Opposite numbers

Opposite numbers are the same distance from 0 on opposite sides, like 6 and −6. Pictures and a quiz for kids, parent help below.

🧒 Kids: flip over zero!

Find the number. Count its steps to 0. Now take the same steps on the other side. That is its opposite! Then try the quiz.

▶ Quiz 🔢 More practice

−8−6−4−2024685 steps5 steps−55

💡 Trick: To find the opposite, just change the sign: 7 → −7 and −7 → 7. Zero stays 0!

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: change the sign

The opposite of a number is the same distance from 0, but on the other side. So to find it, keep the digits and change the sign. A number and its opposite always add to 0.

Patterns to spot

Key words

Why it matters: Opposites are the key to subtracting integers, because subtracting a number means adding its opposite. They also lead to the idea that a number plus its opposite is 0, which children use when solving equations later.

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.

−10−8−6−4−202468106 steps6 steps−66
6 and −6 are opposites: both are 6 steps from 0.
−10−8−6−4−20246810opposite−33
The opposite of 3 is −3. Jump over zero to the same distance on the other side.
sea level = 0−60 m−40 m−20 m0 m20 m40 m60 mKite (30 m)Fish (−30 m)
A kite 30 m up and a fish 30 m down are opposites: 30 and −30.

What your child already knows

Children already know the number line and that negatives sit to the left of zero. They also know words that come in pairs, like up and down or gain and loss. Opposite numbers turn those word pairs into maths.

In real life: Going up 5 floors and down 5 floors, earning $10 and spending $10, or gaining and losing 3 points are opposites. Each pair cancels out back to where you started.

The minus sign means “the opposite of”

A minus sign in front of a number can be read as “the opposite of”. So −5 is the opposite of 5, and −(−5) is the opposite of −5, which is 5.

This idea matters later. In algebra, −x is not always negative: if x is −3, then −x is 3.

Opposites also explain subtraction of integers. Subtracting a number is the same as adding its opposite: 4 − 6 = 4 + (−6).

Try it with your child on a number line. Start at 4 and jump 6 to the left: you land on −2. Now start at 4 and add −6: you land on the same spot.

Worked examples

Example 1: Find the opposite

  1. What is the opposite of −23?
  2. It is 23 steps left of 0.
  3. The same distance on the right is 23.
  4. So the opposite is 23.

Example 2: Opposite of the opposite

  1. Simplify −(−8).
  2. The opposite of −8 is 8.
  3. So −(−8) = 8.

Example 3: In a story

  1. A plane climbs 400 m.
  2. What is the opposite move?
  3. Falling 400 m, written −400.

Common mistakes

Thinking opposites must be negativeSays the opposite of −4 is −4 or “more negative”.Fix: change the sign: the opposite of −4 is 4.
Confusing opposite with reciprocalSays the opposite of 2 is ½.Fix: opposite means the other side of 0, so it is −2.
Giving zero an oppositeSays the opposite of 0 is −0 or 1.Fix: 0 is its own opposite. −0 is just 0.

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 5. How many steps is it to 0?” (5.)
  2. “Keep going 5 steps past 0. Where are you?” (−5.)
  3. “So 5 and −5 are opposites. What is 5 + (−5)?” (0.)
  4. “What is the opposite of −9?” (9.)
  5. “And the opposite of that?” (−9 again.)

Questions to try (answers below)

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

  1. Opposite of 12
  2. Opposite of −31
  3. Opposite of 0
  4. Simplify −(−6)
  5. Simplify −(4)
  6. Which number is 9 steps from 0 on the negative side?
  7. What is 15 + (−15)?
  8. Opposite of “10 m below sea level”
  9. Stretch: if −x = 7, what is x?
Show the answers
  1. −12
  2. 31
  3. 0
  4. 6
  5. −4
  6. −9
  7. 0
  8. 10 m above sea level, or 10
  9. −7

Games to play at home

Mirror walk

Chalk a number line outside. Stand on a number and have your child stand on its opposite.

Opposite snap

Write integers on cards. Snap any two cards that are opposites.

Story flip

Say a move (“up 6 stairs”) and ask for the opposite move and its integer.

A 5-day plan for opposite numbers

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.6a) learns that opposite signs show locations on opposite sides of 0. It also learns that the opposite of the opposite is the number itself. Grade 7 uses opposites to subtract integers. In India, this is part of the class 6 integers chapter.

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

What comes next

Next, learn absolute value, the distance from 0 that opposites share. Try opposites 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

← What are integersAbsolute value →

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

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Questions parents ask

What are opposite numbers?

Two numbers the same distance from 0 on opposite sides of the number line, like 4 and −4.

What is the opposite of a negative number?

A positive number. The opposite of −8 is 8.

What is the opposite of 0?

0. Zero is its own opposite.

What do a number and its opposite add up to?

Always 0. For example, 9 + (−9) = 0.

What grade learns opposite numbers?

Grade 6 under Common Core 6.NS.C.6a. In India, class 6.