Unit 5 – Rates, Ratios, and Proportions
Lesson 1 – Ratios
Blue
Blue – Ratios
1. In a class of students, the ratio of boys to girls is 4:5. What fraction of the class is
boys?
2. A company accountant checks last month’s invoices. The ratio of paid invoices to
unpaid invoices is 5:2. What fraction of the invoices are unpaid?
3. A cordial mix is made up so that the ratio of concentrate to water is 1:8. What
fraction of the mix is water?
4. (skip)
5. (skip)
6. Rainbow boarding kennels has 30 animals over the weekend. The ratio of cats to dogs
is 2:3. How many cats and how many dogs are there?
7. Split these quantities up in the given ratio.
a. 64 into the ratio of 3:5
b. $400 into the ratio of 2:3
c. 540 students into the ratio of 4:5
8. 24 cans of baked beans were to be divided between 2 camping groups in the ratio of
7:5. How many cans did each group get?
9. In a 2 liter jug of soft drink the concentrate and water is mixed in a ratio of 1:4
a. What is the quantity of concentrate and water needed for the 2 liter mixture of
drink?
b. If you wanted to make 5 liters of drink mixture, how much water would be
needed?
10. Mark and Andrea shared a 240g bag of sweets in the ratio of 5:7. How much did each
eat?
11. A grade 6 class decided to buy their math teacher a gift at the end of the year. Boys
and girls contributed in the ratio 5:4. If the gift cost Rp180,000, how much did the
girls contribute?
12. Duncan, Chris, and Phoebe pooled their money in the ratio 3:5:7. If the total money
pooled together was $75, what were the 3 separate amounts put in?
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Unit 5 – Rates, Ratios, and Proportions
Lesson 1 – Ratios
Blue
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Unit 5 – Rates, Ratios, and Proportions
Lesson 1 – Ratios
Blue
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Unit 5 – Rates, Ratios, and Proportions
Lesson 1 – Ratios
Blue
13. Sam, Andy and Tom decide to buy their teacher a Christmas gift. The amount they
contributed for the gift was in the ratio 4:3:2 respectively. They collected 720,000
rupiah altogether. How much money did Sam contribute?
14. A packet of peanuts is divided between 2 children in the ratio of 4:9. If Suzie gets
15 peanuts less than Jong Min, find the total number of peanuts.
15. Tracy had $85 and Anya had $60. After they donated an equal sum of money to
charity, the ratio of Tracy’s money to Anya’s money was 12:7. How much money did
they have left altogether?
16. Melissa has 40 novels. Kevin has 20 more novels than Melissa. What is the ratio of
the number of Melissa’s story books to that of Kevin’s?
17. The ratio of the number of Ann’s picture cards to the number of Wendy’s picture
cards was 7:8. After Wendy gave 8 picture cards to Ann, they each had the same
number of picture cards. How many picture cards did they have altogether?
18. The ratio of the number of cars to the number of bicycles is 10:7. Each car has 4
wheels and each bicycle has 2 wheels. If all the cars and bicycles have a total of 486
wheels, how many wheels do all the cars have altogether?
19. The ratio of the number of Yvonne's stamps to the number of Cherise's stamps is
2:9. If Yvonne has 72 stamps and Cherise gives away 5 of her stamps, how many
stamps does Cherise have left?
20. Denise and Peter shared some coins in the ratio 11:5. If Denise received 30 more
coins than Peter, how many coins were there altogether?
21. The ratio of the number of Maya's stickers to the number of Quentin's stickers is
8:5. If Quentin has 15 fewer stickers than Maya, how many stickers does Maya have?
22. A sum of money is shared between Jasmine and Louisa in the ratio 4:5. If Louisa
were to give $9 to Jasmine, they would have the same amount of money. How much
money does Louisa have now?
Solutions
1. 4
9
2. 2
7
3. 8
9
4. (hakuna matata)
5. (hakuna matata)
6. 12 cats and 18 dogs
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Unit 5 – Rates, Ratios, and Proportions
Lesson 1 – Ratios
Blue
7. a. 24 & 40
b. 160 & 240
240 & 300
8. 14 & 10
9. a. 400 ml of concentrate & 1600 ml of water
b. 4000 ml
10. 100 g & 140 g
11. Rp. 100,000 & Rp. 80,000
12. $15, $25 & $35
13. Total number of portions = 4 + 3 + 2 = 9
9 portions = Rp. 720,000, so 1 portion = Rp. 80,000
Since Sam’s share in the total is 4 portions, he/she contributes Rp. 320,000
14. Suzie and Jong Min add up total 13 units (4 + 9)
So total number of peanuts = 13 x 3 = 39
15. Tracy has $85 and this represents the higher part of the ratio (12 units). Anya has
$60 and this represents the lower part of the ratio (7 units).
The difference in money is $85 - $60 = $25
The difference in ratio is 12 – 7 = 5 units
5 units = $25
1 unit = $5
Total units between them is 12 + 7 = 19 units
ANSWER: the total money between them is 19 * 5 = $95
16. 2:3
17. 240
18. 360
19. 319 stamps
20. 80 coins
21. 40 stickers
22. Louisa has $90 (and Jasmine has $72). If Louisa gives Jasmine $9, then they both
will have $81.
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Unit 5 – Rates, Ratios, and Proportions
Lesson 1 – Ratios
Blue
Bibliography Information
Teachers attempted to cite the sources for the problems included in this problem set. In some cases, sources may
not have been known.
Problems
Bibliography Information
6
Geldof, W. Homework Book 3 /4, 2nd edition.
NZ Mathematics Curriculum, Sigma
Publications, 1999.
1-5, 11
Barton, David. Beta Mathematics. Pearson
Education New Zealand.
WE 2, WE 3
Lee, Joseph D. Primary Mathematics 6:
Challenging Word Problems. Singapore: EPB
Pan Pacific, 2006.
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