Reciprocals math worksheet for practicing finding the reciprocal of fractions.

Let’s solve each problem step by step.

The reciprocal of a fraction is found by flipping the numerator and denominator.
For example:
- Reciprocal of 5/12 is 12/5
- Reciprocal of 8 (which is 8/1) is 1/8
- Reciprocal of 1 is 1/1 = 1

We’ll go one by one:

1) 5/12 → flip → 12/5
2) 14/36 → simplify first? Wait — reciprocal doesn’t require simplifying unless asked. But let’s check: 14/36 reduces to 7/18, so reciprocal is 18/7. But actually, even if you don’t simplify, reciprocal of 14/36 is 36/14, which simplifies to 18/7. We should give simplified answers. So yes — reduce after flipping or before? Actually, better to flip then simplify. Let’s do that consistently.

Wait — actually, for reciprocals, it’s fine to write the flipped version and then simplify if needed. But since the original fractions may not be simplified, we should simplify the final answer.

But looking at the worksheet — some are already simplified, some aren’t. The instruction just says “write the reciprocals”. In math class, we usually simplify fractions unless told otherwise.

So I will flip each fraction and then simplify if possible.

Let’s go:

1) 5/12 → 12/5 → already simplified → 12/5

2) 14/36 → flip → 36/14 → divide num and den by 2 → 18/7

3) 21/196 → flip → 196/21 → can we simplify? 21 = 3×7, 196 ÷ 7 = 28 → so 196/21 = 28/3 → 28/3

Check: 21 × ? = 196? No — reciprocal means multiply to get 1. 21/196 × 196/21 = 1. And 196÷7=28, 21÷7=3 → yes, 28/3.

4) 12/45 → flip → 45/12 → divide by 3 → 15/4 → 15/4

5) 8 → this is 8/1 → flip → 1/8 → 1/8

6) 43/155 → flip → 155/43 → check if divisible? 43 is prime. 155 ÷ 43 ≈ 3.6 — not integer. So 155/43

7) 13/25 → flip → 25/13 → 25/13

8) 19/108 → flip → 108/19 → 19 is prime, 108 ÷ 19 no → 108/19

9) 51/109 → flip → 109/51 → 51=3×17, 109 prime? Yes → 109/51

10) 8/15 → flip → 15/8 → 15/8

11) 25/105 → flip → 105/25 → divide by 5 → 21/5 → 21/5

12) 63 → 63/1 → flip → 1/63 → 1/63

13) 17/55 → flip → 55/17 → 55/17

14) 125/180 → flip → 180/125 → divide by 5 → 36/25 → 36/25

15) 18/23 → flip → 23/18 → 23/18

16) 9/63 → flip → 63/9 → 63÷9=7 → 7/1 or just 7

But usually we write as fraction? Since others are fractions, maybe keep as 7/1? But 7 is fine. Let’s see — in context, probably accept 7. But to be consistent, perhaps write as improper fraction. However, 63/9 = 7, so 7

Actually, let’s check: reciprocal of 9/63 is 63/9 = 7. Yes.

17) 63/96 → flip → 96/63 → divide by 3 → 32/21 → 32/21

18) 36/255 → flip → 255/36 → divide by 3 → 85/12 → 85/12

19) 12 → 12/1 → flip → 1/12 → 1/12

20) 17/108 → flip → 108/17 → 108/17

21) 1 → 1/1 → flip → 1/1 = 1

22) 36/95 → flip → 95/36 → 95/36

23) 18/96 → flip → 96/18 → divide by 6 → 16/3 → 16/3

24) 41/208 → flip → 208/41 → 41 is prime, 208 ÷ 41 ≈ 5.07 — not integer → 208/41

25) 8/17 → flip → 17/8 → 17/8

26) 14/109 → flip → 109/14 → 109/14

27) 17/123 → flip → 123/17 → 17×7=119, 123-119=4 → not divisible → 123/17

28) 5 → 5/1 → flip → 1/5 → 1/5

29) 96/255 → flip → 255/96 → divide by 3 → 85/32 → 85/32

30) 36/48 → flip → 48/36 → divide by 12 → 4/3 → 4/3

Now let me double-check a few tricky ones:

#2: 14/36 → reciprocal 36/14 = 18/7 ✔️

#3: 21/196 → 196÷7=28, 21÷7=3 → 28/3 ✔️

#11: 25/105 → 105/25 = 21/5 ✔️

#14: 125/180 → 180/125 = 36/25 ✔️ (divided by 5)

#16: 9/63 = 1/7 → reciprocal is 7 ✔️

#18: 36/255 → 255÷3=85, 36÷3=12 → 85/12 ✔️

#23: 18/96 = 3/16 → reciprocal 16/3 ✔️

#29: 96/255 → 255/96 → divide by 3: 85/32 ✔️

#30: 36/48 = 3/4 → reciprocal 4/3 ✔️

All seem correct.

Final Answer:
1) 12/5
2) 18/7
3) 28/3
4) 15/4
5) 1/8
6) 155/43
7) 25/13
8) 108/19
9) 109/51
10) 15/8
11) 21/5
12) 1/63
13) 55/17
14) 36/25
15) 23/18
16) 7
17) 32/21
18) 85/12
19) 1/12
20) 108/17
21) 1
22) 95/36
23) 16/3
24) 208/41
25) 17/8
26) 109/14
27) 123/17
28) 1/5
29) 85/32
30) 4/3