Understanding Fractions: Comparing Sizes

Question

Compare the following fractions and identify the largest ones: 3/8,5/12,1/2, 7/16. Explain your reasoning.

Answer 1

The fractions are : 3/8, 5/12, 1/2, and 7/16.

Probably the easiest way to compare is to convert all to have the same denominator, then examine the new numerators.

The least common denominator for 8, 12, 2, and 16 can be determined by thinking of them as having prime factors.

8 = 2(2)(2)

12 = 2(2)(3)

2 = 2

16 = 2(2)(2)(2)

So the LCD (or LCM) must contains prime factors of 2 and 3. There must be four factors of 2 (because 16 contains four 2's) and one factor of 3 (12 is the only denominator with that factor).

So, the LCM is 2(2)(2)(2)(3) = 48.

Convert 3/8 to 18/48 by multiplying numerator and denominator by 6.

Convert 5/12 to 20/48 by multiplying numerator and denominator by 4.

Convert 1/2 to 24/48 by multiplying top and bottom by 24.

Convert 7/16 to 21/48 by multiplying by 3.

So in order from largest to smallest is: 1/2, 7/16, 5/12, 3/8.

Another technique that could be used is to convert each fraction to decimal form. Check it out here:

desmos.com/calculator/wc0jvcpv3e

Answer 2

The fractions are : 3/8, 5/12, 1/2, and 7/16.

One sure way to compare is to convert fractions to have the same denominator.

However, if time is of the essence as during an SAT, PSAT, GRE or GED test, there is a quicker way:

Notice that all fractions are one half or less. We know this since numerators are less than or equal to half their corrresponding denominators.

Only 1/2 has a numerator equal to half its denominator. So it is the largest.

All other fractions have numerators one less than half their denominator.

So 3/8 is 1/8th less than 1/2, 5/12 is 1/12th less than 1/2, and 7/16 is 1/16 less than 1/2.

Thus, larget to smallest is 1/2, 7/16, 5/12 and 3/8.