Multiplication Strategies
Learn different ways to multiply 2-digit and 3-digit numbers with confidence and accuracy.
Mental Multiplication Strategies
These strategies help you multiply numbers in your head by breaking the problem into simpler parts.
1. Doubling and Halving
If one number is even, halve it and double the other. The answer stays the same!
Example: 25 × 16
2. Partitioning (Distributive Property)
Split the larger number into parts, multiply each part, then add the results.
Example: 34 × 6
30 × 6
= 180
4 × 6
= 24
180 + 24 = 204
3. Multiplying by 10, 100 and 1,000
When you multiply by 10, 100 or 1,000, each digit moves to the left in the place value chart.
47 × 10
= 470
47 × 100
= 4,700
47 × 1,000
= 47,000
Written Multiplication (Short Method)
For multiplying a multi-digit number by a 1-digit number, use the short multiplication method. Work from right to left, carrying when needed.
Example: 347 × 6
Ones: 7 × 6 = 42. Write 2, carry 4.
Tens: 4 × 6 = 24, plus 4 carried = 28. Write 8, carry 2.
Hundreds: 3 × 6 = 18, plus 2 carried = 20. Write 20.
Area Model (Grid Method)
Split the number into place value parts and create a grid. This is great for understanding why multiplication works.
Example: 243 × 5
| × | 200 | 40 | 3 |
|---|---|---|---|
| 5 | 1,000 | 200 | 15 |
1,000 + 200 + 15 = 1,215
Multiplying by a 2-Digit Number
When multiplying by a 2-digit number, you can use the extended written method: multiply by the ones, then multiply by the tens, and add.
Example: 38 × 24
38 × 4 = 152, then 38 × 20 = 760. Finally, 152 + 760 = 912.
Key Vocabulary
Product
The result of multiplying two or more numbers together.
Factor
A number that is multiplied by another number. In 6 × 4 = 24, both 6 and 4 are factors.
Partitioning
Breaking a number into its place value parts (e.g. 243 = 200 + 40 + 3).
Distributive Property
The rule that lets us split a multiplication into parts: a × (b + c) = (a × b) + (a × c).
Worked Examples
Use partitioning to solve 56 × 7.
Step 1: Split 56 into 50 + 6.
Step 2: 50 × 7 = 350
Step 3: 6 × 7 = 42
Answer: 350 + 42 = 392
Use doubling and halving to solve 35 × 12.
Step 1: Halve 12 to get 6. Double 35 to get 70.
Step 2: 70 × 6 = 420
Answer: 420
Use the short multiplication method to solve 268 × 4.
Ones: 8 × 4 = 32. Write 2, carry 3.
Tens: 6 × 4 = 24, plus 3 = 27. Write 7, carry 2.
Hundreds: 2 × 4 = 8, plus 2 = 10. Write 10.
Answer: 1,072
Knowledge Check
Select the correct answer for each question.
Question 1
What is 45 × 8?
Question 2
What is 156 × 3?
Question 3
Using doubling and halving, 25 × 12 can be solved as:
Question 4
A school orders 24 packs of pencils. Each pack has 36 pencils. How many pencils in total?
Question 5
What is 63 × 100?
Key Concepts Summary
- ●Doubling and halving keeps the product the same while making the numbers easier to work with.
- ●Partitioning splits a number by place value so you can multiply each part separately.
- ●Multiplying by 10, 100 or 1,000 shifts digits to the left by 1, 2 or 3 places.
- ●The short multiplication method works from right to left, carrying as needed.
- ●The area model helps you see why partitioning and multiplication work together.