Absolute Value
Table Of Contents
🎬 Math Angel Video: Absolute Value Explained
What is Absolute Value?
⏩️
🛎️ Definition of Absolute Value:
The absolute value of a number is its distance from zero on the number line.
🛎️ Key Property of Absolute Value:
Because it represents a distance, absolute value can never be negative.
🛎️ Examples of Absolute Value
- 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?
⏩️
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:
$$
\begin{aligned}
|-2 \times 6 + 3| &= |-12 + 3| \\[1mm]
&= |-9| \\[1mm]
&= 9
\end{aligned}
$$
🛎️ Example 2:
$$
\begin{aligned}
|-2 \times 6| + |3| &= |-12| + |3| \\[1mm]
&= 12 + 3 \\[1mm]
&= 15
\end{aligned}
$$
🚨 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?
⏩️
🛎️ 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?
⏩️
🛎️ Method:
When adding numbers with different signs:
Ignore the signs and compare the absolute values.
Subtract the smaller absolute value from the larger absolute value.
Give the result 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) → $-105$
🍪 Quiz: Practice Absolute Value and Negative Numbers
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