Year 8 Maths: Simplifying Ratios

What is a 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. For example, if there are 2 apples and 3 oranges, we can write the ratio of apples to oranges as 2:3.

What Does It Mean to Simplify a Ratio?

Simplifying a ratio means reducing it to its simplest form. This is similar to simplifying fractions. When we simplify a ratio, we divide both parts of the ratio by the same number until we can’t divide anymore.

Key Rules for Simplifying Ratios

1. Find a Common Factor: Look for the largest number that can divide both parts of the ratio.
2. Divide Both Parts: Once you find the common factor, divide both sides of the ratio by that number.
3. Check Your Work: After simplifying, make sure your new ratio is correct and that it’s in the simplest form.

Example 1: Simplifying a Simple Ratio

Let’s say we have a ratio of 4:8.

1. Find the Common Factor: The common factor of 4 and 8 is 4.
2. Divide Both Parts:
   • Divide the first part: $$4 \div 4 = 1$$
   • Divide the second part: $$8 \div 4 = 2$$
3. Write the Simplified Ratio: The simplified ratio is 1:2.

Example 2: Simplifying a More Complex Ratio

Now, let’s simplify the ratio 10:15.

1. Find the Common Factor: The common factor of 10 and 15 is 5.
2. Divide Both Parts:
   • First part: $$10 \div 5 = 2$$
   • Second part: $$15 \div 5 = 3$$
3. Write the Simplified Ratio: The simplified ratio is 2:3.

Tips and Tricks

• Always Look for the Greatest Common Factor (GCF): This will help you simplify ratios more easily.
• Practice with Real-Life Examples: Think about recipes, sports teams, or any situation where you can compare quantities.
• Use Visuals: Drawing or using objects can help you see the ratio clearly.

Questions for Practice

Easy Level Questions

1. Simplify the ratio 2:4.
2. Simplify the ratio 3:9.
3. Simplify the ratio 6:12.
4. Simplify the ratio 5:10.
5. Simplify the ratio 8:16.
6. Simplify the ratio 1:2.
7. Simplify the ratio 10:20.
8. Simplify the ratio 12:16.
9. Simplify the ratio 15:30.
10. Simplify the ratio 4:8.

Medium Level Questions

11. Simplify the ratio 14:21.
12. Simplify the ratio 18:24.
13. Simplify the ratio 9:27.
14. Simplify the ratio 16:40.
15. Simplify the ratio 35:50.
16. Simplify the ratio 25:35.
17. Simplify the ratio 22:44.
18. Simplify the ratio 30:45.
19. Simplify the ratio 28:42.
20. Simplify the ratio 32:48.

Hard Level Questions

21. Simplify the ratio 60:90.
22. Simplify the ratio 45:60.
23. Simplify the ratio 36:48.
24. Simplify the ratio 81:108.
25. Simplify the ratio 72:96.
26. Simplify the ratio 54:72.
27. Simplify the ratio 99:121.
28. Simplify the ratio 80:200.
29. Simplify the ratio 63:126.
30. Simplify the ratio 50:75.

Answers and Explanations

Easy Level Answers

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

Medium Level Answers

11. 2:3
12. 3:4
13. 1:3
14. 2:5
15. 7:10
16. 5:7
17. 1:2
18. 2:3
19. 2:3
20. 2:3

Hard Level Answers

21. 2:3
22. 3:4
23. 3:4
24. 3:4
25. 3:4
26. 3:4
27. 9:11
28. 1:2.5 or 2:5
29. 1:2
30. 2:3

Now that you know how to simplify ratios, practice with these questions and see how quickly you can simplify them! Remember, practice makes perfect!