You can check your division calculations by using multiplication, the inverse operation.
Understanding the Relationship
Division and multiplication are closely linked. The act of dividing a number (the dividend) by another number (the divisor) gives you a result called the quotient. To confirm the accuracy of your division, you use multiplication. This process is based on the inverse relationship between the two operations.
How to Verify Division with Multiplication
As the reference states, you check a division problem by multiplying the quotient by the divisor. If the result of that multiplication matches the original dividend, then your division was correct. If the result does not match the dividend, you made an error in the division.
- The process in simple terms:
- Perform the division.
- Multiply the quotient by the divisor.
- Compare the result with the original dividend.
- If they match, the division was correct.
Examples
Let's look at some examples to see this in action:
| Division Problem | Quotient | Divisor | Check (Quotient x Divisor) | Dividend | Is Correct? |
|---|---|---|---|---|---|
| 12 ÷ 3 = ? | 4 | 3 | 4 x 3 = 12 | 12 | Yes |
| 20 ÷ 4 = ? | 5 | 4 | 5 x 4 = 20 | 20 | Yes |
| 25 ÷ 5 = ? | 6 | 5 | 6 x 5 = 30 | 25 | No |
- In the first example, 12 divided by 3 equals 4. Checking, 4 x 3 = 12, which is the original dividend, thus the division is correct.
- In the second example, 20 divided by 4 equals 5. Checking, 5 x 4 = 20, which is the original dividend, thus the division is correct.
- In the third example, 25 divided by 5 is incorrectly calculated as 6. Checking, 6 x 5 = 30, which is NOT the original dividend (25), thus the division is incorrect and the correct quotient should be 5.
Practical Insight
It is always important to double check your work in mathematics and this easy check for division helps make sure that you aren't making simple errors. This strategy applies to all numbers, even fractions and decimals, but care must be taken to ensure the accuracy of multiplication when dealing with these.
