The remainder in maths is the amount "left over" after performing division. Here's how to find it:
Steps to Calculate the Remainder
Based on the provided reference, the process to find the remainder involves these three key steps:
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Integer Division: Divide the dividend (the number being divided) by the divisor (the number doing the dividing). Crucially, only consider the whole number part of the result; ignore any decimal portion. This whole number result is called the quotient.
- For example, if dividing 17 by 5, the integer division result (quotient) is 3, ignoring the fact that 17/5 is actually 3.4.
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Multiply Quotient and Divisor: Multiply the divisor by the quotient obtained in step 1.
- Continuing our example, multiply 5 (divisor) by 3 (quotient) to get 15.
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Subtract from the Dividend: Subtract the result from step 2 from the original dividend. This final answer is the remainder.
- From our example, subtract 15 (result of step 2) from 17 (dividend) giving 2, which is the remainder.
Illustrative Example
Let's look at another example: Finding the remainder when 28 is divided by 6:
- Step 1 (Integer Division): 28 divided by 6 gives an integer quotient of 4.
- Step 2 (Multiplication): 6 multiplied by 4 equals 24.
- Step 3 (Subtraction): 28 minus 24 equals 4.
Therefore, the remainder when 28 is divided by 6 is 4.
Summary
| Step | Description | Example (28 ÷ 6) |
|---|---|---|
| 1 | Divide the dividend by the divisor (ignore decimal) | 28 ÷ 6 = 4 |
| 2 | Multiply the divisor by the quotient. | 6 x 4 = 24 |
| 3 | Subtract result of step 2 from the dividend. | 28 - 24 = 4 |
Understanding Remainders
- A remainder will always be less than the divisor. If the remainder was equal to or greater than the divisor, it means that division could have been continued one more time.
- The remainder is essentially what's "left over" when dividing evenly.
- The remainder can be zero, indicating that the divisor divides the dividend perfectly.
