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!