## What you need to know

Things to remember:

• We can extend the number line so that we have numbers on the left of 0.
• We can flip a subtraction, and it will change the answer from positive to negative, or negative to positive.

Usually our number line starts at 0 and goes up in 1s like this:

And we can use our number line to help us with subtractions.

What is $5 -4$?

Using our number line we’d start at 5, and count back 4.

So, we can see that $5-4=1$. But, what would happen if we subtracted a bigger number from a smaller number?

What is $3-6$?

So, we can only subtract 3 before we don’t have anywhere to go, so let’s add our negative numbers.

Now that we have negative numbers, we can start counting back again.

So, we can see that $3-6=-3$. Interestingly, $6-3=3$. Let’s compare these.

$$3-6=-3$$

$$6-3=3$$

If we change the order of the subtraction, then we either add or remove the subtraction.

Earlier we saw that $5-4=1$, so $4-5=-1$. Let’s see some more.

$$8-5=3$$

$$5-8=-3$$

$$12-11=1$$

$$11-12=-1$$

$$25-8=17$$

$$8-25=-17$$

## Example Questions

#### Question 1: What is $5-7$?

So, $5-7=-2$.

Alternatively, we can flip it!

$$7-5=2$$

so

$$5-7=-2$$

#### Question 2: What is $3-8$?

So, $3-8=-5$.

Alternatively, we can flip it!

$$8-3=5$$

so

$$3-8=-5$$