How to multiply and divide common fractions.





Part 1

Download the free support file…We have created a Maths Helper Plus document containing the completed example from this topic. You can use this to practice the steps described below, and as a starting point for solving your own problems.

File name: ‘Multiplying and dividing fractions.alg’ File size: 4kb
Click hereto download the file.

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


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


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

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Part 2

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 checkbox option is not selected:

 Use ÷ signs, eg: 2 ÷ a

and then click

Step 2 Enter the data

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

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

Use the ‘ * ’ symbol for multiply, and the ‘ / ’ symbol for divide.



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.

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