Understand Opposite Quantities Summing to Zero

Students understand that a number and its opposite (additive inverse) always sum to zero. They apply this concept to interpret situations like debts and credits, elevation above and below sea level, and temperature above and below zero.

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Grade 7 · The Number System · question 1 of 3

0 of 20

20 rungs. A star at the top.

−9 + 9 =

How it is taught

0:00 of 2:48

A number plus its opposite is always 0.

That opposite is the additive inverse.

Read it: Adding positive and negative numbers

−5 + 7 starts at −5 on the number line and hops 7 to the right. The hop passes 0 and lands on 2, so −5 + 7 = 2.

Turn any subtraction into adding the opposite: 3 − 5 is 3 + (−5).
Pair any opposites first: a number and its opposite make 0.
Add what is left on the line: hop right for a positive number, left for a negative.

When the two numbers have the same sign, the hop keeps going the same way: add the distances and keep the sign.

When the signs are opposite, the hop turns back: take the shorter distance from the longer, and the longer one's sign wins. Here 7 − 5 = 2.

Subtracting a number is the same as adding its opposite, and a number plus its opposite is 0.

Same signs: add the distances and keep the sign. Opposite signs: subtract the distances and keep the sign of the longer one.

Adding the distances and keeping the first sign: −5 + 7 = −12.

The hop of 7 goes right, back past 0: 7 − 5 = 2.

11 + ___ = 0 — −11. 11 and −11 are opposites: the same distance from 0 on either side.

3 + (−3) = 0

Picture an elevator. It goes up three floors, then comes back down three floors. Where does it end up?

Let's track it on a number line. The elevator starts at zero — the ground floor.

Up three floors — we hop from zero all the way to positive three.

We've moved plus three.

Now it comes down three floors — we hop back from three toward zero.

That's a move of negative three. And look — we're right back at zero!

We can write what just happened: three plus negative three. What does that equal?

Zero. The two moves cancelled each other out perfectly.

Three and negative three are opposites — we call them additive inverses. A number plus its opposite is always zero.

Money in and money out, steps up and steps down, degrees above and below zero — opposites always sum to zero!

Grade 7 · A number plus its opposite always equals zero

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

More of the library

Every skill has a page

Standards

CCSS.7.NS.A.1

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers

CCSS.7.NS.A.1a

Describe situations in which opposite quantities combine to make 0

Grade 7

Quoted from the Common Core State Standards.

Where this sits

Comes after

Locate Rational Numbers on a Number Line

Leads to

What a star here means

A star here is the top of a twenty-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 7

This is one rung of 40 in Grade 7 mathematics, in the order they build on each other.

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free