Math Skills: Fractions

Lesson 4: Lesson Four--Finding Least Common Denominator, Comparing and Ordering Fractions

Section Two: Comparing and Ordering fractions

Now you are ready to compare and order fractions, because the surest way to do this with any set of fractions is to determine what their common denominator is. REMEMBER, YOU CANNOT COMPARE OR ORDER FRACTIONS JUST BY LOOKING AT THE NUMERICAL ORDER OF DENOMINATORS!

Remember that pre-test problem, "Which is larger, 5/16 or 1/3?"

If you said 5/16 was larger, it was because you thought since 16 is larger than 3, then 5/16 must be larger than 1/3 (especially since 5 is bigger than 1!). But it turned out that 1/3 was larger.

If you drew two circles, divided one into 16 parts and colored 5 of those, and divided the other circle into 3 parts and shaded 1 of them, you could easily see (assuming you made each part of equal size) that 1/3 was bigger than 5/16, but since we are working with a keyboard and not a sketch pad, this is harder to show than just working it out, and it can be worked out only by finding the lowest common denominator to 'easily see' which is bigger.

Since 16 and 3 are relatively prime to each other, you can use the LCD of 16 x 3 = 48.

5x3/16x3 = 15/48 and 1x16/3x16 = 16/48. Since the numerator of the second fraction is bigger, then 1/3 is bigger than 5/16. NO GUESSWORK INVOLVED!

So, to find which of two or more fractions is larger (or smaller for that matter), turn the fractions into fractions with a common denominator, then judge by their numerators which is bigger (or smaller).

You do basically the same thing--find the lowest common denominator of the set of fractions--to put the fractions in order.

Let's look at Example 2 of Page 100 of Cambridge GED:

Arrange the following in order from least to greatest: 13/20; 3/5; 3/4

What's the LCD? 20 (20, 4, 5 have an LCM of 20). So we have

13/20, 3/5 which is 12/20, and 3/4 which is 15/20. So from least to greatest, we have:

3/5, then 13/20, then 3/4.

Could you tell just by looking at the three fractions given which was the lowest? Believe me, I couldn't!

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