FreeAlgebra                             Tutorials!

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Multiplying and Dividing Fractions

Multiplication of fractions is straightforward, as illustrated by the following.

Example

Evaluate the following products.

Solution

It is simply a matter of multiplying the numerators and denominators.

In each case the common factors have been cancelled to leave the fraction in its lowest form.

Division of fractions is straightforward once we note that division by a fraction of the form a/b is equivalent to multiplication by the fraction b/a. This can be seen in the following example.

Example 5

Write the following as fractions in the usual way.

Solution

(a) First note that

Divide both sides of this equation by (3/4)

(b) The previous result may be used.

where a common factor 4 has been cancelled.

Exercise 3.

Evaluate each of the following in their lowest terms.

(a) Using exercise 2 part (a) we have

where the common factors of 11 and then 2 have been cancelled.

(b) Using the result of exercise 2 part (b) we have

after recalling that division by 1/3 is the same as multiplication by 3/1=3, and cancelling the common factor 3.

(c) From exercise 2 part (c), the numerator is 31/20. The denominator is evaluated below.

Thus

after cancellation of the common factor 20.

(d) In this case, from exercise 2 part (c), the denominator is 13/12. Evaluating the numerator,

after cancelling the common factor 2. Thus

after cancellation of the common factor 3.