Sign error sprint

Drop or flip a negative sign during arithmetic or algebra.

An error-pattern drill: practice spotting and avoiding this specific SHSAT trap.

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How to avoid sign errors

A sign error is one small slip that changes the whole answer. Take \(-12 - (-9)\). A rushed student writes \(-12 - 9 = -21\). The right answer is \(-12 + 9 = -3\). Subtracting a negative is the same as adding.

Sign errors happen because the minus sign has two jobs: it means "subtract" and it means "negative". When you work fast, one of the two gets lost.

Check habits:

Worked examples

Example 1.
What is \(|8 - (-14)| - 9\)?
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Answer:
A

Evaluate inside the bars first: \(8 - (-14) = 22\). Then take the absolute value: \(|22| = 22\). Then subtract 9: \(22 - 9 = 13\). Taking the absolute value of each number before subtracting gives \(-15\). Forgetting to subtract 9 gives \(22\). Adding 9 instead of subtracting it gives \(31\).

Example 2.
Point A is at \(18\) and point B is at \(-10\) on a number line. What is the distance between A and B?
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Answer:
A

Distance is the absolute value of the difference: \(|-10 - 18| = 28\). Subtracting in the wrong order and keeping the negative result gives \(-28\). Adding the two coordinates instead of subtracting them gives \(8\). Finding the point halfway between A and B instead of the distance gives \(4\).

Example 3.
Evaluate \(-9x + 8y - 7\) when \(x = 5\) and \(y = -4\).
Show answer and explanation
Answer:
A

Substitute: \(-9(5) + 8(-4) - 7 = -45 - 32 - 7 = -84\). (Putting \(-4\) in for \(x\) and \(5\) in for \(y\) gives \(69\). Using \(4\) instead of \(-4\) for \(y\) gives \(-20\). Leaving off the \(- 7\) at the end gives \(-77\).)