Mathematics — Numbers: Multiplication

Age: 11 (Kenyan syllabus) — This note explains what multiplication is, methods to multiply whole numbers, useful rules and worked examples you can use at school.

1. What is multiplication?

Multiplication is a short way of doing repeated addition. For example, 4 × 3 means "4 added 3 times" or "3 added 4 times". Both give the same product:

4 × 3 = 4 + 4 + 4 = 12

Array (visual) model

3 rows of 4 make 12:

So: 3 rows × 4 columns = 12 boxes → 3 × 4 = 12

2. Words you must know

• Factors — the numbers you multiply (e.g. in 6 × 4, 6 and 4 are factors).
• Product — the answer (6 × 4 = 24, so 24 is the product).
• Multiplicand — the number being multiplied (often the first number).
• Multiplier — the number you multiply by (often the second number).

3. Important properties

• Commutative: a × b = b × a (e.g. 6 × 4 = 4 × 6).
• Associative: (a × b) × c = a × (b × c) (useful when multiplying many numbers).
• Distributive: a × (b + c) = a×b + a×c (useful for breaking hard multiplications into easy parts).

4. Multiplication table (1–12)

5. Useful strategies

• By 10, 100, 1000: add zeros. 23 × 10 = 230, 23 × 100 = 2,300.
• Double and halve: If one factor is even, halve it and double the other: 8 × 25 = 4 × 50 = 200.
• Use distributive rule (split one factor): 24 × 6 = (20 + 4) × 6 = 20×6 + 4×6 = 120 + 24 = 144.
• Grid (box) method: good for multiplying larger numbers by splitting into tens and ones.

6. Methods with worked examples

Example A — Grid (box) method: 134 × 27

Split 134 into 100 + 30 + 4 and 27 into 20 + 7.

Add the parts: 2000 + 700 + 600 + 210 + 80 + 28 = 3,618.
So 134 × 27 = 3,618.

Example B — Column (long) method: 24 × 6

Write numbers one under the other and multiply by the single digit:

6 × 4 = 24 (write 4, carry 2). 6 × 2 = 12; plus carry 2 = 14. Answer = 144.

7. Multiply by 10, 100 quickly

• 23 × 10 = 230 (add one zero).
• 7 × 100 = 700 (add two zeros).
• 1,204 × 1,000 = 1,204,000 (add three zeros).

8. How to check answers

• Use division: product ÷ one factor should give the other factor.
• Estimation: round numbers and multiply to check rough size. Example: 134×27 ≈ 130×30 = 3,900 (close to 3,618).

9. Word problems (Kenyan examples)

1. A teacher buys 12 exercise books for each of 25 pupils. How many exercise books does the teacher buy?
   Solution: 12 × 25 = (12 × 100) ÷ 4 = 1,200 ÷ 4 = 300 OR use 12×25=(12×20)+(12×5)=240+60=300. Answer: 300 exercise books.
2. A farmer packs 18 kg of maize in each bag. How much maize is in 14 bags?
   Solution: 18 × 14 = 18 × (10 + 4) = 180 + 72 = 252 kg.
3. A matatu carries 15 passengers. How many passengers do 8 matatus carry?
   Solution: 15 × 8 = 120. Answer: 120 passengers.

10. Practice exercises

Solve these. Try using a method you like (tables, grid, column).

1. 7 × 8
2. 23 × 5
3. 46 × 3
4. 125 × 4
5. 67 × 12 (use grid)
6. 309 × 6
7. 84 × 25 (hint: 84×25 = 84×(100/4) = (84×100)/4)
8. 412 × 30
9. 19 × 18
10. 134 × 27 (repeat the worked example to check you understand)

Answers

1. 56
2. 115
3. 138
4. 500
5. 804 (67×12 = 67×(10+2)=670+134=804)
6. 1,854
7. 2,100 (84×25 = 84×(100/4) = 8,400/4 = 2,100)
8. 12,360
9. 342
10. 3,618

Tips: Learn your multiplication tables (1–12). Use breaking (distributive rule) and grid methods for large numbers. Always check with estimation or division.