🇺🇸 AMC 8 ⇄ switch contest
1996 AMC 8 Stretch

Problem 4

Problem 4 · AMC 8 Stretch Core
Arithmetic & Operations logical-reasoningrecognizing-false-rules
Using the idea that subtracting is the same as 'flip the sign and add,' find the value of \((-3)-(-5)\).
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Answer: 2
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Hint 1 of 4
Turn the subtraction into an addition: \(a-b\) is the same as 'a, plus the sign-flip of b.'
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Hint 2 of 4
Flip the sign of \(-5\). What number do you get? Now the whole thing is just an addition.
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Hint 3 of 4
You now have \((-3)+(+5)\). Add these two signed numbers.
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Approach: Rewrite subtraction as 'flip the sign and add'
  1. Read the middle \(-\) as 'flip the sign and add': \((-3)-(-5)=(-3)+(\text{flip of } -5)=(-3)+(+5)\).
  2. This is the familiar 'a minus times a minus makes a plus' — subtracting \(-5\) becomes adding \(+5\).
  3. Now add: starting at \(-3\) and going up \(5\) on a number line lands at \(2\).
  4. So \((-3)-(-5)=2\).
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