Operations on Larger Numbers — Important Questions

14,91,560

Step 1: Multiply 42,616 × 5 = 2,13,080. Step 2: Multiply 42,616 × 30 = 12,78,480. Step 3: Add the two partial products: 2,13,080 + 12,78,480. Step 4: 2,13,080 + 12,78,480 = 14,91,560. Step 5: Verify by estimation: 40,000 × 35 = 14,00,000, which is close to 14,91,560 ✓. Forgetting to add a zero when multiplying by 30 is a very common mistake.

11,043

Step 1: Divisor is 38 (2 digits), so take first 2 digits: 41. 41 ÷ 38 = 1 (write 1 in quotient). Step 2: 41 − 38 = 3. Bring down 9 → 39. 39 ÷ 38 = 1 (write 1). Step 3: 39 − 38 = 1. Bring down 6 → 16. 38 > 16, so write 0 in quotient. Step 4: Bring down 3 → 163. 163 ÷ 38 ≈ 4 (38×4=152). Write 4. Step 5: 163 − 152 = 11. Bring down 4 → 114. 114 ÷ 38 = 3 (38×3=114). Quotient = 11,043, Remainder = 0. ✓

19,60,000 litres

Step 1: Multiply 15,680 × 125. Step 2: 15,680 × 100 = 15,68,000. Step 3: 15,680 × 25 = 15,680 × 20 + 15,680 × 5 = 3,13,600 + 78,400 = 3,92,000. Step 4: Add: 15,68,000 + 3,92,000 = 19,60,000. Step 5: Verify: 15,680 × 125 = 15,680 × (500÷4) = 78,40,000÷4 = 19,60,000 ✓.

943

Step 1: Use the relationship: Dividend = Divisor × Quotient + Remainder. Step 2: So, Divisor × Quotient = Dividend − Remainder = 3,66,48,067 − 258 = 3,66,47,809. Step 3: Divisor = 3,66,47,809 ÷ 38,863. Step 4: 38,863 × 943 = 38,863 × 900 + 38,863 × 43 = 3,49,76,700 + 16,71,109 = 3,66,47,809 ✓. Step 5: So divisor = 943. This tests the division relationship formula.