Fraction Multiplication

Multiplication of Fractions

Example: A recipe calls for   cup of flour. If you are making only the recipe, how much flour do you use? 

We can draw a diagram to work this problem, but it will take us several steps to work it out.

We begin with a rectangle as our whole to represent a full cup of flour.

Then to represent  of a cup of flour we divide the rectangle into 4 equal pieces and shade 3 of them. The shaded part is of the whole.

So how do we take half of this shaded part of the rectangle when there are 3 shaded parts?

One way would be to split the rectangle in half horizontally. Notice that we still have the same part of the rectangle shaded, but it is now divided into eighths.

Finally, since we want one-half of the partial cup of flour, we choose half of the shaded boxes. This leaves of the rectangle shaded.  

We conclude that of is .

A Word of Caution

It is important to notice that in this problem we have taken half of and have not divided by. Remember that of is usually translated as multiplication. What we have computed is .

Rule for Multiplying Fractions

A more efficient way of multiplying two fractions is to realize that , that is, we can multiply the numerators to get the numerator of the product and we can multiply the denominators to get the denominator of the product. Even better, if we remove all the common factors from the numerator and denominator before we multiply; our final answer will be in simplest form. That is, we can simplify by dividing common factors where for any common factor one is divided from the numerator and one is divided from the denominator.

Example: Evaluate .

 

Example: Evaluate .

 

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