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Understanding Fractions

Parts of a Whole

Imagine you have a pizza and you want to share it equally with a friend. You cut it right down the middle. You each get one piece. That one piece you have is a part of the whole pizza. That's a fraction! Fractions are a way to talk about parts of a whole thing, whether it's a pizza, a candy bar, or even a group of people.

Fractions are a way to represent parts of a whole.

We write fractions using two numbers, one on top of the other, separated by a line. For example, if your pizza was cut into two equal slices and you have one, your share is written as 12\frac{1}{2}.

Numerator and Denominator

Every fraction has two special parts: the numerator and the denominator. They each tell us something important.

denominator

noun

The bottom number in a fraction. It shows the total number of equal parts the whole is divided into.

numerator

noun

The top number in a fraction. It shows how many of the equal parts you are talking about.

Let's look at the fraction 35\frac{3}{5}. The denominator is 5, so we know the whole is cut into five equal pieces. The numerator is 3, which tells us we have three of those pieces.

A good way to remember is Denominator is Down at the bottom. The numerator is the number up top.

Seeing Fractions

Sometimes the easiest way to understand a fraction is to see it. We can draw fractions in a few different ways.

Lesson image

One way is with an area model. This is when we take a shape, like a rectangle or a circle, and divide it into equal parts. The shaded parts show the fraction.

Another way is with a set model. Instead of one whole thing, we look at a group of items. The fraction can tell us about a part of that group. For example, if you have a bag with 5 marbles and 3 of them are blue, then 35\frac{3}{5} of the marbles are blue.

Finally, we can find fractions on a number line. Think about the space between 0 and 1. We can split that space into equal parts. Each mark represents a fraction.

Understanding these models will help you picture what fractions mean and get you ready for working with them in new ways.

Quiz Questions 1/5

What does the top number in a fraction, the numerator, tell us?

Quiz Questions 2/5

In the fraction 34\frac{3}{4}, what does the number 4 represent?