Want to multiply by 25 without a calculator? Use the relationship between 25 and 100. If the number is divisible by 4, divide it by 4 and add two zeros. For example, 36 ÷ 4 = 9, so 36 × 25 = 900.
This shortcut is useful for mental math, homework, quizzes, shopping calculations, and everyday problem-solving. Once you understand why it works, multiplying by 25 becomes quick and easy.
The Quick Multiply-by-25 Trick
Because 25 is one-fourth of 100, multiplying by 25 is the same as dividing by 4 and then multiplying by 100:
Multiplying by 100 simply adds two zeros to a whole number. Therefore, when n ÷ 4 is a whole number, the mental shortcut is:
Example 1: Solve 36 × 25
First, divide 36 by 4:
Now add two zeros to 9:
Example 2: Solve 64 × 25
Divide 64 by 4:
Add two zeros to 16:
Why Does This Trick Work?
The shortcut works because 25 multiplied by 4 equals 100:
If a number n can be written as 4 × k, then:
For 36, the value of k is 9 because 36 = 4 × 9. Therefore, 36 × 25 = 9 × 100 = 900.
A Helpful Table
Here are several examples where the number is divisible by 4:
| Problem | Divide by 4 | Add 00 | Answer |
|---|---|---|---|
| 12 × 25 | 12 ÷ 4 = 3 | 3 → 300 | 300 |
| 20 × 25 | 20 ÷ 4 = 5 | 5 → 500 | 500 |
| 36 × 25 | 36 ÷ 4 = 9 | 9 → 900 | 900 |
| 48 × 25 | 48 ÷ 4 = 12 | 12 → 1,200 | 1,200 |
| 64 × 25 | 64 ÷ 4 = 16 | 16 → 1,600 | 1,600 |
| 80 × 25 | 80 ÷ 4 = 20 | 20 → 2,000 | 2,000 |
What If the Number Is Not Divisible by 4?
The “divide by 4, then add two zeros” version is fastest when the number divides evenly by 4. If it does not, use this always-correct form:
Example: 18 × 25
Multiply 18 by 100, then divide by 4:
Example: 23 × 25
Again, multiply by 100 first and then divide by 4:
This method works for every whole number, even when the number is not a multiple of 4.
Another Way to Think About 25
Since 25 is one-fourth of 100, you can also remember these equivalent forms:
For everyday mental math, the most useful version is usually “divide by 4 and add 00” when the division is exact.
Common Mistakes to Avoid
Do not automatically divide every number by 4 and add two zeros without checking whether the division is exact. For numbers such as 18 or 23, use (n × 100) ÷ 4 instead.
Also remember that adding two zeros means multiplying by 100. It does not mean adding the digits 0 and 0 to the original number. For example, 64 ÷ 4 = 16, and 16 × 100 = 1,600.
Finally, check your answer with a quick estimate. Since 64 × 25 is slightly larger than 64 × 20 = 1,280, the answer 1,600 is reasonable.
Practice Problems
Try solving these without a calculator:
- 16 × 25
- 28 × 25
- 40 × 25
- 72 × 25
- 18 × 25
Answer Key
- 16 × 25 = 400
- 28 × 25 = 700
- 40 × 25 = 1,000
- 72 × 25 = 1,800
- 18 × 25 = 450
Final Takeaway
To multiply a number by 25 quickly, remember that 25 is one-fourth of 100:
When n is divisible by 4, divide by 4 and add two zeros. For every other whole number, multiply by 100 and divide by 4. With this simple pattern, calculations such as 36 × 25 = 900 and 64 × 25 = 1,600 become much faster.
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