Study Guide

Fractions

Fractions

Fractions may look funky at first, but they're actually really useful once we get the hang of them.

The great news is, we're already pros at fractions. We've been thinking about fractions since our rugrat days (even if we didn't know it). Want proof?

We talk about times like "a quarter past two" or "half past three." We know how to split up a pizza into thirds, so with our two friends we all get equal amounts. We've used measuring cups for baking. We're hoarding the half-dollar our Grandma gave us, and we know how to spend three-fourths of our free time playing video games. All fractions.

Fractions are just parts of a whole object, like parts of an hour, parts of a sandwich, or parts of a dollar.

Fractions Vocabulary

  • Numerator: The top number of a fraction, like the 1 in .
  • Denominator: The bottom number of a fraction, like the 2 in .
  • Mixed Number: A number expressed as a whole number and a fraction, like 2 1/2  or 4 3/8.
  • Improper Fraction: A fraction in which the numerator is larger than the denominator, like 13/5 or 25/4.
  • Reciprocal: An inverse fraction. Flip the numerator and denominator. 5/6 and  6/5 are reciprocal fractions.
  • Unit Fraction: A fraction with a 1 in the numerator.

Visualizing Fractions

Start with a circle to represent 1 whole.

whole circle

If we divide this circle into 2 equal pieces, we get two halves. Each side of the circle below represents 1/2 ("one half") of the total circle.

split circle

There's 1/2 on the left and 1/2 on the right. The numerator 1 in 1/2 means we've got 1 piece, and the denominator 2 means it takes 2 pieces to make the whole circle.

Divide it into 3 equal pieces, and we get three thirds. Each piece below represents 1/3 of the entire circle.

Circle in 3 parts

By the way, the fraction 1/3 is called a unit fraction. It represents only one piece and always has a 1 in the numerator. If we wanted two pieces of the circle, we'd write that as .

Now divide the whole circle into 4 equal pieces and we get four 1/4's.

f our part circle

See what we mean? If we know pizza, we know fractions. Here are a few more.

Fifths
five part circe

Sixths
six part circle

Sevenths
seven part circle

Let's also try to visualize these fractions on a number line. Here we have a number line stretching from 0 to 1.

0 to 1 number line


If we divide it in half, we get two parts, or halves:

halves number line

Here it is divided into thirds:

thirds number line

Fourths:

fourths number line

Fifths:

fifths number line

Sixths:

Sixths number line

And Eighths:

eighths number line

All together now!

all lines togetther

We know that probably looks weird, so stick with us. We'll explain why some of those fractions are equal on the next page.