Fractions · Ages 10–11
Does multiplying make it bigger or smaller? worksheet
Part of: Multiplying and dividing fractions
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Does multiplying make it bigger or smaller? worksheet
Fractions · Ages 10–11
Numsprite
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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)
1.29 × 129, 29 × 99, 29 × 109, 29 × 119, 29 × 79. Without working them out, how many of these products are greater than 29?
Answer:
2.44 × 109, 44 × 89, 44 × 89, 44 × 129, 44 × 119. Without working them out, how many of these products are greater than 44?
Answer:
3.Without working them out, put these products in order, smallest first.
- A. 23 × 1
- B. 23 × 43
- C. 23 × 94
- D. 23 × 13
Write the letters in the right order
Answer:
Part B: Choose, or true or false (2 marks each)
4.Without working it out: is 76 × 54 bigger or smaller than 76?
- A. Can't tell without working it out
- B. Greater than 76
- C. Equal to 76
- D. Smaller than 76
Choose the right answer
Answer:
5.28 × 87 is smaller than 28.
True or false?
Answer:
6.91 × 54 is smaller than 91.
True or false?
Answer:
7.Without working it out: is 62 × 27 bigger or smaller than 62?
- A. Smaller than 62
- B. Equal to 62
- C. Can't tell without working it out
- D. Greater than 62
Choose the right answer
Answer:
8.Without working them out, which product is the largest?
- A. 33 × 78
- B. 33 × 98
- C. 33 × 115
- D. 33 × 13
Choose the right answer
Answer:
9.92 × is smaller than 92. Which of these could be?
- A. 95
- B. 1
- C. 45
- D. 54
Choose the right answer
Answer:
10.66 × is smaller than 66. Which of these could be?
- A. 53
- B. 1
- C. 85
- D. 35
Choose the right answer
Answer:
11.22 ÷ 25 is greater than 22.
True or false?
Answer:
12.45 ÷ 37 is greater than 45.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.May copies a picture 12 cm long on a copier that multiplies every length by 13. Is the copy longer or shorter than the picture?
- A. The same length
- B. Can't tell without measuring
- C. Longer
- D. Shorter
Choose the right answer
Working:
Answer:
14.Ming gets $90 pocket money a week. Mum says next week's will be 59 of this week's. Is next week's more or less than this week's?
- A. Less
- B. More
- C. The same
- D. Can't tell without working it out
Choose the right answer
Working:
Answer:
15.A shop has five items, each priced $83. The owner multiplies their prices by 23, 23, 99, 53 and 68 to get the new prices. How many items are now cheaper than before?
Working:
Answer:
16.A train covers 110 km every hour and travels for 76 h. It travels more than 110 km.
True or false?
Working:
Answer:
17.A cake recipe uses 400 g of flour. Ka-yee makes 34 times the recipe, so Ka-yee needs less than 400 g of flour.
True or false?
Working:
Answer:
18.A shop has five items, each priced $53. The owner multiplies their prices by 67, 53, 86, 77 and 53 to get the new prices. How many items are now cheaper than before?
Working:
Answer:
Show the answers and working
Does multiplying make it bigger or smaller? worksheet: Answers and working
Part A: Working out and filling in
1. 3
Every denominator is 9, so just check, one by one, whether each numerator is greater than 9.
Look only at the multipliers: 3 have a numerator greater than the denominator (more than 1). Numerator equal to denominator is 1, no change; a smaller numerator makes it smaller.
2. 3
Every denominator is 9, so just check, one by one, whether each numerator is greater than 9.
Look only at the multipliers: 3 have a numerator greater than the denominator (more than 1). Numerator equal to denominator is 1, no change; a smaller numerator makes it smaller.
3. D → A → B → C
Each is 23 times something, so just order the multipliers. Which is less than 1, and which is more than 2?
The same number times different multipliers: the bigger the multiplier, the bigger the product. 13 < 1 < 43 < 2 < 94.
Part B: Choose, or true or false
4. B. Greater than 76
No working needed: look at the numerator and denominator of 54. Which is bigger?
Just compare the multiplier 54 with 1: more than 1 makes it bigger, less than 1 smaller.
5. False
Compare the numerator 8 and the denominator 7 of 87: is the multiplier more or less than 1?
87 is close to 1, but still compare its numerator and denominator: a smaller numerator means less than 1 and a smaller product; a bigger numerator means more than 1 and a bigger product.
6. False
Compare the numerator 5 and the denominator 4 of 54: is the multiplier more or less than 1?
54 is close to 1, but still compare its numerator and denominator: a smaller numerator means less than 1 and a smaller product; a bigger numerator means more than 1 and a bigger product.
7. A. Smaller than 62
No working needed: look at the numerator and denominator of 27. Which is bigger?
Just compare the multiplier 27 with 1: more than 1 makes it bigger, less than 1 smaller.
8. C. 33 × 115
All four multiply 33, so just compare the multipliers: first find which are more than 1.
The same number times different multipliers: the bigger the multiplier, the bigger the product, and 115 is the biggest.
9. C. 45
For a product smaller than 92, must the multiplier be more or less than 1? Check each option's numerator and denominator.
For less than 92, the multiplier must be less than 1: 45 has a numerator smaller than its denominator.
10. D. 35
For a product smaller than 66, must the multiplier be more or less than 1? Check each option's numerator and denominator.
For less than 66, the multiplier must be less than 1: 35 has a numerator smaller than its denominator.
11. True
Division works the other way round. Is 25 more or less than 1? Then think what dividing by it does.
Division goes the other way: dividing by less than 1 gives more than the number, by more than 1 gives less. For instance ÷ 12 is × 2.
12. True
Division works the other way round. Is 37 more or less than 1? Then think what dividing by it does.
Division goes the other way: dividing by less than 1 gives more than the number, by more than 1 gives less. For instance ÷ 12 is × 2.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. D. Shorter
The new length is 12 × 13. Is 13 more or less than 1?
New length = 12 × 13: more than 1 makes it longer, less than 1 shorter.
14. A. Less
Next week's is 90 × 59. Compare the numerator 5 with the denominator 9.
Next week's = 90 × 59: times more than 1 gives more, times less than 1 gives less.
15. 3 items
Each price is multiplied by a fraction: check, one by one, whether its numerator is smaller than its denominator.
Times less than 1 makes a price cheaper: 3 multipliers are less than 1. Times 1 leaves it the same.
16. True
Distance = km each hour × hours = 110 × 76. Is 76 more or less than 1?
Distance = 110 × 76: if 76 is more than 1 it is more than 110 km, if less than 1, less.
17. True
The flour needed is 400 × 34. Is 34 more or less than 1?
Flour needed = 400 × 34: less than 400 g only if 34 is less than 1.
18. 1 item
Each price is multiplied by a fraction: check, one by one, whether its numerator is smaller than its denominator.
Times less than 1 makes a price cheaper: 1 multipliers are less than 1. Times 1 leaves it the same.
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