What is 9.75 divided by 1.3?

1 Answer
Apr 7, 2018

Answer:

#9.75-:1.3#

#=color(red)(15/2)=color(red)7.5#

Explanation:

The problem is to evaluate

#9.75 -: 1.3#

To do this without a calculator, let's start by expressing each decimal as a fraction.

#9.75#

#=9+7/10+5/100#

#=900/100+70/100+5/100#

#=975/100#

#1.3#

#=1+3/10#

#=10/10+3/10#

#=13/10#

Now we want to divide #975/100# by #13/10#.

To divide two fractions, it is easier to multiply by the reciprocal of the denominator, like so:

#(975/100)/(13/10)=975/100xx10/13=9750/1300#

This is a valid answer, but the fraction is not in its simplest form. It may be difficult to see how to simplify this, but let's try to do it step by step.

First factor out a 10:

#9750/1300=(cancel10*975)/(cancel10*130)#

Now factor a 5:

#975/130=(cancel5*195)/(cancel5*26)#

And finally factor a 13:

#195/26=(cancel13*15)/(cancel13*2)#

#color(red)(15/2=7.5)#

This is our answer in simplest form.