Grade 8 Practice Set: Part-to-Part and Part-to-Whole Relationships

Use and placement

This record is a Grade 8 practice set for learners who have already studied the linked lesson rea.m08.number.ratios-rates-proportions.ratio-concepts.part-whole.lesson and the linked worked examples rea.m08.number.ratios-rates-proportions.ratio-concepts.part-whole.worked-examples. It is designed to build speed, precision, and error-checking before the linked mastery quiz rea.m08.number.ratios-rates-proportions.ratio-concepts.unit-mastery-quiz.

Do not reread this set as a lesson. If you are still unsure how to tell whether a comparison is part-to-part or part-to-whole, return first to the linked lesson and worked examples.

Practice routine

For each question:

1. Name the quantities being compared.
2. Decide whether the comparison is part-to-part or part-to-whole.
3. Write the ratio in the order asked.
4. Simplify only if appropriate.
5. Check that the second quantity is really the whole whenever a part-to-whole ratio is requested.

Common error check

A frequent mistake is to answer a part-to-whole question with a part-to-part ratio, or the reverse. Before finalizing an answer, ask:

• "Did I compare a part to another part?"
• "Or did I compare a part to the total?"

Difficulty key

• E = easier fluency
• M = medium reasoning
• H = harder multi-step reasoning

Problems

Section A: Identify and write ratios

1. E In a basket, there are 6 red apples and 10 green apples. Write the ratio of red apples to green apples.
2. E In the same basket, write the ratio of red apples to all apples.
3. E A class has 12 boys and 15 girls. Write the ratio of girls to boys.
4. E In the same class, write the ratio of boys to total students.
5. E A jar contains 9 blue marbles, 3 yellow marbles, and 6 white marbles. Write the ratio of yellow marbles to blue marbles.
6. E In the same jar, write the ratio of white marbles to all marbles.
7. M A team scored 18 two-point baskets and 7 three-point baskets. Write the ratio of three-point baskets to all baskets made.
8. M A pet store has 14 cats, 9 dogs, and 5 rabbits. Write the ratio of dogs to cats.
9. M In the same pet store, write the ratio of rabbits to all animals.
10. M A shelf holds 8 science books, 12 history books, and 4 novels. Write the ratio of non-science books to all books.

Section B: Decide which ratio matches the statement

11. M In a box of crayons there are 5 red, 8 blue, and 7 green crayons. Which ratio represents blue crayons to all crayons?

• A. 8:5
• B. 8:20
• C. 8:7
• D. 12:20

12. M A school club has 11 Grade 8 students and 9 Grade 7 students. Which ratio represents Grade 7 students to Grade 8 students?

• A. 9:20
• B. 11:9
• C. 9:11
• D. 20:9

13. M A recipe uses 2 cups of milk, 3 cups of flour, and 1 cup of sugar. Which ratio represents milk to total cups of ingredients?

• A. 2:3
• B. 2:6
• C. 2:1
• D. 3:6

14. M At a concert, 120 seats are occupied and 30 are empty. Which ratio represents empty seats to all seats in simplest form?

• A. 30:120 = 1:4
• B. 30:150 = 1:5
• C. 120:150 = 4:5
• D. 30:150 = 2:10

Section C: Convert between part-to-part and part-to-whole

15. M In a game club, the ratio of chess players to checkers players is 4:7. What is the ratio of chess players to total players?
16. M In a garden, the ratio of tulips to daisies is 3:5. What is the ratio of daisies to total flowers?
17. H A bag contains black and white counters in the ratio 5:9. Write:

• a. the ratio of black counters to all counters
• b. the ratio of white counters to all counters
• c. the ratio of all counters to black counters

18. H The ratio of students who walk to school to students who ride the bus is 7:13. Write the ratio of:

• a. walkers to all these students
• b. bus riders to all these students
• c. bus riders to walkers

Section D: Unknown parts and totals

19. H A class has boys and girls in the ratio 4:5. There are 36 students in total. How many boys and how many girls are there?
20. H The ratio of fiction books to non-fiction books in a library display is 3:2. If there are 45 fiction books, how many books are in the display altogether?
21. H At an animal shelter, the ratio of cats to dogs is 5:3. There are 24 dogs. How many cats are there? What is the ratio of cats to all these animals?
22. H In a survey, the ratio of students who prefer juice to those who prefer water is 6:7. If 91 students were surveyed and everyone chose one of these two options, how many preferred juice?

Section E: Mixed interpretation and error-checking

23. H A student says: "If the ratio of red beads to blue beads is 2:5, then the ratio of red beads to all beads is also 2:5." Explain the mistake and give the correct part-to-whole ratio.
24. H In a school band, the ratio of trumpets to flutes is 4:6, and there are also 5 drummers. There are no other instruments.

• a. What is the ratio of trumpets to flutes in simplest form?
• b. What is the ratio of trumpets to all band members?
• c. If there are 8 trumpets, how many flutes and drummers are there? How many band members are there altogether?

