Comparing Ratios: Graded Practice Set (Grade 8)

Grade 8 focus

This record is a dedicated practice set for comparing ratios in the Grade 8 ratios, rates, and proportions strand. Use it after studying the broader ratio-concepts material and the linked worked examples.

Use with linked records

This set deliberately avoids re-teaching the full lesson content already developed in:

• rea.m08.number.ratios-rates-proportions.ratio-concepts.worked-examples
• rea.m08.number.ratios-rates-proportions.ratio-concepts.practice-set
• rea.m08.number.ratios-rates-proportions.equivalent-ratios.scaling-ratios.worked-examples
• rea.m08.number.ratios-rates-proportions.equivalent-ratios.practice-set

If you get stuck on method, return to those records for full conceptual development and additional scaffolding.

What counts as a fair ratio comparison?

When two ratios are being compared, they must represent the same kind of comparison. For example, boys:girls can be compared with boys:girls, but not fairly with boys:total unless one ratio is rewritten to match the same meaning.

Useful comparison methods:

1. Simplify each ratio.
2. Scale to a common first or second term.
3. Convert to fractions and compare.
4. In context, interpret what the ratio means before calculating.

Difficulty tags

• Core = direct comparison with simple numbers
• Stretch = requires a method choice or more than one step
• Challenge = contextual or easily confused comparison

Practice problems

Core

1. Compare 2:3 and 4:6. Are they equal, or is one greater? [Core]
2. Compare 3:5 and 4:5. Which ratio is greater? [Core]
3. Compare 5:8 and 10:16. Are they equal? [Core]
4. Compare 7:9 and 14:15. Which ratio is greater? [Core]
5. Compare 4:7 and 8:15. Which ratio is greater? [Core]
6. Compare 6:11 and 12:22. Are they equal? [Core]
7. Compare 9:10 and 8:9. Which ratio is greater? [Core]
8. Compare 15:20 and 3:4. Are they equal? [Core]

Stretch

9. A red-to-blue bead ratio is 3:7 in Jar A and 6:14 in Jar B. Which jar has the greater red-to-blue ratio, or are they the same? [Stretch]
10. In Class A, the ratio of girls to boys is 5:4. In Class B, the ratio of girls to boys is 15:11. Which class has the greater girls-to-boys ratio? [Stretch]
11. A recipe uses sugar:flour in the ratio 2:5. Another recipe uses 5:12. Which recipe is sweeter relative to flour? [Stretch]
12. Team P won 8 of 12 games. Team Q won 10 of 15 games. Which team has the better win-to-game ratio? [Stretch]
13. A map uses 3 cm for 8 km. Another map uses 5 cm for 14 km. Which map uses the greater drawing-to-real-distance ratio? [Stretch]
14. In one bag, green:white marbles = 7:13. In another bag, green:white marbles = 14:27. Which bag has the greater green-to-white ratio? [Stretch]
15. Compare 11:18 and 13:21. Which is greater? [Stretch]
16. Compare 18:27 and 20:30. Are they equal? If so, explain briefly. [Stretch]

Challenge

17. School A has boys:girls = 12:15. School B has boys:girls = 16:18. Which school has the greater proportion of boys? [Challenge]
18. Mixture X has juice:water = 4:9. Mixture Y has juice:water = 5:11. Which mixture is stronger in juice? [Challenge]
19. In a poll, yes:no = 7:5. In another poll, yes:no = 13:10. Which poll shows stronger support for yes? [Challenge]
20. A rectangle has side ratio length:width = 9:6. Another rectangle has side ratio length:width = 15:10. Which rectangle is more elongated, or are they equally shaped? [Challenge]
21. A fruit drink has apple:orange = 3:2. Another has apple:orange = 10:7. Which has the greater apple-to-orange ratio? [Challenge]
22. Bus Route A had 24 students and 18 adults. Bus Route B had 32 students and 26 adults. Which route had the greater student-to-adult ratio? [Challenge]
23. Compare the ratios of shaded to unshaded squares.

