Arithmetic Operations with Numerical Fractions

In technical applications, calculations are usually done with decimal numbers directly. So, if we need to find a sum such as

we simply use a calculator

(or the equivalent keystrokes on your own calculator), and we get the answer 0.91666666, which we can then round-off appropriately. Obviously, we are getting an approximate answer, since rounding-off must be done. Often, such a procedure is quite adequate for the problem being solved.

However, sometimes it is necessary to carry out the arithmetic with fractions so that the result is an exact answer, often expressed as a fraction in simplest form. In such instances, you can use your calculator to check that your answer is not seriously in error, but you need to do the arithmetic directly with the fractions.

In the next few notes in this series, we demonstrate how to do basic arithmetic with numerical fractions as fractions. So, for example, instead of the decimal answer obtained above, we will be able to find that

exactly.

The methods described here will also be a useful starting point later for understanding how to add, subtract, multiply and divide when algebraic fractions are involved.