. In a class, the ratio of boys to girls is 2:3. If there are 10 boys, how many girls are there?
  5. Simplify the ratio 16:24.
  6. On a map with a scale of 1:50, how many cm does a 2 m distance represent?
  7. If a drawing is made with a scale of 1:10 and a tree is drawn as 5 cm tall, how tall is the real tree?
  8. A model car is made with a scale of 1:25. If the model is 10 cm long, how long is the actual car?
  9. The ratio of red balls to blue balls is 5:2. If there are 35 red balls, how many blue balls are there?
  10. If a painting is drawn at a scale of 1:100 and is 5 cm wide, how wide is it in real life?

Hard Level Questions

  1. The ratio of boys to girls in a school is 3:5. If there are 120 boys, how many girls are there?
  2. A scale model of a building is made with a scale of 1:200. If the model is 15 cm tall, how tall is the real building?
  3. If a recipe requires 4 cups of milk for every 3 cups of cream, what is the ratio of milk to cream?
  4. In a fruit basket, the ratio of apples to bananas is 7:3. If there are 70 apples, how many bananas are there?
  5. A map has a scale of 1:250. If a distance on the map is 12 cm, what is the actual distance?
  6. If a bag contains 6 red marbles and 4 blue marbles, what is the ratio of red to total marbles?
  7. A car travels 120 miles in 2 hours. What is the scale of miles traveled per hour?
  8. If the ratio of teachers to students is 1:20 and there are 5 teachers, how many students are there?
  9. A drawing is made with a scale of 1:15. If a building is represented as 6 cm tall in the drawing, what is its real height?
  10. If a recipe calls for 2 parts sugar to 3 parts flour, what is the total number of parts?

Answers

Easy Level Answers

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

Medium Level Answers

  1. 16 dogs (3:4 means 3 cats to 4 dogs)
  2. 2:3
  3. 3:2
  4. 15 girls (2:3 means 10 boys to 15 girls)
  5. 2:3
  6. 100 cm
  7. 50 cm
  8. 250 cm
  9. 14 blue balls
  10. 500 cm

Hard Level Answers

  1. 200 girls (3:5 means 120 boys to 200 girls)
  2. 3000 cm (30 m)
  3. 4:3
  4. 30 bananas (7:3 means 70 apples to 30 bananas)
  5. 3000 cm
  6. 6:10 or 3:5
  7. 60 miles per hour
  8. 100 students (1:20 means 5 teachers to 100 students)
  9. 90 cm
  10. 5 parts

I hope this helps you understand ratio and scale better! Keep practicing, and you’ll get even better at it!