• Design A: 18 shaded, 30 unshaded
• Design B: 21 shaded, 35 unshaded

Which design has the greater shaded-to-unshaded ratio? [Challenge]

24. Two stores report the ratio of sale items to regular-price items.

• Store A: 45:60
• Store B: 36:50

Which store has the greater sale-to-regular ratio? [Challenge]

Answer key

1. Equal
2. 4:5 is greater
3. Equal
4. 14:15 is greater
5. 4:7 is greater
6. Equal
7. 9:10 is greater
8. Equal
9. Same
10. Class A
11. First recipe (2:5)
12. Equal
13. Second map (5:14)
14. First bag (7:13)
15. 13:21 is greater
16. Equal
17. School B
18. Mixture X
19. First poll (7:5)
20. Equal
21. First drink (3:2)
22. Route A
23. Equal
24. Store A

Full solutions for the hardest third

17. School A has boys:girls = 12:15. School B has boys:girls = 16:18.

We compare boys:girls in each school.

• School A: 12:15 = 4:5
• School B: 16:18 = 8:9

Now compare 4:5 and 8:9.

Use cross-products:

• 4 x 9 = 36
• 5 x 8 = 40

Since 36 < 40, we have 4/5 < 8/9.

So School B has the greater proportion of boys relative to girls.

Answer: School B

18. Mixture X has juice:water = 4:9. Mixture Y has juice:water = 5:11.

A stronger mixture has more juice for the same amount of water, so compare 4:9 and 5:11.

Cross-multiply:

• 4 x 11 = 44
• 9 x 5 = 45

Since 44 < 45, 4/9 < 5/11 is false? Check carefully: comparing 4/9 and 5/11, cross-products give 44 and 45, so 4/9 < 5/11.

That means 5:11 is slightly greater than 4:9? No: because 44 < 45, 4/9 is smaller than 5/11.

So Mixture Y has the greater juice-to-water ratio.

Answer: Mixture Y

19. In a poll, yes:no = 7:5. In another poll, yes:no = 13:10.

Compare 7:5 and 13:10.

Cross-multiply:

• 7 x 10 = 70
• 5 x 13 = 65

Since 70 > 65, 7/5 > 13/10.

So the first poll has stronger support for yes.

Answer: First poll (7:5)

20. Rectangle side ratios are 9:6 and 15:10.

Shape comparison depends on whether the side ratios are equivalent.

Simplify:

• 9:6 = 3:2
• 15:10 = 3:2

The ratios are equal, so the rectangles have the same shape. Neither is more elongated.

Answer: Equal

21. Fruit drink ratios are apple:orange = 3:2 and 10:7.

Compare 3:2 and 10:7.

Cross-multiply:

• 3 x 7 = 21
• 2 x 10 = 20

Since 21 > 20, 3/2 > 10/7.

So the first drink has more apple relative to orange.

Answer: First drink (3:2)

22. Route A had 24 students and 18 adults. Route B had 32 students and 26 adults.

Write the student-to-adult ratios:

• Route A: 24:18 = 4:3
• Route B: 32:26 = 16:13

Compare 4:3 and 16:13.

Cross-multiply:

• 4 x 13 = 52
• 3 x 16 = 48

Since 52 > 48, 4/3 > 16/13.

So Route A has the greater student-to-adult ratio.

Answer: Route A

23. Design A: 18 shaded, 30 unshaded. Design B: 21 shaded, 35 unshaded.

Write each shaded-to-unshaded ratio:

• Design A: 18:30 = 3:5
• Design B: 21:35 = 3:5

They simplify to the same ratio, so the designs are equal in shaded-to-unshaded comparison.

Answer: Equal

24. Store A: 45:60. Store B: 36:50.

Compare sale-to-regular ratios.

Simplify first:

• Store A: 45:60 = 3:4
• Store B: 36:50 = 18:25

Compare 3:4 and 18:25.

Cross-multiply:

• 3 x 25 = 75
• 4 x 18 = 72

Since 75 > 72, 3/4 > 18/25.

So Store A has the greater sale-to-regular ratio.

Answer: Store A

Common errors to watch for

• Comparing ratios with different meanings, such as boys:girls versus boys:total.
• Simplifying only one part of a ratio instead of both parts by the same factor.
• Comparing whole-number differences instead of the ratios themselves.
• Forgetting to interpret the context: for example, a greater juice:water ratio means a stronger mixture.

Quick self-check

You are ready to move on if you can do all of the following reliably:

• decide whether two ratios are equivalent,
• choose a valid comparison method without being told which one to use,
• explain in words what a greater ratio means in context,
• avoid mixing part-to-part and part-to-whole comparisons.