3.2 Add integers  (Page 2/4)

Now let’s see what happens when the signs are different.

Model: $\mathrm{-5}+3.$

Solution

Interpret the expression.	$\mathrm{-5}+3$ means the sum of $\mathrm{-5}$ and $3$ .
Model the first number. Start with 5 negatives.
Model the second number. Add 3 positives.
Remove any neutral pairs.
Count the result.
The sum of −5 and 3 is −2.	$\mathrm{-5}+3=\mathrm{-2}$

Notice that there were more negatives than positives, so the result is negative.

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Model: $5+\left(\mathrm{-3}\right).$

Solution

Interpret the expression.	$5+\left(\mathrm{-3}\right)$ means the sum of $5$ and $\mathrm{-3}$ .
Model the first number. Start with 5 positives.
Model the second number. Add 3 negatives.
Remove any neutral pairs.
Count the result.
The sum of 5 and −3 is 2.	$5+\left(\mathrm{-3}\right)=2$

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Modeling addition of positive and negative integers

Model each addition.

1. ⓐ 4 + 2
2. ⓑ −3 + 6
3. ⓒ 4 + (−5)
4. ⓓ -2 + (−3)

ⓐ
	$4+2$
Start with 4 positives.
Add two positives.
How many do you have?	$6$ $4+2=6$

ⓑ
	$-3+6$
Start with 3 negatives.
Add 6 positives.
Remove neutral pairs.
How many are left?
	$3\mathrm{-3}+6=3$

ⓒ
	$4+(\mathrm{-5})$
Start with 4 negatives.
Add 5 negatives.
Remove neutral pairs.
How many are left?
	$\mathrm{-1}4+(\mathrm{-5})=\mathrm{-1}$

ⓓ
	$\mathrm{-2}+(\mathrm{-3})$
Start with 2 negatives.
Add 3 negatives.
How many do you have?	$\mathrm{-5}\mathrm{-2}+(\mathrm{-3})=\mathrm{-5}$

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Model each addition.

1. ⓐ 3 + 4
2. ⓑ −1 + 4
3. ⓒ 4 + (−6)
4. ⓓ−2 + (−2)

1. ⓐ
   
2. ⓑ
   
   
3. ⓒ
   
   
4. ⓓ
   

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1. ⓐ 5 + 1
2. ⓑ −3 + 7
3. ⓒ 2 + (−8)
4. ⓓ −3 + (−4)

1. ⓐ
   
   
2. ⓑ
   
   
3. ⓒ
   
   
4. ⓓ
   

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Simplify expressions with integers

Now that you have modeled adding small positive and negative integers, you can visualize the model in your mind to simplify expressions    with any integers.

For example, if you want to add $37+\left(\mathrm{-53}\right),$ you don’t have to count out $37$ blue counters and $53$ red counters.

Picture $37$ blue counters with $53$ red counters lined up underneath. Since there would be more negative counters than positive counters, the sum would be negative. Because $53\mathrm{-37}=16,$ there are $16$ more negative counters.

Let’s try another one. We’ll add $\mathrm{-74}+\left(\mathrm{-27}\right).$ Imagine $74$ red counters and $27$ more red counters, so we have $101$ red counters all together. This means the sum is $\text{−101.}$