To find the dividend in division, you use the following formula: Dividend = (Divisor × Quotient) + Remainder.
Understanding the Formula
This formula is derived from the basic principles of division. Let's break down each component:
- Dividend: The number being divided (the number you want to split into equal groups).
- Divisor: The number you are dividing by (the size of each group).
- Quotient: The result of the division (the number of groups).
- Remainder: The amount left over after the division (the amount that doesn't fit evenly into the groups).
Applying the Formula: Examples
Here are a few examples to illustrate how to use the formula to find the dividend:
Example 1:
- Divisor = 5
- Quotient = 7
- Remainder = 2
Dividend = (5 × 7) + 2 = 35 + 2 = 37
Therefore, the dividend is 37.
Example 2:
- Divisor = 12
- Quotient = 3
- Remainder = 0
Dividend = (12 × 3) + 0 = 36 + 0 = 36
Therefore, the dividend is 36. (This is a case of exact division).
Example 3:
- Divisor = 8
- Quotient = 10
- Remainder = 4
Dividend = (8 × 10) + 4 = 80 + 4 = 84
Therefore, the dividend is 84.
Practical Application
This formula is useful for:
- Checking your work: After performing a division, you can use this formula to verify if your calculations are correct.
- Solving word problems: Many word problems involve finding the original number (dividend) when you know the divisor, quotient, and remainder.
- Understanding the relationship between the components of division.
In Summary
Finding the dividend is a straightforward process. By multiplying the divisor and quotient, and then adding the remainder, you can accurately determine the dividend. Remember the formula: Dividend = (Divisor × Quotient) + Remainder.
