Working backwards with division involves reversing the operation and performing multiplication instead. This helps you find the original number or solve for an unknown value.
Here's a breakdown:
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Identify the Division: Recognize that you're trying to undo a division operation.
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Reverse the Operation: Instead of dividing, you'll multiply.
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Multiply: Multiply the result of the division by the divisor (the number you originally divided by) to find the original number.
Example:
Let's say you have the equation: x / 2 = 19. To find 'x' by working backwards:
- Identify the division: x is being divided by 2.
- Reverse the operation: Instead of dividing, multiply.
- Multiply: 19 * 2 = 38. Therefore, x = 38.
General Principle
If you have the equation:
Original Number / Divisor = Quotient
To find the "Original Number" you perform:
Quotient * Divisor = Original Number
Why does this work?
Division and multiplication are inverse operations. Multiplication "undoes" division, and vice versa. By performing the opposite operation, you effectively isolate the unknown variable and solve for its value.
