# How do you reduce 1.2km : 400 m?

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1
Feb 18, 2017

$1.2 k m : 400 m \to 3 : 1$

#### Explanation:

This is a ratio which if you so chose is permissible to write in fraction FORMAT. Do not confuse this with a fraction

So write $\text{ "1.2km:400m" }$ as $\text{ } \frac{1.2 K m}{400 m}$

Known that 1 km is the same as 1000 m. So we can convert the Km into m so that both values are using the same units of measurement.

"(1.2Km)/(400m)$\equiv$$\frac{1.2 \times 1000}{400}$ in metres

The $\equiv$ means equivalent to

$= \frac{1.2 \times 10 \times \cancel{100}}{4 \times \cancel{100}} = \frac{12}{4} \equiv \frac{12 \div 4}{4 \div 4} = \frac{3}{1}$

Remember that this is a ratio

So 1.2 km : 400 m is the same as 3 : 1

Then teach the underlying concepts
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#### Explanation

Explain in detail...

#### Explanation:

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sjc Share
Feb 14, 2017

$3 : 1$

#### Explanation:

Firstly change the $k m$ to metres.

$1. k m : 400 m : : 1200 m : 400 m$

the units now cancel and can be omitted.

$1200 : 400$

now cancel the numbers by their common factors

$1200 : 400 : : 12 : 4$

$12 : 4 : : 3 : 1$

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