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A student worked out −7 − (−12) and wrote −19. Which choice names the mistake and gives the correct answer?

Class 6IntegersIntegers
  • AThere is no mistake; −19 is correct.
  • BThe student added when the numbers should have been subtracted; the answer is −5.
  • CThe student read '− (−12)' as '− 12' instead of '+ 12'; the answer is 5.
  • DThe student should have kept the sign of the bigger digit; the answer is 19.

Step-by-Step Solution

Subtracting a negative means adding its opposite: −7 − (−12) = −7 + 12. The signs now differ, so 12 − 7 = 5, and the larger absolute value (12) is positive, giving 5. Writing −19 comes from collapsing the double minus into a single minus and then adding 7 and 12 as though both were negative.
Answer: C) The student read '− (−12)' as '− 12' instead of '+ 12'; the answer is 5.

Key idea: Subtracting integers

Subtraction of integers is just adding the **opposite**: a − b = a + (−b). So 5 − 8 = 5 + (−8) = −3. And 5 − (−8) = 5 + 8 = 13. The 'minus minus' that looks confusing in symbols is simply: subtracting a negative is the same as adding its positive twin. Always rewrite subtraction as addition of the opposite — it removes every sign-error trap.

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