Comparing Fractions

Comparing fractions is a skill kids acquire at quite a young age - long before they know anything about math!

Try cutting two very unequal sizes of birthday cake at a preschoolers birthday party and wait for the immediate, "That's not a fair share!" from one of the little guests!

Kids can 'visually' see the difference. Then their journey starts, taking on a mathematical meaning in Kindergarten and First Grade, when the anchor fraction of 1/2 is studied and understood. Then we move on to more of the common fractions such as 1/4's, 1/3's. 1/5's, 1/6's, 1/8's and 1/12's and of course the concepts of the math symbols <, = and >, during the study of inequalities.

Comparing visually is an excellent skill to have, but at some point the fractions used will be unfamiliar, so a mathematical way of doing this is required.

Using the following steps, comparing fractions should be straight forward, but will take time. It's a new skill, and one that must be practiced, just like reading and writing.

There are only Four Rules to know when comparing fractions

When comparing fractions when the numerators are both 1, but the denominators are different - then the larger the denominator the smaller the fraction.
When comparing fractions when the numerators are any whole number, but the denominators are the same - then the larger numerator is the larger fraction
When comparing fractions when the numerators and denominators are different - this requires finding a common denominator so Rule 2 can be applied.
When comparing Mixed Numbers - First compare the whole numbers, if different - the larger is the larger number. If the same, compare the fractions using Steps 1, 2 or 3.

When your child is comfortable with applying Rules 1 & 2 , this is when things start getting interesting mathematically speaking. But it is quite straight forward.

You must simply find the common denominator of all the fractions you are comparing. That is, you simplify the fractions until they all have the same denominator. I deal with this in detail on the common denominator section or reducing fractions page.