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Year 7

Adding and subtracting signed integers

Use direction on a number line to reason about positive and negative numbers.

Try five questionsNo account needed

The idea

On a number line, values increase to the right and decrease to the left. Adding a positive number moves right; adding a negative number moves left. Subtracting a number has the same effect as adding its opposite.

Before you begin: Order integers on a number line and recognise zero.

Worked example

Start at negative three and add five.

−3+5
5 steps to the right−4−3−2−101234StartFinish
Adding 5 moves five spaces right: start at −3 and finish at 2.
Step 1

Begin at −3. Adding positive five moves five units right: three to reach zero, then two more.

−3+3=0,
0+2=2
Step 2

Three of the steps take you to zero, leaving two steps to the right.

−3+5=2
Step 3

Subtracting negative five would produce the same movement, because its opposite is positive five.

−3−(−5)=−3+5=2

A mistake to avoid

A negative sign can describe a number or indicate subtraction. Read the whole expression before deciding which direction to move.

Your turn.

Calculate the result using the opposite of the subtracted number.

4−(−2)
Show the solution
4−(−2)=4+2=6

Subtracting negative two is equivalent to adding positive two, so move two units right from four.

Put it into practice.

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