Add Rational Numbers Using Absolute Value

Students interpret p + q as starting at p on a number line and moving a distance of |q| in the direction determined by the sign of q. They use this model to add positive and negative rational numbers including fractions and decimals.

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Grade 7 · The Number System · question 1 of 3

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20 rungs. A star at the top.

−3 + 7 =

How it is taught

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Adding on a number line starts at the first number.

The absolute value is how far you move.

The sign of the second number picks the direction.

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.

−10 + 9 = ___ — −1. Opposite directions: 10 − 9 = 1, and the longer one goes left, so −1.

2 + (−5)

Today we'll add rational numbers using a number line. Let's solve two plus negative five.

Here's our sum. We'll call the first number p and the second number q.

First we start at p. Drop a pin at positive two.

Now look at q. The absolute value of negative five is five — that's how far we move.

Because q is negative, we move to the LEFT — toward smaller numbers.

Five hops left from two: one, zero, negative one, negative two, negative three.

We land on negative three.

So two plus negative five equals negative three. Distance tells us how far, sign tells us which way!

Grade 7 · Add on a number line using direction and distance

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.

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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.1b

Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative

Grade 7

Quoted from the Common Core State Standards.

Where this sits

Comes after

Leads to

Subtract Rational Numbers as Adding the Inverse

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.

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