area
equations
FRACTIONS
fractions
probability

In a fraction you will find a numerator and a denominator.


In this module we will study:

# MULTIPLICATION AND DIVISION OF FRACTIONS

When we multiply fractions, we multiply the numerators individually and the denominators individually.

When we divide a number with a fraction, we multiply the number with the reverse fraction.

 

Let us solve an exercise where two fractions are multiplied:

Let us multiply these fractions:

We multiply the numerators individually and the denominators individually:
Continue:
We simplify the fraction.

 

Let us solve an exercise where two fractions are divided:
Let us divide these fractions:

First we reverse the second fraction. Then we can multiply these fractions:
Let us continue:
We can simplify the fraction:

 

Try some of these tasks:
answer
answer
answer
answer

 



# CONTRACTION OF FRACTIONS

We can only contract fractions when all of the fractions have the same denominator (Common denominator, look below)

If the fractions do not have the same denominator we have to make sure that they do.

This is done in the following fashion:

  • First you find the common denominator
  • Then you expand all of the fractions in a way that makes them have a common denominator.
  • The fractions are converted into one fraction.
  • Contract the terms in the numerator.
  • Simplify the answer if possible.
  • Here is an example on how to attack tasks where fractions are contracted:

    The fractions do not have a common denominator. 12 is the common denominator.
    You expand all of the fractions in a way that makes them have a common denominator.

    The fractions are converted into one fraction. Then you can contract the terms in the numerator. 

    The answer is
    We can simplify the answer. Similar factors in the numerator and the denominator can be abbreviated (if possible).

      

    Try to contract these fractions:
    answer
    answer
    answer


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