 What you need to know

Things to remember:

• As an approximation, 1 mile = 1.6km
• To turn miles into kilometres we divide by 5 and multiply by 8.
• To turn kilometres into miles we divide by 8 and multiply by 5.

How big is big is a km in m?

1km = 1000m

How big is a mile in m?

1 mile = 1600m

How can we find a relationship between km and miles? Well, we can make the metres the same. It is easiest to turn 1000m into 1600m, than 1600m into 1000m.

1km = 1000m

$$1000\times1.6=1600$$

$$1\times1.6=1.6$$

1.6km = 1600m

This gives us the following relationship between miles and km:

1 mile = 1.6km

So, how does this help us with our conversion? Well, how do we turn 1 into 1.6? We multiply by 1.6. So, we get this:

$$\text{miles to km} \rightarrow \times1.6$$

What is 3 miles in km?

$$3\times1.6=4.8$$

3 miles = 4.8km

Now that we have two different miles, we can actually use them to make a new one.

What is 4 miles in km?

4 miles = 3 miles + 1 mile

4 miles = 4.8km + 1.6km

4 miles = 6.4km

But, a neat trick is that we can use is turn our original decimal into a fraction.

$$1mile=\frac{8}{5}km$$

So really, when we are turning miles into km we are finding $\frac{8}{5}$ of it. But, we know how to find fraction amounts of something. We do it in two steps.

What is 25 miles in km?

We are trying to find $\dfrac{8}{5}$ of 25.

Step 1: Divide the miles by 5.

$$25\div5=5$$

Step 2: Multiply by 8.

$$5\times8=40$$

25miles = 40km

So, now we know how to turn miles into km, let’s look at how we get from km to miles.

Turning our miles into km we multiplied by $\frac{8}{5}$, so this time we need to do the opposite. To turn km into miles, we have to divide by $\frac{8}{5}$. Remember, though when we divide by a fraction, we flip it and turn it into a multiplication!

$$\div\frac{8}{5}\rightarrow\times\frac{5}{8}$$

But, again, we know how to multiply by a fraction, so we can turn km into miles with two steps as well.

What is 120km in miles?

Step 1: Divide by 8

$$120\div8=15$$

Step 2: Multiply by 5

$$15\times5=75$$

120km = 75 miles

Example Questions

Step 1: Divide the miles by 5.

$$35\div5=7$$

Step 2: Multiply by 8.

$$7\times8=56$$

35miles = 56km

Step 1: Divide by 8

$$72\div8=9$$

Step 2: Multiply by 5

$$9\times5=45$$

72km = 45 miles