Multiplication & Division
From times tables to long division — master the operations that unlock fractions, algebra, and beyond.
What Is Multiplication?
Multiplication is repeated addition. Instead of adding 4 + 4 + 4 + 4 + 4, you write 4 × 5 = 20. The numbers being multiplied are called factors, and the result is the product.
Times Table Tips
Patterns That Make It Easy
- ×2: Double the number. 7 × 2 = 14
- ×3: Double + one more. 7 × 3 = 14 + 7 = 21
- ×4: Double twice. 7 × 4 = 14 → 28
- ×5: Half the number × 10. 7 × 5 = 3.5 × 10 = 35. Or: multiply by 10 and halve.
- ×9: Multiply by 10 and subtract once. 7 × 9 = 70 - 7 = 63
- ×10: Add a zero. 7 × 10 = 70
- ×11: For single digits, repeat the digit: 7 × 11 = 77. For teens: 14 × 11 → put sum of digits in middle: 1_(1+4)_4 = 154
Multi-Digit Multiplication
Example 1: 34 × 7
Step 1: 4 × 7 = 28. Write 8, carry 2.
Step 2: 3 × 7 = 21. Add carried 2: 23.
Answer: 238
Example 2: 56 × 43
Step 1: Multiply 56 × 3 = 168
Step 2: Multiply 56 × 40 = 2,240
Step 3: Add: 168 + 2,240 = 2,408
Example 3: 125 × 24
Step 1: 125 × 4 = 500
Step 2: 125 × 20 = 2,500
Step 3: 500 + 2,500 = 3,000
What Is Division?
Division splits a number into equal groups. 20 ÷ 4 = 5 means "20 split into 4 groups gives 5 per group." The number being divided is the dividend, the number dividing is the divisor, and the result is the quotient.
Long Division Step-by-Step
Example 4: 846 ÷ 6
Step 1: Does 6 go into 8? Yes, 1 time. 8 - 6 = 2. Bring down 4 → 24.
Step 2: Does 6 go into 24? Yes, 4 times. 24 - 24 = 0. Bring down 6 → 6.
Step 3: Does 6 go into 6? Yes, 1 time. 6 - 6 = 0.
Answer: 141
Example 5: 1,547 ÷ 7
7 into 15 → 2 (remainder 1). Bring down 4 → 14.
7 into 14 → 2 (remainder 0). Bring down 7 → 7.
7 into 7 → 1 (remainder 0).
Answer: 221
Division with Remainders
Sometimes division doesn't come out evenly.
Example: 23 ÷ 5
5 goes into 23 four times (5 × 4 = 20), with 3 left over.
Answer: 4 remainder 3 (or 4 R3, or 4.6)
Divisibility Rules
Quick ways to check if a number divides evenly:
- ÷ 2: Last digit is even (0, 2, 4, 6, 8)
- ÷ 3: Sum of digits divisible by 3. Example: 123 → 1+2+3 = 6 ✓
- ÷ 4: Last two digits divisible by 4. Example: 532 → 32 ÷ 4 = 8 ✓
- ÷ 5: Last digit is 0 or 5
- ÷ 6: Divisible by both 2 AND 3
- ÷ 9: Sum of digits divisible by 9. Example: 729 → 7+2+9 = 18 ✓
- ÷ 10: Last digit is 0
Properties of Multiplication
- Commutative: a × b = b × a (3 × 7 = 7 × 3 = 21)
- Associative: (a × b) × c = a × (b × c)
- Identity: a × 1 = a
- Zero Property: a × 0 = 0
- Distributive: a × (b + c) = (a × b) + (a × c). This is why 7 × 12 = 7 × 10 + 7 × 2 = 84
Relationship Between Multiplication and Division
They're inverse operations. If you know that 6 × 8 = 48, you automatically know:
- 48 ÷ 6 = 8
- 48 ÷ 8 = 6
This is called a fact family and is incredibly useful for checking your work.
🎯 Try It Yourself
Test your understanding with these practice problems.
1. What is 23 × 7?
💡 Hint: 20×7 = 140, 3×7 = 21, add them
2. What is 156 ÷ 12?
💡 Hint: 12 × 10 = 120, 156 - 120 = 36, 36 ÷ 12 = 3
3. What is 45 × 12?
💡 Hint: 45 × 10 = 450, 45 × 2 = 90, add them
4. What is 891 ÷ 9?
💡 Hint: Use the divisibility rule: 8+9+1=18, which is divisible by 9
5. A factory makes 375 widgets per hour. How many in 8 hours?
💡 Hint: 375 × 8
⚠️ Common Mistakes
- ✗Confusing multiplication by 0 (anything × 0 = 0) with multiplication by 1 (anything × 1 = itself).
- ✗In long division, forgetting to include a 0 in the quotient when the divisor doesn't go into a digit.
- ✗Miscounting zeros when multiplying by 10, 100, 1000 — double-check by counting.
- ✗Not checking if the remainder in division is smaller than the divisor.
- ✗Forgetting that division by zero is undefined — you can never divide by 0.
🌍 Real Life Example
Planning a Party
You're hosting a party for 48 people. Each table seats 6 people: 48 ÷ 6 = 8 tables needed. Each person gets 3 slices of pizza: 48 × 3 = 144 slices. Each pizza has 8 slices: 144 ÷ 8 = 18 pizzas needed. Multiplication tells you total quantities; division helps you split things into equal groups.
💡 Key Takeaway
Multiplication is repeated addition, and division is repeated subtraction. They're inverse operations — one undoes the other. Know your times tables well and you'll find that division, fractions, and algebra all become much easier.