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...
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Adding and Subtracting Integers
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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.
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Adding and Subtracting Integers
At the centre of the number line is the integer zero.
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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.
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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.
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Adding and Subtracting Integers
Example: 1 + 3 = ?
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.
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.
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).
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).
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
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
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
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
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
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
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Adding and Subtracting Integers
Example: 1 + 3 = 4
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Adding and Subtracting Integers
Example: 1 - 3 = ?
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Adding and Subtracting Integers
Example: 1 - 3 = ?
We will start at +1 again as this is the
first part of our sum
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
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
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
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
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
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
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
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Adding and Subtracting Integers
Example: 1 - 3 = ?
-3
We end up at negative two.
So… 1 – 3 = -2
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Adding and Subtracting Integers
Example: 1 - 3 = -2
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Adding and Subtracting Integers
What about: -4 - 3 = ?
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Adding and Subtracting Integers
What about: -4 - 3 = ?
We will start at negative four on the
number line
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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
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
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 = ?
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 = ?
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 = ?
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 = ?
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 = ?
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…
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
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Adding and Subtracting Integers
Finally, what do these mean?
5 + -2 ?
5 - -2 ?
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
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 ?
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
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
THE END