Mental Multiplication Strategies
Mental multiplication means multiplying numbers in your head without pen and paper. You break the numbers into simpler parts, use properties of multiplication, and combine the results.
In Class 4, you will learn strategies like splitting numbers, multiplying by 10/100, doubling, and using the distributive property. These tricks make multiplication faster and build number sense.
What is Mental Multiplication Strategies - Class 4 Maths (Multiplication)?
Mental multiplication uses mathematical properties and shortcuts to compute products without writing down long calculations.
Key properties used:
- Distributive property: a × (b + c) = a × b + a × c
- Multiplying by 10: Append a zero. Example: 34 × 10 = 340
- Multiplying by 100: Append two zeros. Example: 7 × 100 = 700
- Doubling and halving: If one factor is even, halve it and double the other.
Mental Multiplication Strategies Formula
a × (b + c) = (a × b) + (a × c)
This is the distributive property — the most powerful tool for mental multiplication. Split one number into a sum, multiply each part, then add the products.
Solved Examples
Example 1: Example 1: Splitting (Distributive Property)
Problem: Calculate 7 × 13 mentally.
Solution:
Step 1: Split 13 = 10 + 3
Step 2: 7 × 10 = 70
Step 3: 7 × 3 = 21
Step 4: 70 + 21 = 91
Answer: 7 × 13 = 91
Example 2: Example 2: Multiplying by 10 and 100
Problem: Find 25 × 40 mentally.
Solution:
Step 1: 40 = 4 × 10
Step 2: 25 × 4 = 100
Step 3: 100 × 10 = 1,000
Answer: 25 × 40 = 1,000
Example 3: Example 3: Doubling and halving
Problem: Find 16 × 5 mentally.
Solution:
Step 1: Halve 16 → 8. Double 5 → 10.
Step 2: 8 × 10 = 80
Answer: 16 × 5 = 80
Example 4: Example 4: Multiplying by 9 (use 10 minus 1)
Problem: Find 9 × 14 mentally.
Solution:
Step 1: 9 = 10 − 1
Step 2: 10 × 14 = 140
Step 3: 1 × 14 = 14
Step 4: 140 − 14 = 126
Answer: 9 × 14 = 126
Example 5: Example 5: Multiplying by 11
Problem: Find 11 × 23 mentally.
Solution:
Step 1: 11 = 10 + 1
Step 2: 10 × 23 = 230
Step 3: 1 × 23 = 23
Step 4: 230 + 23 = 253
Answer: 11 × 23 = 253
Example 6: Example 6: Multiplying by 5 (use ÷ 2 × 10)
Problem: Find 48 × 5 mentally.
Solution:
Step 1: 5 = 10 ÷ 2. So multiply by 10 first, then halve.
Step 2: 48 × 10 = 480
Step 3: 480 ÷ 2 = 240
Answer: 48 × 5 = 240
Example 7: Example 7: Word problem — shopping
Problem: Priya buys 8 notebooks at ₹15 each. Find the total cost mentally.
Solution:
Step 1: Split 15 = 10 + 5
Step 2: 8 × 10 = 80
Step 3: 8 × 5 = 40
Step 4: 80 + 40 = 120
Answer: Total cost = ₹120
Example 8: Example 8: Multiplying by 25 (use ÷ 4 × 100)
Problem: Find 12 × 25 mentally.
Solution:
Step 1: 25 = 100 ÷ 4. So divide by 4 first, then multiply by 100.
Step 2: 12 ÷ 4 = 3
Step 3: 3 × 100 = 300
Answer: 12 × 25 = 300
Example 9: Example 9: Rounding and adjusting
Problem: Find 6 × 48 mentally.
Solution:
Step 1: Round 48 to 50: 6 × 50 = 300
Step 2: We added 2 extra per group: 6 × 2 = 12
Step 3: 300 − 12 = 288
Answer: 6 × 48 = 288
Example 10: Example 10: Cricket score
Problem: Arjun scored 4 runs on each of 17 balls. Find the total runs mentally.
Solution:
Step 1: 4 × 17 = 4 × (20 − 3)
Step 2: 4 × 20 = 80
Step 3: 4 × 3 = 12
Step 4: 80 − 12 = 68
Answer: Arjun scored 68 runs.
Key Points to Remember
- Distributive property: Split one number and multiply in parts. a × (b + c) = ab + ac.
- Multiply by 10: Add one zero to the end.
- Multiply by 5: Multiply by 10 and halve, OR halve first and multiply by 10.
- Multiply by 9: Multiply by 10 and subtract once.
- Multiply by 11: Multiply by 10 and add once.
- Multiply by 25: Divide by 4 and multiply by 100.
- Doubling and halving: Halve one factor, double the other — the product stays the same.
- Round and adjust: Round a number to the nearest 10, multiply, then add/subtract the adjustment.
Practice Problems
- Calculate 6 × 15 mentally using the distributive property.
- Find 35 × 4 mentally.
- Calculate 9 × 23 using the 'multiply by 10 and subtract' strategy.
- Find 16 × 25 mentally using the ÷4 × 100 trick.
- Dev buys 7 pencils at ₹12 each. Find the total mentally.
- Calculate 8 × 99 mentally.
- Find 14 × 5 using doubling and halving.
Frequently Asked Questions
Q1. What is mental multiplication?
Mental multiplication means finding the product of two numbers in your head, without writing the calculation on paper. It uses shortcuts based on mathematical properties.
Q2. What is the distributive property?
The distributive property states a × (b + c) = (a × b) + (a × c). It lets you split a difficult multiplication into two easier ones and add the results.
Q3. How do you multiply by 5 mentally?
Multiply the number by 10 (add a zero), then divide by 2. Or divide the number by 2 first, then multiply by 10. For example, 36 × 5 = 360 ÷ 2 = 180.
Q4. How do you multiply by 9 mentally?
Multiply by 10 and subtract once. For example, 9 × 7 = 10 × 7 − 7 = 70 − 7 = 63.
Q5. What is the doubling and halving trick?
If one number is hard to work with, halve it and double the other. The product stays the same. For example, 14 × 5 = 7 × 10 = 70.
Q6. How do you multiply by 25 mentally?
Since 25 = 100 ÷ 4, divide the other number by 4 and then multiply by 100. For example, 24 × 25 = (24 ÷ 4) × 100 = 6 × 100 = 600.
Q7. Why is mental multiplication important?
It builds number sense, speeds up calculations, helps in everyday situations like shopping and budgeting, and reduces dependence on calculators.
Q8. Can mental multiplication work with large numbers?
Yes. Strategies like breaking numbers into parts, rounding and adjusting, and using factors work for larger numbers too. For example, 8 × 125 = 8 × 100 + 8 × 25 = 800 + 200 = 1000.
