Absolute Value
The distance of a number from zero on the number line.
Key idea
The distance of a number from zero on the number line.
In depth
The absolute value |a| is the distance from a to zero, so it is never negative. It strips the sign but keeps the size.
Worked example
|−7| = 7, |7| = 7, |0| = 0. Distance between −3 and 5 is |5 − (−3)| = 8.
Formula
Real-world uses
- Measuring distance between two locations on a number line
- The size of an error regardless of direction
Common mistake
Writing |−a| = −a. The result of an absolute value is non-negative.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Absolute Value?
The distance of a number from zero on the number line. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Absolute Value?
The key formula is |−5| = 5.
Where is Absolute Value used in real life?
Real-world examples: Measuring distance between two locations on a number line; The size of an error regardless of direction.
What should I learn before Absolute Value?
Make sure you are comfortable with Multiplying Integers, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Absolute Value?
Writing |−a| = −a. The result of an absolute value is non-negative.
How can I practise Absolute Value?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Absolute Value?
Move on to Fractions Basics next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.