Learning Target: I can represent a whole unit using a fraction, and express the unit as a sum of unit fractions.

 

Unit Fractions of the Same Whole


Unit Fractions

A unit fraction is a fraction whose numerator is 1. 

Numbers like , and are unit fractions.  

The denominator of the unit fraction tells how many pieces or parts the whole is cut into.

The top of the unit fraction -- 1 -- identifies one piece of the whole.



Combining Unit Fractions Together to Make One Whole

When you add all the unit fractions of the same whole together they equal 1.

A Model


Example

Think:

The denominator tells how many pieces the whole is cut into.

The numerator shows how many units are shaded.

Model:


We can shade on the model.

Then we can show that each shaded piece equals .

We can write the equation of the sum as:


+ + + = 


 = 1


Rule

Any fraction whose top and bottom are the same equals one!

The bottom tells how many pieces the whole is cut into.

The top tells us that all of them are included in the whole.




Let's Practice Together

Copy the illustrations on a piece of paper to observe how a fraction whose numerator and denominator are the same equals one whole. 

The bottom part of the model shows the number of parts the whole is divided into.  The top part shows how it equals one whole.

1.   Shade the bottom two parts of the model.


 Does  = 1 whole?




2.   Shade the part of the model that shows fourths.


Does = 1 whole?




Your Turn

3.  Draw and shade a new part of the model to show eighths.

Does 8/8 = 1 whole?  


4.  Draw a whole unit and divide it into six pieces.  Express the whole unit as a sum of unit fractions based on the model.



Check for Understanding

1.  Write a fraction that equals one whole by placing the same number on the top as on the bottom.

Draw a model of your fraction.

How many pieces is your whole cut into?

How many pieces are shaded?



















Answers
1.  yes
2.  yes
3.  yes
4.  1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1
Check for Understanding
1.  Answers vary, but the number of pieces the whole is cut into should be the same as the number of pieces that are shaded.