Absolute Value
🎬 Math Angel Video: Absolute Value Explained
What is Absolute Value? (0:01)
Definition: The absolute value of a number is its distance from zero on the number line.
Key Property: Because it represents a distance, absolute value can never be negative.
Examples:
For a positive number, the absolute value is the number itself: $|5| = 5$
For zero, the absolute value is $0$: $|0| = 0$
For a negative number, the absolute value is the positive version: $|-3| = 3$
In general:
$$ |x| \geq 0 $$
How to Simplify Absolute Values? (0:46)
To simplify an absolute value expression, follow these 2 steps:
Work out the calculation inside the bars first.
Then apply the absolute value to make the result non-negative.
Example 1:
$$
\begin{aligned}
|-2 \times 6 + 3| &= |-12 + 3| \\
&= |-9| = 9
\end{aligned}
$$
Example 2:
$$
\begin{aligned}
|-2 \times 6| + |3| &= |-12| + |3| \\
&= 12 + 3 = 15
\end{aligned}
$$
Notice the difference:
- In the first example, the whole expression is inside one set of bars.
- In the second example, there are two separate bars, so we take the absolute value of each part before adding.
How to Calculate When Both Numbers Are Negative? (1:50)
Method: When adding two negative numbers, add their absolute values, then keep the negative sign.
Example 1: – 30 – 120 = ?
$30 + 120 = 150$
Keep the negative sign → $-150$
Example 2: – 25 – 60 = ?
$25 + 60 = 85$
Keep the negative sign → $-85$
Exam Tip: Adding two negatives always makes the result more negative.
How to Add Numbers with Different Signs? (2:45)
Method: When the numbers have different signs, subtract the smaller absolute value from the larger one, then keep the sign of the number with the larger absolute value.
Example 1: – 65 + 15 = ?
- $65 – 15 = 50$
- Larger absolute value is $65$ (negative) → $-50$
Example 2: 25 – 130 = ?
- $130 – 25 = 105$
- Larger absolute value is $130$ (negative) → $-105$
Exam Tip: Different signs mean you subtract the absolute values and keep the sign of the bigger number.
📂 Flashcards: Absolute Value Definition and Examples




🍪 Quiz: Practice Absolute Values and Calculating with Negative Numbers
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