We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.


Fractions may look funky at first, but they’re actually really cool and useful once you get the hang of them.

The great news is, you’re already a pro at fractions. You’ve been thinking about fractions since your rugrat days (even if you didn’t know it). Want proof?

You call out times like “quarter past two” or “half past three.” You know how to split up a pizza into thirds, so you and your two friends all get equal amounts. You've used measuring tapes for building, measuring cups and tablespoons for baking. All fractions.

Fractions are just a simple way to speak of 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.
  • Denominator: the bottom number of a fraction.
  • 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.

Visualizing Fractions

Start with a circle to represent 1 whole.

whole circle

If we divide this circle in 2 equal pieces, we get two 1/2's.

split circle

Divide it into 3 equal pieces, and we get three 1/3's.

Circle in 3 parts

Divide it into 4 equal pieces and we get four 1/4's.

f our part circle

See what we mean? If you know pizza, you know fractions.

five part circe

six part circle

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 number line


fifths number line


Sixths number line

And Eighths:

eighths number line

All together now!

all lines togetther

People who Shmooped this also Shmooped...