Distance between integers

The distance between two integers is the absolute value of their difference: from −4 to 6 is |6 − (−4)| = 10. A quiz is included.

The idea: count the steps between

Distance is how many steps apart two numbers are on the number line. It doesn’t matter which one you start from, and it is never negative.

From −4 to 6, count 4 steps to reach 0 and 6 more to reach 6. That is 10 steps, so the distance is 10.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

−10−8−6−4−2024681046−46
Opposite sides of 0: 4 + 6 = 10.
−10−9−8−7−6−5−4−3−2−10126−9−3
Same side of 0: 9 − 3 = 6.
−10−505103 p.m.−10−50510Midnight
From 3°C to −5°C is a fall of 8 degrees.

Same side or opposite sides of zero

If the numbers are on opposite sides of 0, add their absolute values. From −7 to 5 is 7 + 5 = 12.

If they are on the same side, subtract their absolute values. From −9 to −3 is 9 − 3 = 6, and from 2 to 11 is 11 − 2 = 9.

Both cases fit one formula: distance = |a − b|. For example, |−9 − (−3)| = |−6| = 6.

Find the distance

Type two numbers separated by a comma. The tool marks both and measures the gap.

Change vs. distance

A change has a direction, so it can be negative. If the temperature goes from 3°C to −5°C, the change is −5 − 3 = −8 degrees.

A distance has no direction. The temperatures are |−8| = 8 degrees apart.

Word problems often ask “how much did it rise or fall?” Give the distance and say “rose” or “fell”, or give the signed change.

Distance on a grid

Points with the same x-coordinate sit on a vertical line. Their distance is the distance between their y-coordinates.

So (3, 4) and (3, −2) are |4 − (−2)| = 6 units apart. The coordinate plane guide uses this to find side lengths of shapes.

Key words

Distance in real life

Temperature range: a desert might be 45°C by day and −5°C at night. The range is 45 − (−5) = 50 degrees.

Heights: a mountain peak at 2,000 m and a valley floor at −100 m are 2,100 m apart.

Time: on a timeline with −300 for 300 BC, the time from 300 BC to AD 200 is 200 − (−300) = 500 years.

Golf: a score of −4 and a score of +3 are 7 shots apart.

In each case, the question is “how far apart?”, so the answer is positive.

Using the number line tool

The number line tool above marks both numbers and shows the gap. Try pairs on the same side of 0 and pairs on opposite sides.

Ask your child to predict the distance first, then check. After a few tries, most children see the add-or-subtract pattern for themselves.

A common slip: subtracting across zero

When two numbers are on opposite sides of 0, children often subtract their sizes. From −4 to 6, they say 6 − 4 = 2.

Ask them to count to 0 first: 4 steps from −4 to 0, then 6 more to 6. Ten steps in all. After a few tries with a number line, the rule “opposite sides, add” sticks.

Quiz: distance between integers

How far apart are the numbers? Distances are never negative.

Where this fits: integers step by step

  1. What are integers
  2. Integers on a number line
  3. Opposite numbers
  4. Absolute value
  5. Comparing integers
  6. Negative numbers in real life
  7. Zero pairs
  8. Adding integers
  9. Subtracting integers
  10. Distance between integers (this page)
  11. Multiplying integers
  12. Dividing integers
  13. Integer rules
  14. Order of operations with integers
  15. The coordinate plane
  16. Rational numbers
  17. Integer word problems

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

  1. “Put one finger on −4 and one on 6. How many steps from −4 to 0?” (4.)
  2. “And from 0 to 6?” (6.) “So the distance is…?” (10.)
  3. “Now −9 and −3. Are they on the same side of 0?” (Yes.)
  4. “Then subtract: 9 − 3.” (6.)
  5. “Can a distance be negative?” (No.)

More worked examples

Example 1: opposite sides

From −15 to 8: 15 + 8 = 23.

Example 2: same side

From −20 to −6: 20 − 6 = 14.

Example 3: with the formula

|−2 − 13| = |−15| = 15.

Example 4: elevation

A bird at 25 m and a fish at −10 m are 25 + 10 = 35 m apart.

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

  1. From −3 to 5
  2. From −12 to −2
  3. From 4 to 19
  4. From −8 to 0
  5. |−6 − 9|
  6. |−1 − (−11)|
  7. From −4°C to 7°C
  8. A diver at −18 m and a boat at 0 m
  9. (2, 5) and (2, −3)
  10. Stretch: a number is 6 away from −2. What could it be?
Show the answers
  1. 8
  2. 10
  3. 15
  4. 8
  5. 15
  6. 10
  7. 11 degrees
  8. 18 m
  9. 8 units
  10. 4 or −8

Common mistakes

Subtracting across zeroSays −4 to 6 is 6 − 4 = 2.Fix: the numbers are on opposite sides, so add: 4 + 6 = 10.
Giving a negative distanceWrites the distance from 6 to −4 as −10.Fix: distance is an absolute value, so 10.
Counting marks, not jumpsCounts −2, −1, 0, 1 as 4 steps.Fix: count the jumps between marks: from −2 to 1 is 3.

How to teach it at home

Thermometer gaps

Compare today’s high and low and find how far apart they are.

Lift distance

Floor −2 to floor 5: how many floors does the lift travel?

Two-finger line

On a drawn number line, place two fingers and count the gap.

By grade

More for each grade: Grade 6 math and the CBSE class 6 maths guide; Grade 7 math and the CBSE class 7 maths guide.

Worksheets and practice

Absolute value worksheet, page 1

Absolute value worksheet: printable PDF with an answer key. · Make a fresh test

Integer practice · integer calculator · integer number line · integers for kids · ratios

Last reviewed

Questions parents ask

How do you find the distance between two integers?

Subtract them and take the absolute value: |a − b|.

What is the distance from −4 to 6?

10, because |6 − (−4)| = 10.

Can distance be negative?

No. Distance is always 0 or positive.

How is distance different from change?

Change has a direction and can be negative. Distance is the size of the change.

What grade learns distance between integers?

Grade 6 (6.NS.C.8) and grade 7 (7.NS.A.1c). In India, class 6 and 7.