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Adding and Subtracting Integers
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0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

Dec 31, 2015

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Page 1: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

Adding and Subtracting Integers

Page 2: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

When we add or subtract integers we can use a number line to help us see what is happening

with the numbers.

Page 3: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

At the centre of the number line is the integer zero.

Page 4: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

The positive numbers are to the right along the number line.

When we add integers we move “up” in this direction.

Page 5: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

The negative numbers are to the left along the number line.

When we subtract integers we move “down” in this direction.

Page 6: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 + 3 = ?

Page 7: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 + 3 = ?Let’s start at the first integer in our sum, that is, positive one.

Page 8: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 + 3 = ?Let’s start at the first integer in our sum, that is, positive one.

Page 9: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 + 3 = ?Let’s start at the first integer in our sum, that is, positive one.We are going to add +3 so we need to move 3 places up (to theRight on our number line).

Page 10: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 + 3 = ?Let’s start at the first integer in our sum, that is, positive one.We are going to add +3 so we need to move 3 places up (to theRight on our number line).

Page 11: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 + 3 = ?Let’s start at the first integer in our sum, that is, positive one.We are going to add +3 so we need to move 3 places up (to theRight on our number line).

+1

Page 12: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 + 3 = ?Let’s start at the first integer in our sum, that is, positive one.We are going to add +3 so we need to move 3 places up (to theRight on our number line).

+2

Page 13: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 + 3 = ?Let’s start at the first integer in our sum, that is, positive one.We are going to add +3 so we need to move 3 places up (to theRight on our number line).

+2

Page 14: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 + 3 = ?Let’s start at the first integer in our sum, that is, positive one.We are going to add +3 so we need to move 3 places up (to theRight on our number line).

+2

Page 15: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 + 3 = ?Let’s start at the first integer in our sum, that is, positive one.We are going to add +3 so we need to move 3 places up (to theRight on our number line).

+3

Page 16: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 + 3 = ?Let’s start at the first integer in our sum, that is, positive one.We are going to add +3 so we need to move 3 places up (to theRight on our number line).

+3

We end up at the value 4.

So… 1 + 3 = 4

Page 17: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 + 3 = 4

Page 18: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 - 3 = ?

Page 19: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 - 3 = ?

We will start at +1 again as this is the

first part of our sum

Page 20: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 - 3 = ?

This time we are subtracting 3 so we

will move “down” (to the left) on our

number line

Page 21: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 - 3 = ?

This time we are subtracting 3 so we

will move “down” (to the left) on our

number line

Page 22: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 - 3 = ?

This time we are subtracting 3 so we

will move “down” (to the left) on our

number line

-1

Page 23: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 - 3 = ?

This time we are subtracting 3 so we

will move “down” (to the left) on our

number line

-1

Page 24: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 - 3 = ?

This time we are subtracting 3 so we

will move “down” (to the left) on our

number line

-2

Page 25: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 - 3 = ?

This time we are subtracting 3 so we

will move “down” (to the left) on our

number line

-2

Page 26: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 - 3 = ?

This time we are subtracting 3 so we

will move “down” (to the left) on our

number line

-3

Page 27: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 - 3 = ?

-3

We end up at negative two.

So… 1 – 3 = -2

Page 28: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Example: 1 - 3 = -2

Page 29: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

What about: -4 - 3 = ?

Page 30: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

What about: -4 - 3 = ?

We will start at negative four on the

number line

Page 31: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

What about: -4 - 3 = ?

We are subtracting 3 so we will move

“down” (to the left) on our number line by

3 units

Page 32: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

What about: -4 - 3 = ?

We are subtracting 3 so we will move

“down” (to the left) on our number line by

3 units

Page 33: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

What about: -4 - 3 = ?

Page 34: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

What about: -4 - 3 = ?

Page 35: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

What about: -4 - 3 = ?

Page 36: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

What about: -4 - 3 = ?

Page 37: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

What about: -4 - 3 = ?

Page 38: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

What about: -4 - 3 = ?

We end up at negative seven, so…

Page 39: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

What about: -4 - 3 = -7

Page 40: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Finally, what do these mean?

5 + -2 ?

5 - -2 ?

Page 41: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Finally, what do these mean?

5 + -2 ?

5 - -2 ? A plus and minus together means the same as subtract. So replace them

with a minus sign

Page 42: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Finally, what do these mean?

5 + -2 is the same as 5 - 2

5 - -2 ?

Page 43: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Finally, what do these mean?

5 + -2 is the same as 5 - 2

5 - -2 ?Two minus signs together means the same as add. So replace them with a

plus sign

Page 44: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

0 1 2 3 4 5 6 7 8 9 10-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Adding and Subtracting Integers

Finally, what do these mean?

5 + -2 is the same as 5 - 2

5 - -2 is the same as 5 + 2

Page 45: 0 12345678910-10-9-8-7-6-5-4-3-2 When we add or subtract integers we can use a number line to help us see what is happening with the numbers.

THE END


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