Equivalent Fractions Sheet 5 - Practice identifying improper fractions and comparing fractions using symbols.

Let's solve Equivalent Fractions Sheet 5 step by step, explaining each part clearly.

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🔷 Part 1: Find the missing numerator or denominator to make equivalent fractions

We are given a fraction on the left and need to find the missing number so that both sides are equivalent. We'll use cross-multiplication or scaling (multiplying numerator and denominator by the same number).

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#### 1) $\frac{3}{3} = \frac{\boxed{}}{9}$
- Simplify: $\frac{3}{3} = 1$
- So we want $ \frac{x}{9} = 1 \Rightarrow x = 9 $
✔ Answer: 9

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#### 2) $\frac{2}{8} = \frac{\boxed{}}{32}$
- Scale up: $ \frac{2}{8} = \frac{?}{32} $
- Multiply numerator and denominator by 4: $ \frac{2 \times 4}{8 \times 4} = \frac{8}{32} $
✔ Answer: 8

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#### 3) $\frac{4}{7} = \frac{\boxed{}}{28}$
- $ \frac{4}{7} = \frac{?}{28} $
- Multiply top and bottom by 4: $ \frac{4 \times 4}{7 \times 4} = \frac{16}{28} $
✔ Answer: 16

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#### 4) $\frac{4}{9} = \frac{\boxed{}}{45}$
- $ \frac{4}{9} = \frac{?}{45} $
- Multiply by 5: $ \frac{4 \times 5}{9 \times 5} = \frac{20}{45} $
✔ Answer: 20

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#### 5) $\frac{3}{4} = \frac{\boxed{}}{36}$
- $ \frac{3}{4} = \frac{?}{36} $
- Multiply by 9: $ \frac{3 \times 9}{4 \times 9} = \frac{27}{36} $
✔ Answer: 27

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#### 6) $\frac{1}{8} = \frac{\boxed{}}{48}$
- Multiply by 6: $ \frac{1 \times 6}{8 \times 6} = \frac{6}{48} $
✔ Answer: 6

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#### 7) $\frac{2}{9} = \frac{12}{\boxed{}}$
- $ \frac{2}{9} = \frac{12}{x} $
- Cross multiply: $ 2x = 12 \times 9 = 108 \Rightarrow x = 54 $
✔ Answer: 54

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#### 8) $\frac{3}{10} = \frac{21}{\boxed{}}$
- $ \frac{3}{10} = \frac{21}{x} $
- Cross multiply: $ 3x = 210 \Rightarrow x = 70 $
✔ Answer: 70

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#### 9) $\frac{4}{3} = \frac{\boxed{}}{18}$
- $ \frac{4}{3} = \frac{x}{18} $
- Multiply by 6: $ \frac{4 \times 6}{3 \times 6} = \frac{24}{18} $
✔ Answer: 24

> ✔ Note: This is an improper fraction since $4 > 3$

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#### 10) $\frac{2}{6} = \frac{\boxed{}}{60}$
- Simplify: $ \frac{2}{6} = \frac{1}{3} $
- $ \frac{1}{3} = \frac{x}{60} \Rightarrow x = 20 $
✔ Answer: 20

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#### 11) $\frac{6}{5} = \frac{18}{\boxed{}}$
- $ \frac{6}{5} = \frac{18}{x} $
- Cross multiply: $ 6x = 90 \Rightarrow x = 15 $
✔ Answer: 15

> ✔ Improper fraction: $6 > 5$

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#### 12) $\frac{4}{7} = \frac{24}{\boxed{}}$
- $ \frac{4}{7} = \frac{24}{x} $
- $ 4x = 168 \Rightarrow x = 42 $
✔ Answer: 42

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#### 13) $\frac{5}{12} = \frac{\boxed{}}{60}$
- Multiply by 5: $ \frac{5 \times 5}{12 \times 5} = \frac{25}{60} $
✔ Answer: 25

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#### 14) $\frac{7}{11} = \frac{28}{\boxed{}}$
- $ \frac{7}{11} = \frac{28}{x} $
- $ 7x = 308 \Rightarrow x = 44 $
✔ Answer: 44

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#### 15) $\frac{5}{4} = \frac{35}{\boxed{}}$
- $ \frac{5}{4} = \frac{35}{x} $
- $ 5x = 140 \Rightarrow x = 28 $
✔ Answer: 28

> ✔ Improper fraction: $5 > 4$

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#### 16) $\frac{11}{12} = \frac{\boxed{}}{72}$
- Multiply by 6: $ \frac{11 \times 6}{12 \times 6} = \frac{66}{72} $
✔ Answer: 66

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#### 17) $\frac{4}{9} = \frac{\boxed{}}{81}$
- Multiply by 9: $ \frac{4 \times 9}{9 \times 9} = \frac{36}{81} $
✔ Answer: 36

