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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.)Â 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:Â Â Â Â Â Â Â

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

eg: Â Â Â Â Â Â

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.Â

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

#### Step 1Â  Set display options

Click Â 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 Â .

#### Step 2Â  Enter the left hand fraction

Click Â 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 Â 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.

Â Â Â Â Â Â  Maths...

Â  Â 3/4

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and then click

#### Step 3Â  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

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#### Step 4Â  Multiply or divide the two fractionsÂ Â Â Â Â Â Â

Click Â to multiply the two fractions:Â

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

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

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

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

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

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

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