Grade 5 Mathematics Numbers – Multiplication Notes

Mathematics — Numbers

Subtopic: Multiplication (Age 10 — Kenya)

Multiplication is a quick way of adding the same number many times. Example: 4 + 4 + 4 = 3 groups of 4 = 3 × 4 = 12.

• Repeated addition: 5 × 4 = 5 + 5 + 5 + 5.
• Groups: 6 × 3 means 3 groups of 6 objects.
• Array: objects arranged in rows and columns.
• Area model (grid): break numbers into tens and ones, multiply parts then add.

• Commutative: a × b = b × a. (3 × 4 = 4 × 3)
• Associative: (a × b) × c = a × (b × c). (2 × 3) × 4 = 2 × (3 × 4)
• Distributive: a × (b + c) = a × b + a × c. Example: 6 × (10 + 2) = 6×10 + 6×2 = 60 + 12 = 72.
• Identity: a × 1 = a
• Zero: a × 0 = 0

To multiply by 10 add one zero: 14 × 10 = 140. By 100 add two zeros: 7 × 100 = 700.

1. Vertical method (one-digit multiplier):
   Example: 46 × 7

     46
    ×  7
   ─────
    322

   Steps: 6×7=42 write 2 carry 4. 4×7=28 plus carry 4 = 32 → answer 322.
2. Grid / area (for two-digit × two-digit):
   Example: 23 × 15. Break into tens and ones:

   23 = 20 + 3   and   15 = 10 + 5

   20×10 = 200   20×5 = 100
   3×10 = 30      3×5 = 15

   Add: 200+100+30+15 = 345

• Double or halve: 14 × 6 = 14 × (3 × 2) = (14 × 3) × 2 = 42 × 2 = 84.
• Use 10s: 7 × 18 = 7 × (10 + 8) = 70 + 56 = 126.
• Round and adjust: 9 × 6 = (10 × 6) − (1 × 6) = 60 − 6 = 54.

1. 5 × 7 = ?
2. 8 × 6 = ?
3. 23 × 4 = ?
4. 46 × 7 = ?
5. 34 × 12 (use grid method) = ?
6. Juma buys 3 packets of sugar. Each packet has 5 kg. How many kg altogether?
7. A school has 12 benches. Each bench sits 3 pupils. How many pupils can sit?
8. If one textbook costs KSh 220, how much for 4 textbooks?