Answer key

1. 6:10 = 3:5
2. 6:16 = 3:8
3. 15:12 = 5:4
4. 12:27 = 4:9
5. 3:9 = 1:3
6. 6:18 = 1:3
7. 7:25
8. 9:14
9. 5:28
10. 16:24 = 2:3
11. B
12. C
13. B
14. B
15. 4:11
16. 5:8
17. a. 5:14 b. 9:14 c. 14:5
18. a. 7:20 b. 13:20 c. 13:7
19. 16 boys, 20 girls
20. 75 books
21. 40 cats; cats to all animals = 40:64 = 5:8
22. 42 students
23. Mistake: 5 counts only blue beads, not all beads. Correct ratio is 2:7.
24. a. 2:3 b. 8:25 c. 12 flutes, 5 drummers, 25 total members

Full solutions for the hardest third

17. Black and white counters in the ratio 5:9

The ratio 5:9 compares black : white.

First find the total number of parts:

• 5 + 9 = 14 total parts

Now rewrite each requested ratio.

a. Black to all counters:

• black = 5 parts
• all = 14 parts
• ratio = 5:14

b. White to all counters:

• white = 9 parts
• all = 14 parts
• ratio = 9:14

c. All counters to black counters:

• all = 14 parts
• black = 5 parts
• ratio = 14:5

Final answers:

• a. 5:14
• b. 9:14
• c. 14:5

18. Walkers to bus riders is 7:13

The ratio 7:13 compares walkers : bus riders.

Find the total number of parts:

• 7 + 13 = 20 parts

a. Walkers to all students:

• walkers = 7 parts
• all = 20 parts
• ratio = 7:20

b. Bus riders to all students:

• bus riders = 13 parts
• all = 20 parts
• ratio = 13:20

c. Bus riders to walkers:

• bus riders = 13 parts
• walkers = 7 parts
• ratio = 13:7

Final answers:

• a. 7:20
• b. 13:20
• c. 13:7

19. Boys to girls is 4:5, total 36 students

The ratio 4:5 means:

• boys = 4 equal parts
• girls = 5 equal parts

Total parts:

• 4 + 5 = 9 parts

These 9 parts make 36 students, so each part is:

• 36 / 9 = 4 students per part

Now find each group:

• boys = 4 x 4 = 16
• girls = 5 x 4 = 20

Check:

• 16 + 20 = 36

Final answer:

• 16 boys
• 20 girls

20. Fiction to non-fiction is 3:2, with 45 fiction books

The ratio 3:2 means fiction corresponds to 3 equal parts.

If 3 parts = 45 books, then 1 part is:

• 45 / 3 = 15 books

Non-fiction is 2 parts:

• 2 x 15 = 30 books

Total books:

• 45 + 30 = 75

Final answer:

• 75 books altogether

21. Cats to dogs is 5:3, with 24 dogs

The ratio 5:3 means:

• cats = 5 parts
• dogs = 3 parts

If 3 parts = 24 dogs, then 1 part is:

• 24 / 3 = 8

Cats:

• 5 x 8 = 40

Total animals:

• 40 + 24 = 64

Cats to all animals:

• 40:64
• simplify by dividing both numbers by 8
• 40:64 = 5:8

Final answer:

• 40 cats
• cats to all animals = 5:8

22. Juice to water is 6:7, total 91 students

The ratio 6:7 means:

• juice = 6 parts
• water = 7 parts

Total parts:

• 6 + 7 = 13 parts

If 13 parts = 91 students, then 1 part is:

• 91 / 13 = 7

Students who prefer juice:

• 6 x 7 = 42

Check:

• water would be 7 x 7 = 49
• 42 + 49 = 91

Final answer:

• 42 students preferred juice

23. Explaining the mistake in 2:5

Given ratio:

• red : blue = 2:5

The student incorrectly says red : all is also 2:5. That is wrong because 5 represents only the blue beads, not the whole set.

To find red to all, add the parts:

• 2 + 5 = 7 total parts

So:

• red : all = 2:7

Final answer:

• mistake: confusing blue beads with all beads
• correct part-to-whole ratio = 2:7

24. Trumpets to flutes is 4:6, plus 5 drummers

Start with the given ratio:

• trumpets : flutes = 4:6

a. Simplify trumpets to flutes

Both 4 and 6 are divisible by 2:

• 4:6 = 2:3

b. Trumpets to all band members

The original part counts are useful here:

• 4 trumpet parts
• 6 flute parts
• 5 drummers

Total parts or members in this comparison:

• 4 + 6 + 5 = 15

So trumpets to all members is:

• 4:15

But part (c) gives a real trumpet count of 8, so scale factor matters there, not for the ratio in part (b) from the base counts.

c. If there are 8 trumpets

Since 4 parts correspond to 8 trumpets, the scale factor is:

• 8 / 4 = 2

So flutes are:

• 6 x 2 = 12

Drummers stay 5 because the problem states there are 5 drummers.

Total band members:

• 8 + 12 + 5 = 25

Now the actual ratio of trumpets to all members is:

• 8:25

Final answers:

• a. 2:3
• b. 8:25
• c. 12 flutes, 5 drummers, 25 members altogether

Self-check prompts

After finishing, verify these three ideas:

• A part-to-part ratio compares one category with another category.
• A part-to-whole ratio compares one category with the total of all relevant categories.
• When converting from part-to-part to part-to-whole, add the compared parts first.

Suggested next step

If you can complete this set accurately and explain errors in Questions 23 and 24, move to rea.m08.number.ratios-rates-proportions.ratio-concepts.unit-mastery-quiz.