Fractions · Ages 11–12
Ratio and rate worksheet
Covers: What a ratio is, Equivalent ratios and simplest form, Sharing in a ratio, Ratios and fractions, Rates and unit prices, Map and model scales, Enlarging and shrinking shapes
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Ratio and rate worksheet
Fractions · Ages 11–12
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.The ratio of boys to all the children is 4 : 9. The ratio of boys to girls is 4 : .
Answer:
2.Write 9 : 21 : 3 in its simplest form: : :
Fill in each blank
Answer:
3.The ratio of 🦆 to 🐵 is 1 : 2, and there are 6 altogether. There are 🦆 and 🐵.
Fill in each blank
Answer:
4.The ratio of 📎 to 🐶 to 🍎 is 1 : 2 : 3, with 30 altogether. There are 📎, 🐶 and 🍎.
Fill in each blank
Answer:
5.The ratio of red beads to blue beads is 7 : 4. What fraction of all the beads are blue?
Answer in simplest form
Answer:
6.The ratio of Chi-keung's stickers to Ka-yan's is 5 : 8. What fraction of Ka-yan's number is Chi-keung's?
Answer in simplest form
Answer:
7.1 m = 100 cm. A model bus is made to a scale of 1 : 25, and the model is 44 cm long. How long is the real bus, in metres?
Answer:
8.A rectangle is 6 cm long and 3 cm wide. It is shrunk to 13 of its size. How wide is the new rectangle, in cm?
Answer:
Part B: Choose, or true or false (2 marks each)
9.A fruit basket holds 7 mangoes and 9 apples. What is the ratio of apples to mangoes?
- A. 7 : 9
- B. 7 : 16
- C. 9 : 16
- D. 9 : 7
Choose the right answer
Answer:
10.56 : 64 in its simplest form is 28 : 32.
True or false?
Answer:
11.The same water bottle is sold in four packs. Which is the best buy?
- A. 5 for $15
- B. 5 for $35
- C. 6 for $24
- D. 4 for $36
Choose the right answer
Answer:
12.When buying kites, “6 for $66” is a better buy than “3 for $24”.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.A bus has 34 passengers: 11 are standing and the rest are sitting. The ratio of sitting passengers to all the passengers is : .
Fill in each blank
Working:
Answer:
14.For pineapple buns, the ratio of flour to sugar by weight is 4 : 3. The baker uses 240 g of flour. How many grams of sugar are needed?
Working:
Answer:
15.A ribbon 240 cm long is cut into two pieces in the ratio 5 : 7. How long is the longer piece, in cm?
Working:
Answer:
16.On a shelf, the ratio of storybooks to picture guides is 9 : 4. What fraction of all the books on the shelf are storybooks?
Answer in simplest form
Working:
Answer:
17.A supermarket sells cereal in two packs: a small 500 g pack for $35 and a big 800 g pack for $64. Which is the better buy?
- A. The small pack
- B. They are equally good buys
- C. There isn't enough to tell
- D. The big pack
Choose the right answer
Working:
Answer:
18.A projector enlarges a picture 11 cm wide and 8 cm high onto a wall, where it is 209 cm wide. How high is the picture on the wall, in cm?
Working:
Answer:
Show the answers and working
Ratio and rate worksheet: Answers and working
Part A: Working out and filling in
1. 5
Of the 9 parts, boys take 4. How many parts are girls?
Of the 9 parts, boys are 4, so girls are 9 − 4 = 5: 4 : 5.
2. 3, 7, 1
Find the H.C.F. of 9, 21 and 3, then divide all three by it.
The H.C.F. of all three terms is 3; divide all three by 3: 3 : 7 : 1.
3. 2, 4
There are 1 + 2 boxes. Find one box first: 6 ÷ (1 + 2).
Each box is 6 ÷ 3 = 2; 🦆: 1 × 2 = 2, and 🐵: 2 × 2 = 4.
4. 5, 10, 15
There are 1 + 2 + 3 boxes. Find one box first.
6 boxes in all, each 30 ÷ 6 = 5: 5, 10 and 15.
5. 411
For a fraction of the whole, the denominator is all the parts: 7 + 4.
7 + 4 = 11 parts in all, and blue is 4 of them: 411.
6. 58
Compared with Ka-yan, the denominator is Ka-yan's parts and the numerator Chi-keung's.
Compared with Ka-yan, the denominator is Ka-yan's 8 parts: Chi-keung has 58 of Ka-yan's number.
7. 11 m
1 cm of the model stands for 25 cm. Find the real bus in centimetres, then change to metres.
44 × 25 = 1100 cm, which is 11 m.
8. 1 cm
Shrinking to 13 divides every side by 3. The question asks for the width.
Shrinking to 13 divides every side by 3: 3 ÷ 3 = 1.
Part B: Choose, or true or false
9. D. 9 : 7
Check the order in the question: apples first, then mangoes. Which comes first in the ratio?
It asks for apples to mangoes, so the 9 apples come first: 9 : 7.
10. False
Find the H.C.F. of 56 and 64, then see whether 28 : 32 can be simplified any further.
The H.C.F. of 56 and 64 is 8; dividing by 8 gives 7 : 8. Dividing by a smaller common factor doesn't reach the simplest form.
11. A. 5 for $15
Turn each pack into the price for one: total ÷ how many. Then compare.
Change each to a unit price: the cheapest is $3 each.
12. False
Turn both into the price for one: 66 ÷ 6 and 24 ÷ 3.
Unit prices: 66 ÷ 6 = 11 and 24 ÷ 3 = 8; the lower one is the better buy.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 23, 34
Find how many are sitting first, 34 − 11, then compare with all the passengers.
34 − 11 = 23 are sitting, out of all 34: 23 : 34.
14. 180 g
Flour is 4 parts, 240 g. Find one part first.
240 ÷ 4 = 60, so a part is 60 g; sugar: 3 × 60 = 180 g.
15. 140 cm
There are 5 + 7 parts. Find one part first; the longer piece is the one with more parts.
Each part is 240 ÷ (5 + 7) = 20 cm; the longer piece has more parts: 140 cm.
16. 913
For a fraction of all the books, the denominator is all the parts: 9 + 4.
9 + 4 parts in all, storybooks 9: 913.
17. A. The small pack
Turn both packs into the price for each 100 g, then compare.
For each 100 g: small 35 ÷ 5 = $7, big 64 ÷ 8 = $8; the lower one is the better buy.
18. 152 cm
Find the scale factor first: how many times 11 is the wall width, 209?
The scale factor is 209 ÷ 11 = 19; height 8 × 19 = 152.
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