Now that we have had some practice representing the values of fractions, we need to look at how their values compare to one another. The following activity will ask you to create images that represent the values of two fractions and then to determine a fraction whose value lies between the two that were given.

This activity might not be viewable on your mobile device.Interactive exercise. Assistance may be required. Click on the image below to access the activity. You will divide the square into equal-sized pieces and then click to shade the part of the square that is the same as the fraction shown.

Instructions

  1. Use the +Col, -Col, +Row, and –Row buttons to divide the square into the same number of equal-sized pieces as the denominator of the fraction (or a simpler equivalent fraction).

  2. Click to shade the same number of these pieces as the numerator of the fraction.

  3. Click the check button to see if you have correctly represented the fraction. When you have correctly created pictures for each fraction, a third box will appear.

  4. Use the buttons to create an image that represents a fraction that falls between the red and blue fractions.

  5. When you click the 'Check' button, a space will appear for you to type in the value of the fraction you created.

On a piece of paper, fill in the following table:
Red Fraction Picture Blue Fraction Picture Green Fraction Picture
           
           
           
           
           

Interactive exercise. Assistance may be required. Based on what you have learned, drag the following fractions to the correct locations on the number line:

When you are able to make a good sketch of a fraction, you can use this method to compare fractions. Fractions like halves, thirds, fourths, eighths, etc. are relatively easy to model with a picture. This may not always be the case. If the fractions that you are comparing are difficult to model with a drawing, you may want to use a calculator to convert them to decimals and then use the number line like in section 2. To convert a fraction into a decimal, divide the numerator by the denominator.

Use a calculator to complete the following table in your notes.

Fraction
1 2
- 15 8
5 7
15 6
- 5 4
- 2 3
Decimal

Check Your Answer
Fraction
1 2
- 15 8
5 7
15 6
- 5 4
- 2 3
Decimal
0.5
-1.875
0.714
(rounded)
2.5
-1.25
-0.667
(rounded)
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Interactive exercise. Assistance may be required.