# Operations On Whole Numbers

Operations on whole numbers are discussed here:

The four basic operations on whole numbers are addition; subtraction; multiplication and division. We will learn about the basic operations in more detailed explanations along with the examples.

Worked-out problems related to Operations on whole numbers

**1. Solve using rearrangement: **

(a) 784 + 127 + 216

**Solution: **

784 + 127 + 216

= (784 + 216) + 127

= 1000 + 127

= 1127

(b) 25 × 8 × 125 × 4

**Solution: **

25 × 8 × 125 × 4

= (125 × 8) × (25 × 4)

= 1000 × 100

= 100000

**2. Find the value using distributive property. **

(a) 2651 × 62 + 2651 × 38

**Solution: **

2651 × 62 + 2651 × 38

Property: a × b + a × c = a × (b + c)

= 2651 × (62 + 38)

= 2651 × 100

= 265100

(b) 347 × 163 – 347 × 63

**Solution: **

347 × 163 – 347 × 63

Property: a × b – a × c = a × (b – c)

= 347 × (163 – 63)

= 347 × 100

= 34700

(c) 128 × 99 + 128

**Solution: **

128 × 99 + 128

Property: a × b – a × c = a × (b + c)

= 128 × 99 + 128

= 128 × (99 + 1)

= 12800

**3. Find the product using distributive property: **

(a) 237 × 103

**Solution: **

237 × 103

237 × (100 + 3)

Property: a × (b + c) = a × b + a × c

Therefore, 237 × (100 + 3)

= 237 × 100 + 237 × 3

= 23700 + 711

= 24411

(b) 510 × 99

**Solution: **

510 × 99

510 × (100 – 1)

Property: a × (b – c) = a × b – a × c

Therefore, 510 × (100 – 1)

= 510 × 100 – 510 × 1

= 51000 – 510

= 50490

**4. Verify the following: **

(a) 537 + 265 = 265 + 537

**Solution: **

537 + 265 =265 + 537

**L.H.S.** = 537 + 265 = 802

**R.H.S.** = 265 + 537 = 802

Property: a + b =b + a

Therefore, L.H.S. = R.H.S.

Hence, verified.

(b) 25 × (36 × 50) = (25 × 36) × 50

**Solution: **

25 × (36 × 50) = (25 × 36) × 50

L.H.S.= 25 × (36 × 50) = 25 × 1800 = 45000

R.H.S. = (25 × 36) × 50 = 900 × 50 = 45000

Property: a × (a × c) = (a × b) × c

Therefore, L.H.S. = R.H.S.

Hence, verified.

**5. ** Find the least number that must be subtracted from 1000 so that 45 divides the difference exactly.

**Solution: **

Divide 1000 by 45.

Now 1000 – 10 = 990

Therefore, 10 should be subtracted from 1000 so that difference 990 is divisible by 45.

**6. ** Find the least number that should be added to 1000 so that 65 divides the sum exactly.

**Solution: **

Divide 1000 by 65.

Now finding the difference between the divisor and remainder, we get

65 – 25 = 40

Therefore, 40 must be added to 1000 so that the sum 1040 is exactly divisible by 65.

**7. ** Find the number which when divided by 15 gives 7 as the quotient and 3 as the remainder.

**Solution: **

Dividend = divisor × quotient + remainder

= 15 × 7 + 3

= 105 + 3 = 108

Therefore, the required number is 108