Question

A car travelled `213` miles on `14 2/10` gallon of gas. How many miles per gallon did it get?

Answer 1

`15` miles per gallon

Explanation:

To figure out how many miles per gallon the car got, divide the number of miles by the number of gallons:

`"miles" -:"gallons" = "miles per gallon"`

Now substitute the values given in the problem into that equation:

`213 -: 14 2/10 = "miles per gallon"`

Now turn `2/10` into a decimal. It would be `0.2`, so put `14color(blue).2` in:

`213 -: 14.2`

Use a calculator or long division to divide:

`213 -: 14.2 = 15`

So the car got `15` miles per gallon.

Answer 2

The method used in the other two solutions would be based on this approach.

`color(blue)("For 1 gallon the miles travelled is 15.")`

Explanation:

The units of measurement required are

miles per gallon `->("miles")/("gallons")` so I am going to use this format. In other words; ratio in fraction format.

`("miles")/("gallons") -> 213/14.2`

But we need miles for 1 gallon so we need to change the `14.2` into 1. We do this by dividing it by itself.

For multiply or divide, what we do to the bottom we also do to the top.

`color(green)(("miles")/("gallons") -> 213/14.2 -> (color(red)(213-:14.2))/(14.2-:14.2) = color(red)(15)/1)`

Now you can see where the other methods come from: `color(red)(213-:14.2)`

`color(blue)("So for 1 gallon the miles travelled is 15.")`

In the UK this is a very high consumption and I would get rid of that car. Replacing it with a more economical one.