You write the relationship between dividend, divisor, quotient, and remainder using the following formula:
Dividend = (Divisor × Quotient) + Remainder
This equation describes how division works. Let's break down each component:
- Dividend: The number being divided.
- Divisor: The number by which you are dividing.
- Quotient: The whole number result of the division.
- Remainder: The amount left over after the division, which is always less than the divisor.
Understanding the Formula
The formula essentially states that if you multiply the divisor by the quotient and then add the remainder, you'll get the original dividend. This provides a way to check your division work.
Examples
Here are a couple of examples to illustrate the formula:
Example 1:
- Dividend: 25
- Divisor: 4
- When you divide 25 by 4, you get a quotient of 6 and a remainder of 1.
So, 25 = (4 × 6) + 1
Example 2:
- Dividend: 47
- Divisor: 7
- When you divide 47 by 7, you get a quotient of 6 and a remainder of 5.
So, 47 = (7 × 6) + 5
How to Find the Components
- Dividend: This is usually the starting number in the problem.
- Divisor: This is the number you are dividing by.
- Quotient: Perform the division (either long division or using a calculator) and identify the whole number part of the answer.
- Remainder: The remainder is the amount left over after the division. This can be found using long division or by calculating: Remainder = Dividend - (Divisor × Quotient)
Checking Your Work
Use the formula Dividend = (Divisor × Quotient) + Remainder to verify that your division is correct. If the equation holds true, your calculations are accurate.
