Equivalent fractions worksheet for practicing identifying and comparing fractions, including improper fractions.

Let's solve this step-by-step. The worksheet is titled "Equivalent Fractions 5" and has two main parts:

1. Finding equivalent fractions (fill in the blanks)
2. Comparing fractions using >, <, or = symbols

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🔹 Part 1: Equivalent Fractions

We need to find missing numerators or denominators so that the fractions are equivalent.

We use the rule:
> If $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$
> Or, we can multiply numerator and denominator by the same number.

Let’s go through each one.

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#### 1) $\frac{3}{3} = \frac{?}{9}$

$\frac{3}{3} = 1$, so $\frac{?}{9} = 1$ → ? = 9
✔ Answer: 9

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#### 2) $\frac{2}{8} = \frac{?}{32}$

Simplify $\frac{2}{8} = \frac{1}{4}$
Now, what times 4 = 32? → 8
So, $\frac{1}{4} = \frac{8}{32}$
✔ Answer: 8

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#### 3) $\frac{4}{7} = \frac{?}{28}$

7 × 4 = 28 → Multiply numerator by 4:
4 × 4 = 16
✔ Answer: 16

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#### 4) $\frac{4}{9} = \frac{?}{45}$

9 × 5 = 45 → 4 × 5 = 20
✔ Answer: 20

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#### 5) $\frac{3}{4} = \frac{?}{36}$

4 × 9 = 36 → 3 × 9 = 27
✔ Answer: 27

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#### 6) $\frac{1}{8} = \frac{?}{48}$

8 × 6 = 48 → 1 × 6 = 6
✔ Answer: 6

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#### 7) $\frac{2}{9} = \frac{12}{?}$

We have numerator 12, which is 2 × 6 → So denominator must be 9 × 6 = 54
✔ Answer: 54

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#### 8) $\frac{3}{10} = \frac{21}{?}$

3 × 7 = 21 → 10 × 7 = 70
✔ Answer: 70

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#### 9) $\frac{4}{3} = \frac{?}{18}$

3 × 6 = 18 → 4 × 6 = 24
✔ Answer: 24

> ⚠️ This is an improper fraction (numerator > denominator)

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#### 10) $\frac{2}{6} = \frac{?}{60}$

Simplify $\frac{2}{6} = \frac{1}{3}$
3 × 20 = 60 → 1 × 20 = 20
✔ Answer: 20

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#### 11) $\frac{6}{5} = \frac{18}{?}$

6 × 3 = 18 → 5 × 3 = 15
✔ Answer: 15

> ⚠️ Improper fraction

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#### 12) $\frac{4}{7} = \frac{24}{?}$

4 × 6 = 24 → 7 × 6 = 42
✔ Answer: 42

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#### 13) $\frac{5}{12} = \frac{?}{60}$

12 × 5 = 60 → 5 × 5 = 25
✔ Answer: 25

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#### 14) $\frac{7}{11} = \frac{28}{?}$

7 × 4 = 28 → 11 × 4 = 44
✔ Answer: 44

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#### 15) $\frac{5}{4} = \frac{35}{?}$

5 × 7 = 35 → 4 × 7 = 28
✔ Answer: 28

> ⚠️ Improper fraction

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#### 16) $\frac{11}{12} = \frac{?}{72}$

12 × 6 = 72 → 11 × 6 = 66
✔ Answer: 66

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#### 17) $\frac{4}{9} = \frac{?}{81}$

9 × 9 = 81 → 4 × 9 = 36
✔ Answer: 36

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#### 18) $\frac{9}{10} = \frac{54}{?}$

9 × 6 = 54 → 10 × 6 = 60
✔ Answer: 60

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#### 19) $\frac{4}{13} = \frac{?}{52}$

13 × 4 = 52 → 4 × 4 = 16
✔ Answer: 16

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#### 20) $\frac{8}{3} = \frac{24}{?}$

8 × 3 = 24 → 3 × 3 = 9
✔ Answer: 9

> ⚠️ Improper fraction

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#### 21) $\frac{3}{10} = \frac{?}{60}$

10 × 6 = 60 → 3 × 6 = 18
✔ Answer: 18

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#### 22) $\frac{5}{2} = \frac{?}{12}$

5 × 6 = 30 → 2 × 6 = 12 → So numerator = 30
✔ Answer: 30

> ⚠️ Improper fraction

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#### 23) $\frac{9}{12} = \frac{3}{?}$

