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

Fill in the Blanks

What is the opposite of:

-4/3

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

Fill in the Blanks

Use the number line to find the sum of 1.5 + (–5)

​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

Fill in the Blanks

What is the value of ∣40∣?

Fill in the Blanks

What is the value of ∣-25.3∣

Fill in the Blanks

Musa has just moved into a new area. The local masjid is 400 metres from his home. However, on his first day to the masjid he ended up walking 100 metres in the opposite direction first before he turned around towards the correct direction. What was the distance he travelled? ( Write your answer as

m)

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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