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

1 Answer
Apr 1, 2018

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!