Arithmetic Operations
Arithmetic Solved Examples – Hundreds of Worked Problems
The best way to master arithmetic is to work through many examples. Each problem below shows every step of the solution so you can follow the reasoning, not just the answer.
Addition
Ones: 7+4=11, write 1 carry 1. Tens: 4+6+1=11, write 1 carry 1. Hundreds: 8+5+1=14, write 4 carry 1. Thousands: 3+2+1=6. Answer: 6,411
Align decimals. Pad: 0.473 + 1.580 + 2.900. Thousandths: 3. Hundredths: 7+8=15, write 5 carry 1. Tenths: 4+5+9+1=19, write 9 carry 1. Ones: 0+1+2+1=4. Answer: 4.953
Subtraction
All zeros — borrow chain. 4,999+1 method: 5,000 − 2,836 = 4,999 − 2,835 = 2,164. Check: 2,164 + 2,836 = 5,000 ✓
Multiplication
456 × 8 = 3,648. 456 × 30 = 13,680. 3,648 + 13,680 = 17,328. Check: 456 × 38 ≈ 460 × 40 = 18,400 (close) ✓
25 × 4 = 100. Total d.p. = 3. Answer: 0.100 = 0.1
Division
12 into 17 = 1 r 5. Bring 6: 56. 12 into 56 = 4 r 8. Bring 4: 84. 12 into 84 = 7. Answer: 147. Check: 147 × 12 = 1,764 ✓
KCF: 3/8 × 4/3 = 12/24 = 1/2
Mixed Operations
Brackets: 12 − 16 = −4. Expression: 3 + 5 × (−4) ÷ 2 = 3 + (−20) ÷ 2 = 3 + (−10) = −7
Practice Yourself
- 4,523 + 1,879
- 10,000 − 4,567
- 234 × 47
- 8,352 ÷ 24
- (7 + 3)² − 4 × 6 ÷ 2
- 2/3 + 3/4 − 1/2
- Find 35% of 480.
- Share £150 in ratio 2 : 3 : 5.