INSTRUCTIONS

When Compare Fractions starts,  you will be given two fractions to compare, as in the example below:

You are to choose which of the two fractions is the larger.

Keep this in mind as you make your choice - the larger the numerator the larger the fraction and the larger the denominator the smaller the fraction. If the denominators are the same, the fraction with the larger numerator is larger and if the numerators are the same, the fraction with the larger denominator is smaller.

One method is to visualize the fractions as pictured below in red:

As you can see 2/5 is less than half the circle while 1/2 is half the circle - so 1/2 is larger.

Here, we will introduce the idea of the least common denominator or LCD.  LCD is an idea that will be used in comparing fractions, and in adding and subtracting fractions. The LCD is the smallest number that both 5 and 2 will divide into evenly. Ten is the LCD for the fractions 2/5 and 1/2 because both denominators 5 and 2 divide evenly into 10. 

Once the LCD is found, each fraction is written with  the LCD. As you can see by the illustration, 2/5 is equal to 4/10 and 1/2 is equal to 5/10. Once each fraction is renamed with a common denominator, you only have to compare the numerators - the larger the numerator the larger the fraction.

See the program  RENAME IN HIGHER TERMS for more information on renaming fractions.

One way to determine the LCD is to see if the smaller denominator 2 will divide evenly into the larger denominator 5.  If not, then multiply the larger denominator by 2 to get 10.  Will the smaller denominator 5 divide into 10? Yes, so 10 is the LCD. If not, multiply the larger denominator by 3, then 4, etc. until the smaller denominator divides into the product.

Another method is to multiply the two denominators and then divide that product by the greatest common factor(GCF) of the two denominators. The greatest common factor is the largest number that will divide evenly into the two denominators. In the example above the GCF of 5 and 2 is 1.  The product of 5 and 2 is 10. Divide 10 by 1 and you get 10 for the LCD.

Choose the < (less than) button if you think the first fraction is smaller than the second, or > (greater than) if you think the fraction is larger. If correct, circles showing the comparative sizes of the two fractions will appear.  The dotted lines in the circles will show the two fractions with the LCD.