Comparing fractions
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How to compare fractions with one another.

This topic is part of the TCS FREE high school mathematics 'How-to Library'. It shows you how to compare fractions with one another.
(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 Maths Helper Plus software. Click here for instructions.

Theory:

There are many ways of writing the same fraction. For example, each of these values is the same:

0.75 is a decimal fraction, 3/4 is a common fraction, while 6/8 is an equivalent common fraction no reduced to its lowest terms.

Fractions such as:  4/3 which have a numerator (top number) bigger than the denominator (bottom number) are called 'improper'. Commonly, improper fractions are written as 'mixed numbers'. Converting 4/3 to a mixed number we have:

and where:

Because there are so many different ways of writing fractions, it can be quite difficult to compare fractions in their different forms. For example, put the following numbers in ascending order, (from smallest to greatest):

2/3,   7/8,   3/4,   0.7,  13/10

The solution is to convert the fractions to the same form, then they can be easily compared.

Often it is easiest to convert all of the fractions to decimal fractions:

2/3  =  2.0 3 = 0.66666...

7/8  =  0.875

3/4  =  3.0 4 = 0.75

0.7

13/10  =  1 + (3.0 10) =  1.3

These numbers can now be easily compared and put into ascending order, like this...

smallest  2/3,   0.7,  3/4,   7/8,   13/10  greatest

Method:

Maths Helper Plus can convert a group of fractions to decimal form, and display the results graphically on a number line. This makes comparing different types of fractions very easy.

The diagram below shows how Maths Helper Plus displays the five fractions from the 'Theory' section above:

Step 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:  'Number Line 1.mhp'   File size: 11kb
Click here to download the file.

If you choose 'Open this file from its current location', then Maths Helper Plus should open the document immediately. If not, try the other option: 'Save this file to disk', then run Maths Helper Plus and choose the 'Open' command from the 'File' menu. Locate the saved file and open it. If you do not yet have Maths Helper Plus installed on your computer, click here for instructions.

 

Step 2  Display the parameters box and enter values

Press the F5 key to display the parameters box:

 

Click on the edit boxes of the parameters box to enter up to five different fractions. Use the formats described in this table:

 

Fraction Type Example Enter like this:
decimal fraction 0.7 0.7
common fraction 3/4
mixed number 1 + 1/3

 

When you have entered your fractions, click the 'Update' button on the parameters box to refresh the display. Your fractions will all be displayed in decimal form so that they can easily be compared.

 

Step 3  Adjust the number line scale and position

If the number line in Maths Helper Plus displays all of the numbers you have entered, then you are finished, otherwise:

 

1. If the number line is too short to display all of the numbers you entered, hold down a 'Ctrl' key and briefly press the left arrow key. Repeat until all numbers are displayed.

(To undo this operation: Ctrl+right arrow.)

 

2. If the numbers entered are very close together, spread them out by holding down a 'Ctrl' key and briefly pressing the right arrow key.

(To undo this operation: Ctrl+left arrow.)

 

3. To move the number line left or right without changing the spread of numbers, hold down 'Ctrl' and 'Shift' while you press the left or right arrow keys.

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