Absolute value

Absolute value is a number’s distance from 0, so it is never negative: |−7| = 7. Pictures and a quiz for kids, parent help below.

🧒 Kids: how far from zero?

Count the steps from the number to 0. That count is the absolute value. Steps are never negative! Then try the quiz.

▶ Quiz 🔢 More practice

−8−6−4−2024687 steps−7

💡 Trick: |−7| means “how far is −7 from 0?” It is 7 steps, so |−7| = 7!

More integers: What are integers · Opposite numbers · Absolute value · Comparing integers · Integers on a number line · Zero pairs

For parents and teachers ↓

This part is for grown-ups: the key idea, pictures to draw, what to say, common mistakes, questions with answers and a free worksheet.

The trick: count the steps to zero

Absolute value measures distance from 0, and a distance is never negative. The bars | | around a number mean “absolute value of”. For a positive number or 0 it stays the same; for a negative number, drop the minus sign.

Patterns to spot

Key words

Why it matters: Absolute value lets children talk about size without direction: how deep, how far or how much is owed. It appears again in distance on the coordinate plane, in the rules for adding integers and in algebra.

See it: pictures to draw with your child

Draw these on paper or a whiteboard. A quick sketch makes the idea concrete before any rules.

−10−8−6−4−20246810|−7| = 7|7| = 7−77
−7 and 7 are both 7 steps from 0, so both have absolute value 7.
sea level = 0−60 m−40 m−20 m0 m20 m40 m60 mPlane (50 m)Submarine (−40 m)
The submarine is at −40 m. Its depth, |−40| = 40 m, is the absolute value.
−10−8−6−4−20246810distance 10−46
From −4 to 6 is 4 + 6 = 10 steps. Distance = |6 − (−4)| = 10.

What your child already knows

Children already know how to count steps on a number line and that distances are always positive. Absolute value just gives that distance from 0 a name and a symbol.

In real life: A diver at −12 m is 12 m deep. A temperature of −8°C is 8 degrees below freezing. A balance of −$25 is a debt of $25. Each time, the absolute value is the size without the direction.

Absolute value vs. order

A bigger absolute value does not always mean a bigger number. −20 has a bigger absolute value than 5, because it is further from 0. But −20 is less than 5.

In real life, ask “how big?” or “how far?” for absolute value. Ask “which is more?” for order.

A debt of $30 is a balance of −30. Its absolute value, 30, is the size of the debt. So a balance less than −30 means a debt greater than $30.

A quick test helps children keep the two ideas apart. Ask “Which number is further from 0?” for absolute value, then “Which number is further right?” for order. For −20 and 5, the answers are different: −20, then 5.

Worked examples

Example 1: Find it

  1. Find |−15|. −15 is 15 steps from 0.
  2. So |−15| = 15.

Example 2: Compare sizes

  1. Which has the greater absolute value, −11 or 8? |−11| = 11 and |8| = 8.
  2. So −11 has the greater absolute value, even though −11 is less than 8.

Example 3: Real life

  1. Ana’s account shows −$40.
  2. Ben’s shows −$15.
  3. Who owes more? |−40| = 40 and |−15| = 15, so Ana owes more.

Common mistakes

Thinking bars mean “make negative”Writes |8| = −8.Fix: absolute value is a distance, so it is never negative: |8| = 8.
Confusing size and orderSays −20 > 5 because 20 > 5.Fix: −20 is further from 0, but it is to the left of 5, so −20 < 5.
Mixing up −|x| and |−x|Writes −|6| = 6.Fix: work inside the bars first: |6| = 6, then the outside minus makes −6.

What to say to your child

A short script for your first session. Pause after each line and let your child answer.

  1. “Put your finger on −6. Count the steps to 0.” (6.)
  2. “So the absolute value of −6 is 6. We write |−6| = 6.”
  3. “What is |6|?” (6.)
  4. “Which is further from 0, −9 or 4?” (−9.)
  5. “Is −9 bigger than 4, though?” (No, it is less.)

Questions to try (answers below)

Ask these out loud or write them down. The last one is a stretch.

  1. |−18|
  2. |25|
  3. |0|
  4. |−4| + |−5|
  5. −|7|
  6. Which has the greater absolute value: −13 or 10?
  7. Two numbers have absolute value 6. What are they?
  8. A diver is at −35 m. How deep is she?
  9. Stretch: distance from −9 to 5
Show the answers
  1. 18
  2. 25
  3. 0
  4. 9
  5. −7
  6. −13
  7. 6 and −6
  8. 35 m
  9. 14

Games to play at home

Step count

Lay out a number line with tape. Your child stands on a negative number and counts steps to 0.

Deepest dive

Make up depths below sea level and ask who is deepest, using absolute value.

Same distance pairs

Call out an absolute value, like 8. Your child names both numbers with that absolute value.

A 5-day plan for absolute value

Ten minutes a day is enough. Short, regular practice works far better than one long session.

By grade

Grade 6 (Common Core 6.NS.C.7c and 7d) learns absolute value as distance from 0 and tells it apart from order. Grade 6 also finds distances between points (6.NS.C.8), and grade 7 uses absolute value in subtraction. In India, absolute value appears in class 6 and 7 integers.

More for each grade: Grade 6 math and the CBSE class 6 maths guide.

What comes next

Next, see comparing integers, where absolute value and order meet. Find distances on the integer number line.

Worksheet and more practice

Print a free worksheet with an answer key, or keep practicing online with integer practice.

Printable PDFs: comparing integers · absolute value · adding and subtracting integers · make a fresh integers test

← Opposite numbersComparing integers →

More: integers for kids · integer calculator · integer number line · integer practice · multiplying integers · ratios for kids

Last reviewed

Questions parents ask

What is absolute value?

A number’s distance from 0 on the number line. |−7| = 7 and |7| = 7.

Can absolute value be negative?

No. A distance is never negative, so absolute value is 0 or positive.

What does |−5| mean?

The absolute value of −5, which is 5.

Is a bigger absolute value a bigger number?

Not for negatives. −20 has a bigger absolute value than 5, but −20 is less than 5.

What grade learns absolute value?

Grade 6 under Common Core 6.NS.C.7c. In India, class 6 and 7.