Learning Basic Fractions

What's a Fraction?

If you divide something into smaller pieces, each piece is a fraction of the whole thing. For instance, when you cut a pizza into slices, each slice is a fraction of the whole pizza. In a bag of candy, each piece represents a fraction of the whole amount of candy.

In math, we have a special way of writing fractions: we use two numbers that are written one above the other and separated by a line. The number that's on top of the line is called the numerator, and the number that's under the line is called the denominator. The denominator tells you the total number of pieces there are of something, and the numerator tells you how many of those pieces the fraction represents.

As an example, imagine that you cut a pie into eight slices and served three of them. Since your pie is divided into eight pieces, the denominator of your fraction is eight. Your fraction represents three of the eight slices, so the three goes on top (3/8).

Comparing Fractions

When fractions have the same denominator and they come from the same whole, the fraction with the larger numerator is greater. Returning to the pie example, we have already mentioned that you served three out of eight slices, or 3/8. That means that you still have five slices (5/8) of the pie left. Since five is greater than three, you can say that 5/8 is greater than 3/8. This makes sense, since five slices of pie is certainly more than three slices. Here are a few more examples:

2/3 > 1/3

1/5 < 4/5

7/10 > 3/10

Equivalent Fractions

Imagine that you split a large pizza into 12 slices, keeping half (6/12) for yourself and giving the other half to a friend. Since six is half of 12, you each have half of the pizza. Now, imagine that your neighbor orders an identical pizza, and divides it into just four slices. He keeps two of those four slices (2/4) for himself, and he gives the rest of the pizza to his friend. Since two is half of four, both he and his friend have half of the pizza.

The two pizzas in these examples are identical, so we can say that 6/12 of the first pizza is equal to 2/4 of the second pizza. Two of the four large slices would be equal to six of the 12 smaller slices. Fractions are equivalent if the relationship between the top and bottom numbers is the same in both. Other fractions that would be equal to 2/4 and 6/12 are 5/10 and 4/8, because the numerators are half of the denominator. Here are a few more examples of equivalent fractions:

2/6 = 3/9

2/2 = 5/5

3/12 = 1/4