Equivalent fractions worksheet with problems to find missing numerators and compare fractions using >, <, and = symbols.

Of course! Let's solve the worksheet step by step.

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## 📌 Part 1: Find the Missing Numbers to Make Equivalent Fractions

We are given fractions with one part missing. We need to find the number that makes the two fractions equivalent.

The key idea: To get an equivalent fraction, multiply (or divide) both numerator and denominator by the same number.

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✔ Problems 1–24:

1) `3/3 = ?/9`
→ Multiply denominator 3 by 3 → 9. So multiply numerator 3 by 3 → 9
✔ Answer: 9

2) `2/8 = ?/32`
→ 8 × 4 = 32 → 2 × 4 = 8
✔ Answer: 8

3) `4/7 = ?/28`
→ 7 × 4 = 28 → 4 × 4 = 16
✔ Answer: 16

4) `4/9 = ?/45`
→ 9 × 5 = 45 → 4 × 5 = 20
✔ Answer: 20

5) `3/4 = ?/36`
→ 4 × 9 = 36 → 3 × 9 = 27
✔ Answer: 27

6) `1/8 = ?/48`
→ 8 × 6 = 48 → 1 × 6 = 6
✔ Answer: 6

7) `2/9 = 12/?`
→ 2 × 6 = 12 → 9 × 6 = 54
✔ Answer: 54

8) `3/10 = 21/?`
→ 3 × 7 = 21 → 10 × 7 = 70
✔ Answer: 70

9) `4/3 = ?/18`
→ 3 × 6 = 18 → 4 × 6 = 24
✔ Answer: 24

10) `2/6 = ?/60`
→ 6 × 10 = 60 → 2 × 10 = 20
✔ Answer: 20

11) `6/5 = 18/?`
→ 6 × 3 = 18 → 5 × 3 = 15
✔ Answer: 15

12) `4/7 = 24/?`
→ 4 × 6 = 24 → 7 × 6 = 42
✔ Answer: 42

13) `5/12 = ?/60`
→ 12 × 5 = 60 → 5 × 5 = 25
✔ Answer: 25

14) `7/11 = 28/?`
→ 7 × 4 = 28 → 11 × 4 = 44
✔ Answer: 44

15) `5/4 = 35/?`
→ 5 × 7 = 35 → 4 × 7 = 28
✔ Answer: 28

16) `11/12 = ?/72`
→ 12 × 6 = 72 → 11 × 6 = 66
✔ Answer: 66

17) `4/9 = ?/81`
→ 9 × 9 = 81 → 4 × 9 = 36
✔ Answer: 36

18) `9/10 = 54/?`
→ 9 × 6 = 54 → 10 × 6 = 60
✔ Answer: 60

19) `4/13 = ?/52`
→ 13 × 4 = 52 → 4 × 4 = 16
✔ Answer: 16

20) `8/3 = 24/?`
→ 8 × 3 = 24 → 3 × 3 = 9
✔ Answer: 9

21) `3/10 = ?/60`
→ 10 × 6 = 60 → 3 × 6 = 18
✔ Answer: 18

22) `5/2 = ?/12`
→ 2 × 6 = 12 → 5 × 6 = 30
✔ Answer: 30

23) `9/12 = 3/?`
→ 9 ÷ 3 = 3 → 12 ÷ 3 = 4
✔ Answer: 4

24) `5/? = 30/54`
→ 30 ÷ 6 = 5 → 54 ÷ 6 = 9
✔ Answer: 9

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## 📌 Part 2: Compare Fractions Using >, <, or =

We need to compare two fractions and decide which is greater, or if they’re equal.

Strategy: Find a common denominator OR cross-multiply.

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✔ Problems 25–32:

25) `3/7` vs `10/14`
→ Simplify 10/14 → 5/7
→ Now compare 3/7 and 5/7 → 3 < 5 → <
✔ Answer: <

26) `2/3` vs `8/15`
→ Cross multiply: 2×15 = 30, 3×8 = 24 → 30 > 24 → >
✔ Answer: >

27) `1/2` vs `12/20`
→ Simplify 12/20 → 3/5
→ Compare 1/2 and 3/5 → Cross multiply: 1×5=5, 2×3=6 → 5 < 6 → <
✔ Answer: <

28) `4/5` vs `16/20`
→ Simplify 16/20 → 4/5 → They are equal → =
✔ Answer: =

29) `3/7` vs `5/14`
→ Common denominator: 14 → 3/7 = 6/14 → 6/14 > 5/14 → >
✔ Answer: >

30) `4/9` vs `8/18`
→ Simplify 8/18 → 4/9 → Equal → =
✔ Answer: =

31) `1/6` vs `3/24`
→ Simplify 3/24 → 1/8
→ Compare 1/6 and 1/8 → Since denominators are different, bigger denominator = smaller fraction → 1/6 > 1/8 → >
✔ Answer: >

32) `2/3` vs `7/9`
→ Common denominator: 9 → 2/3 = 6/9 → 6/9 < 7/9 → <
✔ Answer: <

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## 🐢 Final Answers Summary:

Part 1: Fill in the blanks

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: Comparison Symbols

25) <
26) >
27) <
28) =
29) >
30) =
31) >
32) <

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## 💡 Bonus: Improper Fractions

The worksheet asks: “Can you spot the improper fractions?”

An improper fraction has a numerator > denominator.

From the problems above, here are the improper fractions:

- Problem 9: `4/3` → 4 > 3 → Improper
- Problem 11: `6/5` → 6 > 5 → Improper
- Problem 20: `8/3` → 8 > 3 → Improper
- Problem 22: `5/2` → 5 > 2 → Improper

Also, in the comparisons:

- `10/14` → Not improper (10 < 14)
- `12/20`, `16/20`, `8/18`, `3/24`, `7/9` — all proper.

So only 9, 11, 20, 22 are improper fractions.

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✔ You’ve now completed the entire worksheet correctly!

Let me know if you’d like this formatted as a printable answer key or explained differently!