Fractions · Ages 9–10
Equivalent fractions: expanding and reducing worksheet
Part of: Improper fractions, mixed numbers and same denominators
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Equivalent fractions: expanding and reducing worksheet
Fractions · Ages 9–10
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)
1.310 = 50
Answer:
2.3042 = 7
Answer:
3.910 = 40
Answer:
4.410 = 5
Answer:
5.Simplify 4277 as far as it goes. What is it?
Answer in simplest form
Answer:
6.Simplify 3055 as far as it goes. What is it?
Answer in simplest form
Answer:
7.29 = 45 = 12
Fill in each blank
Answer:
8.23 = 12 = 4
Fill in each blank
Answer:
Part B: Choose, or true or false (2 marks each)
9.Which fraction is equal to 59?
- A. 1014
- B. 2545
- C. 545
- D. 259
Choose the right answer
Answer:
10.In which picture does the shaded part show a fraction equal to 13?
- A
- B
- C
- D
Choose the right picture
Answer:
11.49 = 813
True or false?
Answer:
12.Which fraction is equal to 78?
- A. 716
- B. 148
- C. 1416
- D. 910
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.A pizza is cut into 8 equal slices and Ming eats 1. Another pizza the same size is cut into 16 equal slices. How many must May eat to have as much as Ming?
Working:
Answer:
14.Ka-lok did 30 maths questions and got 5 right. In simplest form, what fraction of them were right?
Answer in simplest form
Working:
Answer:
15.A box holds 32 chocolates, and Chi-keung eats 18 of the box. How many chocolates does Chi-keung eat?
Working:
Answer:
16.A box holds 28 chocolates, and May eats 17 of the box. How many chocolates does May eat?
Working:
Answer:
17.Tsz-ching did 36 maths questions and got 32 right. In simplest form, what fraction of them were right?
Answer in simplest form
Working:
Answer:
18.A pizza is cut into 6 equal slices and Ka-yan eats 3. Another pizza the same size is cut into 12 equal slices. How many must Ka-yee eat to have as much as Ka-yan?
Working:
Answer:
Show the answers and working
Equivalent fractions: expanding and reducing worksheet: Answers and working
Part A: Working out and filling in
1. 15
The denominator goes from 10 to 50: times what? The numerator must be multiplied by the same number.
The denominator 10 times 5 is 50, so the numerator is times 5 too: 3 × 5 = 15.
2. 5
The denominator goes from 42 to 7: divided by what? Divide the numerator by the same number.
The denominator 42 ÷ 6 is 7, so the numerator is ÷ 6 too: 30 ÷ 6 = 5.
3. 36
The denominator goes from 10 to 40: times what? The numerator must be multiplied by the same number.
The denominator 10 times 4 is 40, so the numerator is times 4 too: 9 × 4 = 36.
4. 2
The denominator goes from 10 to 5: divided by what? Divide the numerator by the same number.
The denominator 10 ÷ 2 is 5, so the numerator is ÷ 2 too: 4 ÷ 2 = 2.
5. 611
Find the highest common factor of 42 and 77, and divide the numerator and denominator by it.
The highest common factor of 42 and 77 is 7; divide both by 7: 611.
6. 611
Find the highest common factor of 30 and 55, and divide the numerator and denominator by it.
The highest common factor of 30 and 55 is 5; divide both by 5: 611.
7. 10, 54
First box: 9 times what makes 45? Multiply the numerator by it too.
Second box: 2 times what makes 12? Multiply the denominator by it too.
9 × 5 = 45, so the numerator is 2 × 5 = 10; 2 × 6 = 12, so the denominator is 9 × 6 = 54.
8. 8, 6
First box: 3 times what makes 12? Multiply the numerator by it too.
Second box: 2 times what makes 4? Multiply the denominator by it too.
3 × 4 = 12, so the numerator is 2 × 4 = 8; 2 × 2 = 4, so the denominator is 3 × 2 = 6.
Part B: Choose, or true or false
9. B. 2545
Equal fractions have the numerator and denominator multiplied by the same number. Check each option: are both multiplied by the same number?
Numerator and denominator both times 5: 59 = 2545.
10. B
Write 13 with denominator 9: what is the numerator? Then find the picture with that many parts shaded.
13 = 39: 9 parts with 3 shaded.
11. False
From 4 to 8 and from 9 to 13: is that multiplying both by the same number, or adding the same number?
Equal fractions come from multiplying (or dividing) the numerator and denominator by the same number; adding a number changes the size.
12. C. 1416
Equal fractions have the numerator and denominator multiplied by the same number. Check each option: are both multiplied by the same number?
Numerator and denominator both times 2: 78 = 1416.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 2 slices
The pizzas are the same size. The slices go from 8 to 16: times what? Multiply 1 by that too.
18 = □16: the denominator is times 2, so the numerator is too: 2 slices.
14. 16
5 out of 30 were right. Find the highest common factor of 5 and 30 and simplify by it.
530 were right; divide numerator and denominator by 5: 16.
15. 4 chocolates
Write 18 with denominator 32: 8 times what makes 32?
The whole box is 3232, and 18 = 432: 4 chocolates.
16. 4 chocolates
Write 17 with denominator 28: 7 times what makes 28?
The whole box is 2828, and 17 = 428: 4 chocolates.
17. 89
32 out of 36 were right. Find the highest common factor of 32 and 36 and simplify by it.
3236 were right; divide numerator and denominator by 4: 89.
18. 6 slices
The pizzas are the same size. The slices go from 6 to 12: times what? Multiply 3 by that too.
36 = □12: the denominator is times 2, so the numerator is too: 6 slices.
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