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India
Class VI

Add and subtract integers

Lesson

 

Adding using the number line

When we add $5$5 to $2$2 using the number line, we first find $2$2 on the number line, and count five units to the right to arrive at $7$7 like this:

We say "$2$2 plus $5$5 equals $7$7", and write the equation $2+5=7$2+5=7.

 

Subtracting using the number line

When we subtract $5$5 from $2$2 using the number line, we first find $2$2 on the number line, and count five units to the left to arrive at $-3$3 like this:

We say "$2$2 minus $5$5 equals negative $3$3", and write the equation $2-5=-3$25=3

 

Examples

Here are some examples to think about:

Example 1

Evaluate: $6+0$6+0

Think: Adding $0$0 to any number on the number line will not change its value. In mathematics, we call the number $0$0 the identity for addition.

Do: $6+0=6$6+0=6

 
Example 2

Evaluate: $6+4-12$6+412

Think: Adding $4$4 to $6$6 gives a total of $10$10, and then subtracting $12$12 from $10$10 results in the number $-2$2.

Do: $6+4-12=-2$6+412=2

 

Example 3

The absolute value of a number is the distance it is away from $0$0 on the number line. This means for example that the absolute value of $3$3 and $-3$3 are exactly the same. They are both $3$3 units away from $0$0.

We write the absolute value of any number $n$n by surrounding the number with vertical lines, as in $|n|$|n|.

So we have that $|3|=|-3|$|3|=|3| because they are both $3$3 units from $0$0.

In this way, the absolute values of numbers can always be considered positive numbers.

 
Example 4

Evaluate: $8+\left(-2\right)$8+(2)

Think: Sometimes we use brackets when adding or subtracting a negative number.

Adding a negative number to another number is exactly the same as subtracting its absolute value.

Do: This means that $8+\left(-2\right)$8+(2) is exactly the same problem as $8-2$82.

$8-2=6$82=6

You can remember this by thinking that a positive and negative sign sitting together can be replaced by a single negative sign.

So $+-$+ or $-+$+ is exactly the same as $-$.

 
Example 5

Evaluate: $8-\left(-2\right)$8(2)

Think: Subtracting a negative number from another number is exactly the same as adding its absolute value.

Do: This means that $8-\left(-2\right)$8(2) is exactly the same problem as $8+2$8+2.

$8+2=10$8+2=10

You can remember that two negatives make a positive when they sit next to each other.

So $--$ is exactly the same as $+$+

 
Example 6

Evaluate: $-32+63$32+63

Think: The absolute value of $63$63 is larger than the absolute value of $-32$32, that is $\left|63\right|>\left|32\right|$|63|>|32|. This means our answer will be positive. As we are adding two numbers together, we can re-arrange the order: $-32+63=63+\left(-32\right)$32+63=63+(32)

Do: 

$-32+63$32+63 $=$= $63+\left(-32\right)$63+(32)
  $=$= $63-32$6332
  $=$= $31$31
Example 7

Evaluate: $5-(-9)+(-15)+0$5(9)+(15)+0

Think: Subtracting a negative number from another number is exactly the same as adding its absolute value. Adding a negative number is the same as subtracting its absolute value. We can then work from left to right. Adding zero will not change the number.

Do: 

$5-\left(-9\right)+\left(-15\right)+0$5(9)+(15)+0 $=$= $5+\left|-9\right|-\left|-15\right|+0$5+|9||15|+0
  $=$= $5+9-15+0$5+915+0
  $=$= $14-15+0$1415+0
  $=$= $-1+0$1+0
  $=$= $-1$1

More Worked Examples

Question 1

Find the value of $-8+19$8+19.

Question 2

In Moscow last night the temperature fell to $-9$9 °C. By midday today it is forecast to be $16$16 °C.

How much is the temperature expected to rise by?

Question 3

Evaluate $-8+8$8+8.

Question 4

The next train to Timbuktu is scheduled to be in $52$52 minutes, however there is a $34$34 minute delay. After $23$23 minutes pass, how long will it be before the train departs?

 

Outcomes

6.NS.NMI.2

Identification of integers on the number line, operation of addition and subtraction of integers, showing the operations on the number line (addition of negative integer reduces the value of the number) comparison of integers, ordering of integers.

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