 Add and Subtract Three Integers | KS3 Maths Resources

## What you need to know

Things to remember:

• Addition and subtraction can be done in any order (this is called the commutative law)
• When you subtract a negative, it is the same as adding the number part.
• Because the order of additions doesn’t matter, we can just add and subtract going from left to right.

Consider the following:

$$5+2=7$$

$$2+5 = 7$$

$$12-4=8$$

$$-4+12=8$$

Looking at these, we can see that the order we add and subtract doesn’t matter. This is called the “commutative law”. This is true for any number of additions and subtractions.

$$2-4+5=3$$

$$5-4+2=3$$

$$-4+2+5=3$$

$$5+2-4=3$$

We need to remember two key points:

• Adding a negative number is the same as subtracting.
• Subtracting a negative number is the same as adding.

$$5+-2=5-3=3$$

$$5 - -2= 5+2 = 7$$

These points work for any number of additions and subtractions, but we will focus on when we have three. We can do these in two steps.

Find the value of $12- - 13-6$

Step 1: Change the double negatives into additions.

$$12 - - 13 -6 = 12 + 13 -6$$

Step 2: Do the additions and subtractions starting on the left.

$$12 + 13 -6=25-6=19$$

Find the value of $-4 -9 --17$

Step 1: Change the double negatives into additions.

$$-4 -9 --25 = -4-9+17$$

Step 2: Do the additions and subtractions starting on the left.

$$-4-9+17=-13+17=4$$

## Example Questions

Step 1: Change the double negatives into additions.

$$- -7 +3-2=+7+3-2=7+3-2$$

Step 2: Do the additions and subtractions starting on the left.

$$7+3-2=10-2=8$$

Step 1: Change the double negatives into additions.

$$- -11- -15 - -9=+11+15+9=11+15+9$$

Step 2: Do the additions and subtractions starting on the left.

$$11+15+9=26+9=35$$

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