Interpret and compute absolute value on the number line and within expressions.
Free, timed SHSAT practice sets on absolute value— every question includes a full worked explanation, and there's no account required.
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The absolute value of a number is its distance from 0, so it is never negative: \(|-9| = 9\) and \(|9| = 9\).
To evaluate an expression: treat the bars like parentheses.
Example: \(|-12 - (-9)| + (-10)\). Inside: \(-12 + 9 = -3\). Then \(|-3| = 3\). Then \(3 + (-10) = -7\). The final answer can be negative, because the \(-10\) is outside the bars.
Distance between two numbers: subtract them and take the absolute value. From \(-13\) to \(4\): \(|4 - (-13)| = 17\).
Common traps:
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 \(31\).
Evaluate inside the bars first: \(-15 - (-9) = -6\). Then take the absolute value: \(|-6| = 6\). Then subtract 4: \(6 - 4 = 2\). Dropping the absolute value bars gives \(-10\). Forgetting to subtract 4 gives \(6\). Adding 4 instead of subtracting it gives \(10\).
Distance is \(|1 - (-2)| = |1 + 2| = 3\). Subtracting 2 from 1 as if both points were positive gives \(-1\). Subtracting 1 from -2 and keeping the negative result gives \(-3\). Counting the integers from -2 to 1 instead of the steps between them gives \(4\).