Simplify $\frac{9}{12} = \frac{3}{4}$ → So denominator = 4
✔ Answer: 4

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#### 24) $\frac{?}{?} = \frac{30}{54}$

Wait — it says: $\frac{5}{?} = \frac{30}{54}$

So, let’s solve: $\frac{5}{x} = \frac{30}{54}$

Cross-multiply:
5 × 54 = 270
30 × x = 270 → x = 270 / 30 = 9

✔ Answer: 9

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✔ Summary of Part 1 Answers:

| # | Answer |
|---|--------|
| 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 |

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🔹 Part 2: Compare Fractions

Use >, <, or = to compare.

We'll simplify or convert to common denominators.

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#### 25) $\frac{3}{7} \quad \square \quad \frac{10}{14}$

Simplify $\frac{10}{14} = \frac{5}{7}$

Now: $\frac{3}{7} < \frac{5}{7}$ → So $\frac{3}{7} < \frac{10}{14}$
✔ Answer: <

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#### 26) $\frac{2}{3} \quad \square \quad \frac{8}{15}$

Find common denominator: LCM of 3 and 15 is 15

$\frac{2}{3} = \frac{10}{15}$, $\frac{8}{15} = \frac{8}{15}$

10/15 > 8/15 → So $\frac{2}{3} > \frac{8}{15}$
✔ Answer: >

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#### 27) $\frac{1}{2} \quad \square \quad \frac{12}{20}$

$\frac{12}{20} = \frac{3}{5}$

Compare $\frac{1}{2} = 0.5$, $\frac{3}{5} = 0.6$

0.5 < 0.6 → So $\frac{1}{2} < \frac{12}{20}$
✔ Answer: <

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#### 28) $\frac{4}{5} \quad \square \quad \frac{16}{20}$

$\frac{16}{20} = \frac{4}{5}$ → Equal
✔ Answer: =

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#### 29) $\frac{3}{7} \quad \square \quad \frac{5}{14}$

LCM of 7 and 14 is 14

$\frac{3}{7} = \frac{6}{14}$, $\frac{5}{14} = \frac{5}{14}$

6/14 > 5/14 → So $\frac{3}{7} > \frac{5}{14}$
✔ Answer: >

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#### 30) $\frac{4}{9} \quad \square \quad \frac{8}{18}$

$\frac{8}{18} = \frac{4}{9}$ → Equal
✔ Answer: =

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#### 31) $\frac{1}{6} \quad \square \quad \frac{3}{24}$

Simplify $\frac{3}{24} = \frac{1}{8}$

Compare $\frac{1}{6} \approx 0.166$, $\frac{1}{8} = 0.125$

0.166 > 0.125 → So $\frac{1}{6} > \frac{3}{24}$
✔ Answer: >

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#### 32) $\frac{2}{3} \quad \square \quad \frac{7}{9}$

LCM of 3 and 9 is 9

$\frac{2}{3} = \frac{6}{9}$, $\frac{7}{9} = \frac{7}{9}$

6/9 < 7/9 → So $\frac{2}{3} < \frac{7}{9}$
✔ Answer: <

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✔ Summary of Part 2 Answers:

| # | Answer |
|---|--------|
|25 | < |
|26 | > |
|27 | < |
|28 | = |
|29 | > |
|30 | = |
|31 | > |
|32 | < |

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🟨 Spotting Improper Fractions

The question asks: *"Some of these fractions are improper fractions – can you spot them?"*

An improper fraction has numerator > denominator.

Look at the original fractions:

- $\frac{4}{3}$ → yes (9)
- $\frac{6}{5}$ → yes (11)
- $\frac{5}{4}$ → yes (15)
- $\frac{8}{3}$ → yes (20)
- $\frac{5}{2}$ → yes (22)

Also, check if any answers are improper?

But the question is asking about the given fractions, not the answers.

So the original fractions that are improper:

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

✔ These are all improper.

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✔ Final Answer Summary

#### 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) <

#### Improper Fractions (from original problems):
- #9: $\frac{4}{3}$
- #11: $\frac{6}{5}$
- #15: $\frac{5}{4}$
- #20: $\frac{8}{3}$
- #22: $\frac{5}{2}$

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Let me know if you'd like this formatted as a printable answer sheet!