To check division with a remainder, you multiply the quotient by the divisor and then add the remainder. The result should equal the original dividend.
Here's a more detailed breakdown:
Understanding Division with Remainders
When dividing, a remainder occurs when one number cannot be divided evenly by another. The remainder is the "leftover" amount after the division is performed as completely as possible. For example, in 17 ÷ 5, the quotient is 3 and the remainder is 2 because 5 goes into 17 three times with 2 left over.
The Check Formula
To verify a division problem that has a remainder, you use this formula:
(Quotient × Divisor) + Remainder = Dividend
- Dividend: The number being divided.
- Divisor: The number you are dividing by.
- Quotient: The result of the division (the whole number of times the divisor goes into the dividend).
- Remainder: The amount left over after the division.
Steps to Verify Division with Remainder
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Identify the dividend, divisor, quotient, and remainder from your division problem.
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Multiply the quotient by the divisor.
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Add the remainder to the result from step 2.
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Compare the final result with the original dividend. If they match, your division is correct.
Example
Let's say we are dividing 23 by 4:
- 23 ÷ 4 = 5 with a remainder of 3.
To check this using the formula:
- Quotient = 5
- Divisor = 4
- Remainder = 3
- (5 × 4) + 3 = 20 + 3 = 23
Since the result, 23, matches the original dividend, the division is correct.
Another Example with Table Format
Let's check the division problem 38 ÷ 7 = 5 R 3
| Component | Value |
|---|---|
| Dividend | 38 |
| Divisor | 7 |
| Quotient | 5 |
| Remainder | 3 |
| Formula | (5 * 7) + 3 |
| Calculation | 35 + 3 = 38 |
| Result | 38 |
The result matches the dividend. So the division was correct.
Common Pitfalls
- Forgetting to add the remainder. Always ensure this step is included in your check.
- Incorrect multiplication. Double-check your multiplication step.
Summary
Checking division with remainders is an essential skill for ensuring accuracy in calculations. By understanding and applying the formula (Quotient × Divisor) + Remainder = Dividend, you can confidently verify your division results.
