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Mathematics Class 5th Grade » Fractions
 Fractions

Fractions are parts of a whole.  If an amount is divided into equal parts, or fair shares, we can understand and name fractions.

The top number in a fraction is called a numerator.  The bottom number in a fraction is called a denominator.

Fractions that have the same numerator and denominator always equal 1 whole.  The examples below all equal 1 whole because the numerator and denominator are the same.

Fraction names can be shown in numbers, words, or pictures.

To understand a fraction we need to answer 3 questions:

 The Three Fraction Questions What is the whole and how big is it? Into how many equal parts has the whole been divided ? The denominator of the fraction answers this question. How many of the equal parts are we using? The numerator of the fraction answers this question.

To identify fractions we count how many equal pieces have been used (numerator) and how many equal pieces there are altogether (denominator).  For example:  In the fraction below we used 2 equal pieces and there are 3 equal pieces altogether.

Equivalent fractions describe the same portion of a whole divided in different ways.  For example: half a piece of paper can be represented as 1/2, 2/4, 3/6, 4/8, or 5/10, etc.

The circles below are examples of equivalent fractions.  1/2 and 3/6 are equivalent because 1 piece of the first circle equals 3 pieces of the second circle and 2 pieces of the first circle equals 6 pieces of the second circle.

Sometimes we can simplify or reduce fractions to make them easier to understand.  When we simplify fractions we use the smallest numbers possible.  You can divide the numerator and denominator by the same number to simplify.  For example:  below is an example of how to simplify 100/200.

The easiest way to find a number you can divide into the numerator and denominator evenly to simply is to find the greatest common factor.  For example:  to simplify 27/108 find the greatest common factor of 27 and 108.  Then divide the numerator and denominator by the factor to simplify.

The factors of 27 are  1, 3, 9, and 27.

The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.

27 is the highest factor of the numbers 27 and 108 so we divide by 27.

Adding and subtracting like fractions.  Like fractions are fractions with the same denominator.  For example:  1/6  and 3/6 are like fractions because both fractions have 6 as the denominator.

To add and subtract like fractions you add or subtract the numerator and the denominator stays the same.  For example:  in the problem below you would add the numerators (2+1=3) and the denominator stays the same (4).  The answer is 3/4.

Adding and subtracting unlike fractions.  Unlike fractions are fractions with different denominators.  For example:  1/5  and 3/8 are unlike fractions because the fractions have different denominator.

To add and subtract unlike fractions you must first make the denominators the same by finding the least common multiple of the denominators.  For example:  in the problem below you would find the least common multiple of 2 and 3.  The least common denominator is 6.

We need to make this our new denominator....

Change the :

Change the :

To multiply fractions you multiply straight across and then reduce or simplify your answer.

To divide fractions you flip the second fraction and multiply.

Proper fractions are fractions in which the numerator is less than the denominator.

Improper fractions are fractions with a numerator equal to or greater than the denominator.

A mixed number is a number that includes a whole number and a proper fraction.

In the real world we compare fractions to see which one is smaller or larger.  If you were hungry would you want a slice of the first pizza below or the second pizza?  Since the pieces in the first pizza are larger if you were hungry you would want a slice from this pizza.

If you compare like fractions all you have to do is compare the numerators because the denominators are the same.  For example:  if you compare 3/8 to 7/8 you only need to compare the numerators 3 and 7.

When we round fractions we decide if the fraction is closest to 0, 1/2, or 1.

Like fractions can be ordered on a number line just as whole numbers can be ordered.  In number line a the number line has been divided into 5ths.  As you move to the right each fraction is larger.  1/5 < 2/5 < 3/5 < 4/5 < 5/5.

To complete a fraction tutorial.

To review fractions.

To practice identifying fractions.

To practice comparing fractions.

To practice equivalent fractions.

To practice 1/2 and 1/4 fractions.

To practice fractions on a number line.

To see a video on simplifying fractions.

Mrs. Travis' Classroom
Dorchester County Public Schools
Choptank Elementary
1103 Maces Lane
Cambridge, Maryland 21613