Arithmetic · real student question

Use addition to rewrite the subtraction expression -20 - (-6) without changing the digits. Do not solve.

Question

Use addition to rewrite the subtraction expression below without changing the digits. Do not solve.

20(6)-20-(-6)

Step-by-step solution

  1. State the rule being tested. Subtraction is defined as adding the opposite:

    ab=a+(b).a-b=a+(-b).

    The instruction to keep the digits unchanged means only signs may move — 2020 stays 2020 and 66 stays 66.

  2. Identify a and b in the expression. Here a=20a=-20 and b=6b=-6. The first minus is a sign attached to 2020; the second minus is the operation; the third is the sign attached to 66.

  3. Replace the operation and take the opposite of b. The operation becomes addition, and b=6b=-6 has opposite (6)=+6-(-6)=+6:

    20(6)=20+6.-20-(-6)=-20+6.

    Only the middle two signs changed — this is the 'keep, change, change' pattern: keep the first number, change the operation, change the sign of the second.

  4. Watch what did not change. The leading 20-20 keeps its own negative sign. A frequent mistake is to flip that one too and write 20+620+6, which is a different number entirely.

  5. Confirm the two forms agree. The task says not to solve, but as a private check: 20(6)-20-(-6) means starting at 20-20 and removing a debt of 66, which lands on 14-14; and 20+6=14-20+6=-14 as well. The rewritten expression is 20+6-20+6.

Answer

20(6)=20+6-20-(-6)=-20+6

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