Question

.... fraction are less than one whole and .... fraction have more than one whole

Answer 1

Identifying Proper and Improper Fractions

 

In a proper fraction, the numerator is always less than the denominator. Examples of proper fractions include  and .

 

In an improper fraction, the numerator is always greater than or equal to the denominator. Examples of improper fractions include  and .

 

 

Identify  as a proper or improper fraction.

 

A) proper

 

B) improper

 

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Changing Improper Fractions to Mixed Numbers

 

An improper fraction can also be written as a mixed number. Mixed numbers contain both a whole number and a proper fraction. Examples of mixed numbers include  and .

 

Let’s look at a quick example. Below are three whole pizzas that are each cut into four pieces. A fourth pizza is there as well, but someone has taken one piece, leaving only three pieces.

 







 



 

You can use fractions to compare the number of pieces you have to the number of pieces that make up a whole. In this picture, the denominator is the total number of pieces that make up one whole pizza, which is 4. The total number of all pieces of pizza, which is 15, represents the numerator.

You can use the improper fraction  to represent the total amount of pizza here. Think: “Each whole pizza is cut into 4 equal pieces, and there are 15 pieces total. So, the total amount of whole pizzas is .”

 

As you looked at the image of the pizzas, however, you probably noticed right away that there were 3 full pizzas and one pizza with a piece missing. While you can use the improper fraction  to represent the total amount of pizza, it makes more sense here to use a mixed number – a fraction that includes both a whole number and a fractional part. For this pizza scenario, you can use the fraction .

 



 

The mixed number  can be easier to understand than the improper fraction . However, both forms are legitimate ways to represent the number of pizzas.

 

Rewriting an improper fraction as a mixed number can be helpful, because it helps you see more easily about how many whole items you have.

 

Let’s look again at the pizzas above.

The improper fraction  means there are 15 total pieces, and 4 pieces makes a whole pizza. If you didn’t have the picture, you could change  into a mixed fraction by determining:

–    How many groups of 4 pieces are there in 15 pieces? Since 15 ÷ 4 = 3 with a remainder, there are 3 whole pizzas.

–    What is the remainder?  The remainder is 3. So, there are 3 pieces of the last pizza left, out of the 4 that would make a whole pizza. So,  of a pizza is left.

Now, put the number of whole pizzas with the fraction of a pizza that is left over. The mixed number is .