MAP4C - Converting between imperial and metric units

In the first example, you're going from 3 inches to mm.

\(3\ in.\ \rightarrow \ mm\)

There isn't a way to predict whether you end up multiplying or dividing, as each conversion is unique. So let's see why we did what we did. Notice that the conversion ratio is 1 inch = 25.4 mm.

As I pointed out in the video, every conversion ratio can be written either in two ways:

\(\frac{1\ in.}{25.4\ mm}\) OR \(\frac{25.4\ mm}{1\ in.}\)

We've got to choose the correct version. Notice that in \(\frac{25.4\ mm}{1\ in.}\), the inches unit is at the bottom. We want this because it will cancel out with the inches unit in 3 in. when we multiply. The unit we want (mm) needs to be in the top position.

\(3\ in.\times \frac{25.4\ mm}{1\ in.}\)

If it makes you feel comfortable, you can place a 1 under the 3 in. to make it into a fraction...

\(\require{cancel} \frac{3\ in.}{1}\times \frac{25.4\ mm}{1\ in.} \Rightarrow \frac{3 \cancel{in.} \times 25.4\ mm}{1 \cancel{in.}} = 76.2\ mm\)

In the second example, 8.9 km to miles, we look at the conversion ratio 1 miles = 1.609 km. Again, every conversion ratio can be written either in two ways:

\(\frac{1\ mile}{1.609\ km}\) OR \(\frac{1.609\ km}{1\ mile}\)

Next we multiply 8.9 km by one of these. Which one? Look for the one with kilometers at the bottom, so:

\(8.9\ km\times \frac{1\ mile}{1.609\ km}\)

This can be written as:

\(\frac{8.9\ km}{1}\times \frac{1\ mile}{1.609 \ km}\Rightarrow \frac{8.9\ \cancel{km}\times 1\ mile}{1.609 \cancel{km}}\)

As you can see, to evaluate the fraction on the right, we need to multiply 8.9 by 1, then divide by 1.609. This will eventually cancel out the km units, leaving you with miles (the unit at the top). Therefore, we divide here by there's a number other than 1 in the denominator of the conversion factor.

Does that help?

It kinda does but not really. I’ll just keep practicing thank-you.

I think maybe why you don't understand it fully is because you forgot how to multiply fractions?

To multiply fractions:

\(\frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}\)

Reread my response above in light of this new revelations.

Good luck