The word fraction means a part or a piece of something.  What something? Anything!

The thing could be a gallon of gasoline, a whole class, a team, a day, anything that you can divide in equal parts. Once you decide on the parts, you call each one a fraction.

Click on the note to see how it all works in music and other situations.

A fraction is just a quick way to tell the number of parts something has been broken into. 

Fractions have two parts. The top number and the bottom number.

  -> This fraction shows that you are talking about 3 parts out of a total of 4 possible parts.

The bottom number (the denominator) tells how how many parts make up the whole. In the figure below, the whole is a octagon (a figure with 8 sides). If you divide the octagon into four parts, the denominator would be 4.

  Four parts make up the whole.

The top number (the numerator) in a fraction tells how many parts are selected.

  One part is selected. So the fraction is

You will also see fractions written with a slash instead of a line to separate the numbers. = 1/4    = 3/4

Fraction Practice

To show what fraction might look like, draw a figure and divide into equal parts. Shade some of the parts. You can now write a fraction. Use the bottom number to show how many parts something is broken into.  Use the top number to show how many parts are shaded.

Here is an example of a fraction as a figure.  Let’s use the fraction ¾.

The bottom number is 4.

The top number is 3.

This figure shows what ¾ means.  (Three parts out of four.)

Look at what happens when you shade three parts out of six.  Half of the space is red.  That means that with something with six parts, three parts are the same as half of it.  In numbers, you could say that 3/6 = ½.

Here is an eight-part figure.  How many parts would be the same as one half of the whole thing?  Tip:  Imagine half of this in a different color.  Write down two ways to show half of this figure using words or numbers.

ANSWER four eighths or 4/8 because 4/8=1/2

Here is a four-part figure.  How many parts would be the same as one half of the whole thing?  Write down two ways to show half of this figure using words or numbers.

ANSWER two fourths or 2/4 because 2/4 = 1/2

Here is a figure with only two parts.  How many parts would be the same as one half of the whole thing? Write down two ways to show half of this figure using words or numbers.

ANSWER one half or 1/2

Think about it.  Anything can be broken into as many pieces as necessary.

For example, you and a friend are sharing some bread.  There are two of you, so you slice the bread in two equal pieces.  Each one of you gets one piece of the two, one half or ½. 

Three friends sharing bread slice the bread into three equal pieces.  Each one gets one piece out of the three, or one third, or 1/3.

Four friends are sharing bread, so you slice the bread into four equal pieces.  Each of you gets one piece out of the four, or one fourth, or ¼.

You have 10 rows in your vegetable garden.  Two of the rows are for squash.  Three of the rows are for tomatoes.  One of the rows is for beans.  The remaining four rows are for lettuce.  What part of the garden is planted with each vegetable?  Use fractions for your answers.

ANSWER 2/10 squash, 3/10 tomatoes/ 1/10 beans, 4/10 lettuce

Bob's Tires only has 5 snow tires left.  A customer buys 3 tires.  What part of his tires does Bob have left?  Use a fraction for the answer.

ANSWER 2/5

Everyone in Fort Stockton is sick with the flu.  The local pharmacy is running out of cold and flu medication.  There are only 8 packages left on the shelf.  Mrs. Smith comes in and buys 5 of them.  How much did she buy out of the whole amount?  Use a fraction for the answer.

ANSWER 5/8

There was a heavy snowfall last night.  By the end of the day, the county's plow has only cleared 12 miles of mountain roads out of the 25 miles the county is responsible for.  What part of the roads have been cleared?  What part of the roads are left?  Use fractions for your answers.

ANSWER 12/25 have been cleared; 13/25 are left.

There are 10 toddlers in the Little Bunnies Day Care toddler room.  Four of the toddlers are boys.  Six of the toddlers are girls.  Use fractions to show the part of the group that is boys and the part that is girls.

ANSWER 4/10 are boys, 6/10 are girls