Adding and Subtracting Rational Numbers on a Number Line

by Salma Musa

Adding & Subtracting Rational numbers

Open Ended

What do you remember about Adding Rational Numbers from last lesson? (HINT: Look through your notes

​Additive Inverse (Adding the Opposite)

When you add the opposite of a number - the same number with the opposite sign - this will neutralise the number. ​The easy way to find this is to ask yourself: what will get me to zero?

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​You can use a number line to show the addition of additive inverses.

This number line shows 3 + (–3). Start at 3, move left 3 units, and arrive at 0.

Multiple Choice

What is the opposite of:

18.5

• 18.5

• 16

• -18.5

• -17

Multiple Choice

Bilal answered one question incorrectly on a test and lost 3 points, but then he earned 3 points on an extra-credit question.

• Additive Inverse

• Not Additive Inverse

​ADDING on a Number Line

​When you use a number line to add two numbers, start at the first number. If you add a positive number, move that many units to the right to arrive at the sum.

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​​If you add a negative number, move that many step to the left.

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The steps to adding on a number line:

• Identify the starting point.

• Identify the direction.

• Identify the distance.

• Identify the sum.

​Starting point

​Sum

​Distance

Multiple Choice

Which equation does this number line show?

• 2 + 4 = 6

• 6 + 2 = 4

• 4 + (-6) = 2

• 6 + (-4) = 2

Multiple Choice

Select the number line that shows 3 + (–7) = –4

​Absolute Value

​The distance between two numbers on a number line is ALWAYS positive.

The absolute value of a number is its distance from 0 on a number line. Its value is always positive.

• The absolute value of 8 is written as |8|. Its value is 8.

• The absolute value of –8 is written as |–8|. Its value is also 8.

Absolute value is always either 0 or POSITIVE, because it represents a DISTANCE.

Multiple Choice

What is the value of ∣-158∣?

• 158

• -158

Subtraction as Addition of the Additive Inverse​

​One way to subtract a number from another is to add its additive inverse. In other words, you can subtract a number by adding its opposite.

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Be careful of signs!

If no sign appears with a number, the number is positive. Because 0 is neither positive nor negative, it should never have a sign.​

Multiple Choice

Rewrite 13 – (–4) as an addition problem

• 13 - (+4)

• 13 + (-4)

• 13 + 4

​Use a number line to subtract rational numbers

​Subtracting a negative is the same thing as adding a positive. Move right on a number line to add.

​Let's get back to Absolute Value...

​The distance between any two numbers on the number line is the absolute value of their difference.

​Find the distance between –2 and 5.

​Find the difference of –2 and 5. The subtraction problem is –2 – 5.

Start at –2 on the number line and move left 5 units.

–2 – 5 = –7

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The difference is –7. The distance between –2 and 5 is |–7| = 7.

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