Introduction to Ratios

Hello, Year 8! Today, we’re going to learn how to use bar diagrams to solve ratio word problems. Ratios are a way to compare two or more quantities. They help us understand how much of one thing there is compared to another.

What is a Ratio?

A ratio tells us how much of one thing there is compared to another. For example, if there are 2 apples and 3 oranges, we can say the ratio of apples to oranges is 2:3.

Using Bar Diagrams

Bar diagrams are a visual way to represent ratios. They help us see the relationship between different quantities clearly.

How to Draw a Bar Diagram

  1. Identify the Ratio: Look at the problem and find the ratio given.
  2. Draw Bars: Draw a bar for each part of the ratio.
  3. Label the Bars: Write what each bar represents.
  4. Calculate the Total: If you know the total amount, divide it according to the ratio.
  5. Fill in the Values: Write the amounts above each bar.

Example Problem

Let’s work through an example together.

Problem: Sarah and Tom have a ratio of 3:2 for the number of stickers they have. If Sarah has 15 stickers, how many stickers does Tom have?

  1. Identify the Ratio: The ratio of Sarah to Tom is 3:2.
  2. Draw Bars: Draw 3 parts for Sarah and 2 parts for Tom. Sarah: |---|---|---| Tom: |---|---|
  3. Total Parts: Add the parts together: 3 + 2 = 5 parts.
  4. Calculate the Value of Each Part: If Sarah has 15 stickers (3 parts), then each part is \frac{15}{3} = 5
    stickers.
  5. Calculate Tom’s Stickers: Tom has 2 parts, so 2 \times 5 = 10
    stickers.

Answer: Tom has 10 stickers.

Key Rules for Using Bar Diagrams

  1. Always simplify the ratio if possible before creating the bar diagram.
  2. Make sure the total number of parts adds up correctly.
  3. Check your work by adding the amounts you calculated.

Tips and Tricks

  • Use a ruler for neat bars.
  • Colour-code different parts for better clarity.
  • Practice with different examples to get comfortable.

Questions to Practice

Easy Level Questions

  1. The ratio of cats to dogs is 2:3. If there are 4 cats, how many dogs are there?
  2. In a class, the ratio of boys to girls is 1:2. If there are 5 boys, how many girls are there?
  3. The ratio of red to blue marbles is 1:4. If there are 3 red marbles, how many blue marbles are there?
  4. Sarah and John have a ratio of 1:1 for their toy cars. If Sarah has 6 cars, how many does John have?
  5. The ratio of apples to bananas is 2:5. If there are 10 apples, how many bananas are there?
  6. The ratio of pencils to erasers is 3:1. If there are 9 pencils, how many erasers are there?
  7. The ratio of students to teachers in a school is 4:1. If there are 12 students, how many teachers are there?
  8. The ratio of chocolate to vanilla cupcakes is 3:2. If there are 12 chocolate cupcakes, how many vanilla cupcakes are there?
  9. In a fruit basket, the ratio of oranges to apples is 2:3. If there are 8 oranges, how many apples are there?
  10. The ratio of cars to trucks is 5:2. If there are 25 cars, how many trucks are there?

Medium Level Questions

  1. The ratio of boys to girls in a school is 3:5. If there are 15 boys, how many girls are there?
  2. In a recipe, the ratio of flour to sugar is 4:1. If there are 12 cups of flour, how much sugar is needed?
  3. The ratio of chocolate to strawberry ice creams is 5:3. If there are 25 chocolate ice creams, how many strawberry ice creams are there?
  4. The ratio of red to green apples is 3:2. If there are 18 red apples, how many green apples are there?
  5. The ratio of fish to chips is 2:5. If there are 10 fish, how many chips are there?
  6. The ratio of men to women in a meeting is 4:3. If there are 28 attendees, how many are women?
  7. The ratio of books to magazines is 3:1. If there are 15 books, how many magazines are there?
  8. The ratio of students to computers is 5:1. If there are 40 students, how many computers are there?
  9. The ratio of roses to lilies is 3:4. If there are 21 roses, how many lilies are there?
  10. The ratio of cars to bicycles is 2:7. If there are 14 bicycles, how many cars are there?

Hard Level Questions

  1. The ratio of red to blue balls is 3:5. If the total number of balls is 64, how many are red?
  2. In a fruit shop, the ratio of apples to oranges is 4:3. If there are 84 pieces of fruit in total, how many apples are there?
  3. The ratio of boys to girls in a sports team is 7:5. If there are 48 players, how many are girls?
  4. The ratio of teachers to students in a class is 1:20. If there are 25 students, how many teachers are there?
  5. The ratio of cats to dogs is 2:3. If the total number of pets is 50, how many cats are there?
  6. The ratio of chocolate to vanilla cones is 5:4. If there are 90 cones in total, how many are vanilla?
  7. The ratio of pencils to pens is 7:3. If there are 60 writing instruments, how many are pencils?
  8. The ratio of red to green cars is 2:5. If there are 70 cars in total, how many are red?
  9. The ratio of boys to girls in a classroom is 3:4. If there are 42 students, how many are boys?
  10. The ratio of books to notebooks is 5:2. If there are 70 items in total, how many are notebooks?

Answers

Easy Level Answers

  1. 6 dogs
  2. 10 girls
  3. 12 blue marbles
  4. 6 cars
  5. 25 bananas
  6. 3 erasers
  7. 3 teachers
  8. 8 vanilla cupcakes
  9. 12 apples
  10. 10 trucks

Medium Level Answers

  1. 25 girls
  2. 3 cups of sugar
  3. 15 strawberry ice creams
  4. 12 green apples
  5. 25 chips
  6. 21 women
  7. 5 magazines
  8. 8 computers
  9. 28 lilies
  10. 4 cars

Hard Level Answers

  1. 24 red balls
  2. 48 apples
  3. 20 girls
  4. 1 teacher
  5. 20 cats
  6. 40 vanilla cones
  7. 42 pencils
  8. 20 red cars
  9. 18 boys
  10. 20 notebooks

Feel free to go back and revise the concepts or try working through the questions again. Happy learning, everyone!