Question

How do you multiply mixed rational numbers like a decimal and a fraction?

Answer 1

See explanation below.

Explanation:

To multiply two rational numbers without a calculator, it is easiest to express them both as fractions, then multiply their numerators and denominators.

For example, if you have

`1.6xx5/9=?`

You can express `1.6` as `8/5`, so it becomes

`8/cancel5xxcancel5/9=8/9=0.88888...`

How did I know that `1.6=8/5`?

Try to see that 1.6 can be expressed as:

`color(red)1.6`

`=1+6/10`

`=10/10+6/10`

`=16/10`

`=(cancel2xx8)/(cancel2xx5)`

`=color(red)(8/5)`

Similarly, if we had a really weird number like 1.234, we can do the same thing:

`color(red)1.234`

`=1+2/10+3/100+4/1000`

`=1000/1000+200/1000+30/1000+4/1000`

`=1234/1000`

`=(cancel2xx617)/(cancel2xx500)`

`=color(red)(617/500)`

Using this method, ANY rational number, by definition, can be expressed as a fraction.

Hope this helps!