ICSE Mathematics – Multiplication & Division
(Class 1 – 10)
Aim – Understand how numbers combine when we “multiply” (repeat addition) and “divide” (share or split).
1. Simple Explanation
| Operation | What it means | Everyday example |
|---|---|---|
| Multiplication | “Repeat adding the same number many times.” | 3 apples × 4 people = 12 apples (3 apples for each of 4 people). |
| Division | “Share or split a total into equal parts.” | 12 apples ÷ 4 people = 3 apples per person. |
Important:
- Multiplication and division are opposites.
- The symbol
×(or*) means multiply. - The symbol
÷(or/) means divide.
2. Key Points
| Concept | What to remember |
|---|---|
| Zero & One | 0 × anything = 0; 1 × anything = that thing. |
| Anything ÷ 1 = same thing; 0 ÷ anything = 0. | |
| Commutative Law | a × b = b × a; a ÷ b ≠ b ÷ a (division is not commutative). |
| Associative Law | a × (b × c) = (a × b) × c. |
| Distributive Law | a × (b + c) = a × b + a × c. |
| Identity Elements | For multiplication: 1. For division: no identity, but a ÷ a = 1 (if a ≠ 0). |
| Inverse Elements | Multiplicative inverse of a is 1/a. Division a ÷ b = a × (1/b). |
| Multiplying Decimals | Count total decimal places in both factors; result has that many decimal places. |
| Dividing Decimals | Move decimal in divisor to make it an integer; move same distance in dividend. |
| Multiplying Fractions | Multiply numerators, multiply denominators; simplify if possible. |
| Dividing Fractions | Multiply by the reciprocal of the divisor. |
| Word Problems | Identify how much, how many, how many do each get, how many groups, etc. |
3. Worked Example
Problem (Class 4 level)
A basket contains 24 apples. If we divide them equally among 6 friends, how many apples does each friend get? Also, how many baskets are needed if each basket holds 4 apples?
Step‑by‑step Solution
-
Divide the apples among friends
[ 24 \div 6 = ? ] Think of “24 apples ÷ 6 friends” → “How many apples per friend?”- 6 goes into 24 exactly 4 times.
- Answer: 4 apples per friend.
-
Find how many baskets are needed
Each basket holds 4 apples.[ 24 \div 4 = ? ]
- 4 goes into 24 exactly 6 times.
- Answer: 6 baskets are needed.
Quick Check
| Operation | Result |
|---|---|
| 24 ÷ 6 | 4 |
| 24 ÷ 4 | 6 |
4. Quick Revision Summary
| Topic | Recall |
|---|---|
| Multiplication | Repeat addition → a × b. |
| Division | Share equally → a ÷ b. |
| Zero & One | 0×a=0; 1×a=a; a÷1=a. |
| Commutativity | a×b=b×a. |
| Associativity | a×(b×c)=(a×b)×c. |
| Distributive | a(b+c)=ab+ac. |
| Decimals | Count decimal places; move decimal for division. |
| Fractions | Multiply numerators/denominators; divide by reciprocal. |
| Common Mistake | Forgetting to simplify fractions or decimal places. |
Quick Tips
- Multiplication table: Memorise 1–12 tables to speed up.
- Check units: “Apples per basket” vs “baskets per apple”.
- Use estimation: Round numbers to check if the answer is reasonable.
- Practice word problems: Identify how many, how many each, how many groups.
End of Notes – Keep practising with different numbers and word problems to build confidence!