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#### 18) $\frac{9}{10} = \frac{54}{\boxed{}}$
- $ \frac{9}{10} = \frac{54}{x} $
- $ 9x = 540 \Rightarrow x = 60 $
✔ Answer: 60

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#### 19) $\frac{4}{13} = \frac{\boxed{}}{52}$
- Multiply by 4: $ \frac{4 \times 4}{13 \times 4} = \frac{16}{52} $
✔ Answer: 16

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#### 20) $\frac{8}{3} = \frac{24}{\boxed{}}$
- $ \frac{8}{3} = \frac{24}{x} $
- $ 8x = 72 \Rightarrow x = 9 $
✔ Answer: 9

> ✔ Improper fraction: $8 > 3$

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#### 21) $\frac{3}{10} = \frac{\boxed{}}{60}$
- Multiply by 6: $ \frac{3 \times 6}{10 \times 6} = \frac{18}{60} $
✔ Answer: 18

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#### 22) $\frac{5}{2} = \frac{\boxed{}}{12}$
- $ \frac{5}{2} = \frac{x}{12} $
- Multiply by 6: $ \frac{5 \times 6}{2 \times 6} = \frac{30}{12} $
✔ Answer: 30

> ✔ Improper fraction: $5 > 2$

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#### 23) $\frac{9}{12} = \frac{3}{\boxed{}}$
- Simplify: $ \frac{9}{12} = \frac{3}{4} $
- So $ \frac{3}{x} = \frac{3}{4} \Rightarrow x = 4 $
✔ Answer: 4

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#### 24) $\frac{5}{\boxed{}} = \frac{30}{54}$
- Simplify $ \frac{30}{54} = \frac{5}{9} $
- So $ \frac{5}{x} = \frac{5}{9} \Rightarrow x = 9 $
✔ Answer: 9

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🔷 Part 2: Compare fractions using >, <, or =

We compare two fractions and insert the correct symbol.

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#### 25) $\frac{3}{7} \square \frac{10}{14}$
- Simplify $ \frac{10}{14} = \frac{5}{7} $
- $ \frac{3}{7} < \frac{5}{7} $
✔ Answer: <

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#### 26) $\frac{2}{3} \square \frac{8}{15}$
- Convert to common denominator: LCD of 3 and 15 is 15
- $ \frac{2}{3} = \frac{10}{15}, \frac{8}{15} = \frac{8}{15} $
- $ \frac{10}{15} > \frac{8}{15} $
✔ Answer: >

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#### 27) $\frac{1}{2} \square \frac{12}{20}$
- $ \frac{12}{20} = \frac{3}{5} $
- $ \frac{1}{2} = 0.5, \frac{3}{5} = 0.6 $
- $ 0.5 < 0.6 $
✔ Answer: <

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#### 28) $\frac{4}{5} \square \frac{16}{20}$
- $ \frac{16}{20} = \frac{4}{5} $
- So they are equal
✔ Answer: =

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#### 29) $\frac{3}{7} \square \frac{5}{14}$
- Common denominator: 14
- $ \frac{3}{7} = \frac{6}{14}, \frac{5}{14} = \frac{5}{14} $
- $ \frac{6}{14} > \frac{5}{14} $
✔ Answer: >

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#### 30) $\frac{4}{9} \square \frac{8}{18}$
- $ \frac{8}{18} = \frac{4}{9} $
- So they are equal
✔ Answer: =

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#### 31) $\frac{1}{6} \square \frac{3}{24}$
- $ \frac{3}{24} = \frac{1}{8} $
- $ \frac{1}{6} \approx 0.1667, \frac{1}{8} = 0.125 $
- $ 0.1667 > 0.125 $
✔ Answer: >

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#### 32) $\frac{2}{3} \square \frac{7}{9}$
- Common denominator: 9
- $ \frac{2}{3} = \frac{6}{9}, \frac{7}{9} = \frac{7}{9} $
- $ \frac{6}{9} < \frac{7}{9} $
✔ Answer: <

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✔ Final Answers:

#### Part 1: Equivalent Fractions
1) 9
2) 8
3) 16
4) 20
5) 27
6) 6
7) 54
8) 70
9) 24
10) 20
11) 15
12) 42
13) 25
14) 44
15) 28
16) 66
17) 36
18) 60
19) 16
20) 9
21) 18
22) 30
23) 4
24) 9

#### Part 2: Comparisons
25) <
26) >
27) <
28) =
29) >
30) =
31) >
32) <

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🟡 Improper Fractions Spotted (numerator > denominator):

- #9: $ \frac{4}{3} $
- #11: $ \frac{6}{5} $
- #15: $ \frac{5}{4} $
- #20: $ \frac{8}{3} $
- #22: $ \frac{5}{2} $

✔ These are all improper fractions.

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