Uvero — STEM Learning

Checking Subtraction with Addition

Subtraction and addition are inverse operations, so a difference can be checked by adding it to the smaller number. If $a-b=c$ , then $c+b=a$ . A careful solution names the quantities, keeps place value or units visible, and explains why each operation fits.

Worked reasoning

Add the difference and subtrahend.
$626+278=904$ , so the subtraction is correct.

A learner calculates $904-278=626$ . What total checks the answer by addition?

Which statement best captures the central mathematical idea in Checking Subtraction with Addition?

If $a-b=c$ , then $c+b=a$ .

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Checking Subtraction with Addition, which move is most reliable?

Represent the given information clearly and identify the operation or relationship required for checking subtraction with addition.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Checking Subtraction with Addition?

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

If $a-b=c$ , then $c+b=a$ .

Represent the given information clearly and identify the operation or relationship required for checking subtraction with addition.

Estimate first, then reverse the operation or use a second representation to check that the answer is reasonable.