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How to multiply and divide common fractions.

 This topic is part of the TCS FREE high school mathematics 'How-to Library'. It shows you how to multiply and divide common fractions. (See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Algematics. Click here for instructions.

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### Theory:

When multiplying two common fractions, the procedure is to multiply the numerators and denominators separately and then simplify the resulting fraction.

eg:

To divide a number by a common fraction, you multiply by the reciprocal of the fraction.

eg:

Algematics will multiply or divide two common fractions and then simplify the answer to its lowest terms.

### Method:

The steps below demonstrate how to multiply or divide common fractions showing working.

NOTE: To multiply or divide mixed numbers, first convert to common fractions.

As an example, we will multiply three quarters by six ninths, eg:

#### Step 1  Set display options

Click  to display the ‘Set Colours And Fonts’ Dialog Box.

Make sure that this check box option is not selected:

o Use ¸ signs, eg: 2¸a

and then click  .

#### Step 2  Enter the left hand fraction

Click  and type your expression into the maths box in the data entry box.

If the ‘EMPTY’ message is not displayed between the blue buttons, click the  button until the message: ‘INSERT’ appears.

Use a divide symbol: ‘ / ’ to enter the fraction.
Do not use the ratio ‘ : ’ symbol, or some of the working steps will not be shown.

Maths...

3/4

and then click

#### Step 3  Enter the right hand fraction

Click on the input box and type in the right hand fraction.
Once again, be careful to use a ‘ / ’ in the fraction, like this: 6/9

#### Step 4  Multiply or divide the two fractions

Click  to multiply the two fractions:

OR  click  to divide the two fractions: (This multiplies by the reciprocal.)

#### Step 5  Multiply the numerator and denominator factors

To multiply the numerator and denominator factors separately, click  and then  so that both buttons are down.

Now click the  (simplify) button twice so that both the numerator and denominator are multiplied:

After completing these multiplying steps, click  and  again so that both buttons are now up.

Click the  (simplify) button once more to reduce the answer to its lowest terms:

Go back to step 2 to multiply or divide more common fractions.