Working backward means starting with a known result and reversing a sequence of operations in the opposite order to determine an unknown starting value, using inverse relationships such as addition and subtraction or multiplication and division. In one- and multistep problems involving whole numbers, fractions, and decimals, the reasoning must preserve operation order and account for the meaning of each quantity; this supports solving equations and checking solutions without extending to formal symbolic generalizations.
To work backward, start with the known result and undo each operation in the reverse order. Use the inverse operation:
Example: A number is multiplied by , and then is added. The result is . What was the starting number?
The last operation was adding , so undo it first:
The first operation was multiplying by , so undo it next by dividing:
The starting number was .
Check: Work forward from :
The result matches, so the answer is correct.
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