Addition & subtraction of rational numbers | Physics Wallah - Free Printable

Let’s solve each problem step by step.

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Problem 1: Add 5/12 and 3/8

To add fractions, we need a common denominator.

Find the least common multiple (LCM) of 12 and 8.

Multiples of 12: 12, 24, 36...
Multiples of 8: 8, 16, 24, 32...

LCM = 24

Convert both fractions to have denominator 24:

5/12 = (5 × 2)/(12 × 2) = 10/24
3/8 = (3 × 3)/(8 × 3) = 9/24

Now add:
10/24 + 9/24 = 19/24

✔ Answer: (c) 19/24

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Problem 2: Sum is -3/5. One number is -9/20. Find the other.

Let the unknown number be x.

So:
x + (-9/20) = -3/5
→ x = -3/5 + 9/20

Common denominator of 5 and 20 is 20.

-3/5 = (-3 × 4)/(5 × 4) = -12/20

So:
x = -12/20 + 9/20 = (-12 + 9)/20 = -3/20

✔ Answer: (d) -3/20

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Problem 3: What should be subtracted from -5/9 to get 8/9?

Let the number to subtract be x.

So:
(-5/9) - x = 8/9

Solve for x:

-x = 8/9 + 5/9
-x = 13/9
→ x = -13/9

✔ Answer: -13/9

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Problem 4: Sum is -8. One number is -15/7. Find the other.

Let the unknown number be y.

y + (-15/7) = -8
→ y = -8 + 15/7

Write -8 as a fraction with denominator 7:
-8 = -56/7

So:
y = -56/7 + 15/7 = (-56 + 15)/7 = -41/7

✔ Answer: -41/7

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Problem 5: What should be added to -7/8 to get 5/9?

Let the number to add be z.

z + (-7/8) = 5/9
→ z = 5/9 + 7/8

Find LCM of 9 and 8 → 72

5/9 = (5 × 8)/(9 × 8) = 40/72
7/8 = (7 × 9)/(8 × 9) = 63/72

Add:
40/72 + 63/72 = 103/72

✔ Answer: 103/72

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Final Answer:
1. 19/24
2. -3/20
3. -13/9
4. -41/7
5. 103/72