When an object is divided into a number of equal parts then each part is called a fraction. For example, two fifths of an object can be written as Now let us have a closer look at the common fraction:

2 numerator says how many parts in the fraction

vinculum = "divide by" 5denominator says how many equal parts in the whole object

Always remember: denominator can NEVER be 0.

Why? Because you cannot divide by 0.

FRACTION TYPES

There are 3 different types of fractions:

Proper FractionsNumerator < Denominator Proper fractions have the nominator part smaller than the denominator part,
for example , or .

Improper FractionsNumerator > Denominator or Numerator = Denominator,
Improper fractions have the nominator part greater or equal to the denominator part,
for exampleor .

Mixed Fractions
Mixed fractions have a whole number plus a fraction, for example 2or 123 .

The word EQUIVALENT means the same as EQUAL or, more precisely, of equal value. For example, you can see that the colored part of each of thecircles below is exactly the same.

WHEN FRACTIONS ARE EQUIVALENT.

Equivalent fractions are obtained by multiplying or dividingboth the numeratorand the denominator by the samenumber.

SIMPLIFYING FRACTIONS

Many fractions can be reduced down and written in a simpler form.

For example, if your mum cut a big, creamy cake into 8 pieces and you ate 4 of them, she will say to a doctor that you got sick from eating half of the cake. To simplify a fraction, both the numerator and denominator must be divided bythe same number. This method is also called canceling down or reducing the fraction. The fraction is in the SIMPLEST FORM when it cannot be any more simplified.

When you are asked to simplify or reduce down a fraction, you should always try to simplify as much as you can to achieve the simplest form. You will do it by dividing both numerator and denominator by their Highest Common Factor( or H.C.F.). Do not worry too much about H.C.F. now. Just keep simplifying the fraction until it cannot be simplified.

Adding and Subtracting Fractions

When adding and subtracting fractions, the fractions being added or subtracted must have the same denominator. When denominators are different, you will need to convert each fraction into an equivalent fraction by finding the least common denominator (LCD) for the fractions. The two new fractions should have the same denominator, making them easy to add or subtract. (Determining the LCD of a set of fractions was reviewed in the unit Comparing Fractions.)

Rule for Addition of Fractions

When adding fractions, you must make sure that the fractions being added have the same denominator. If they do not, find the LCD for the fractions and put each in its equivalent form. Then, simply add the numerators of the fractions.

Rule for Subtraction of Fractions

When subtracting fractions, you must make sure that the fractions being subtracted have the same denominator. If they do not, find the LCD for the fractions and put each in its equivalent form. Then, simply subtract the numerators of the fractions.

Multiplying Fractions

Multiplying two fractions is the easiest of any of the operations.

Rule for Multiplication of Fractions

When multiplying fractions, you simply multiply the numerators together and then multiply the denominators together. Simplify the result.

Example

What do you get when you multiply 1/2 and 3/7?
The result of multiplying these two fractions is 3/14.

Dividing Fractions

Dividing one fraction by another is almost as easy as multiplying two fractions. It even involves multiplying fractions! First, let's look at how division of two fractions may be represented. If we wish to divide 3/5 by 2/3, we could write that as:

Rule for Division of Fractions

When you divide two fractions, you take the reciprocal of the second fraction, or bottom fraction, and multiply. (Taking the reciprocal of a fraction means to flip it over.)

WHAT IS A FRACTIONWhen an object is divided into a number of equal parts then each part is called a fraction.For example, two fifths of an object can be written as

Now let us have a closer look at the

common fraction:

vinculum = "divide by"2 numeratorsays how many parts in the fraction5denominatorsays how many equal parts in the whole objectAlways remember: denominator can NEVER be0.Why?Because you cannot divide by 0.

There are 3 different types of fractions:FRACTION TYPES

Play this fraction gameProper FractionsNumerator < DenominatorProper fractions have the nominator part

smallerthan the denominator part,for example , or .

Improper FractionsNumerator > DenominatororNumerator = Denominator,Improper fractions have the nominator part

greater or equalto the denominator part,for exampleor .

Mixed FractionsMixed fractions have a

whole number plus a fraction, for example2or123 .Equivalent fractions## WHAT EQUIVALENT MEANS

The word EQUIVALENT means the same as EQUAL or, more precisely, of equal value.For example, you can see that the colored part of each of thecircles below is exactly the same.

WHEN FRACTIONS ARE EQUIVALENT.Equivalent fractions are obtained by multiplying or dividingboth the numeratorand the denominator by the samenumber.

Many fractions can be reduced down and written in a simpler form.SIMPLIFYING FRACTIONSFor example, if your mum cut a big, creamy cake into 8 pieces and you ate 4 of them, she will say to a doctor that you got sick from eating

halfof the cake.To simplify a fraction, both the numerator and denominator must be divided bythe same number. This method is also called canceling down or reducing the fraction.The fraction is in the SIMPLEST FORM when it cannot be any more simplified.When you are asked to simplify or reduce down a fraction, you should always try to simplify as much as you can to achieve the simplest form. You will do it by dividing both numerator and denominator by their Highest Common Factor( or H.C.F.). Do not worry too much about H.C.F. now. Just keep simplifying the fraction until it cannot be simplified.

## Adding and Subtracting Fractions

When adding and subtracting fractions, the fractions being added or subtracted must have the same denominator. When denominators are different, you will need to convert each fraction into an equivalent fraction by finding the least common denominator (LCD) for the fractions. The two new fractions should have the same denominator, making them easy to add or subtract. (Determining the LCD of a set of fractions was reviewed in the unit Comparing Fractions.)

## Rule for Addition of Fractions

When adding fractions, you must make sure that the fractions being added have the same denominator. If they do not, find the LCD for the fractions and put each in its equivalent form. Then, simply add the numerators of the fractions.

## Rule for Subtraction of Fractions

When subtracting fractions, you must make sure that the fractions being subtracted have the same denominator. If they do not, find the LCD for the fractions and put each in its equivalent form. Then, simply subtract the numerators of the fractions.

## Multiplying Fractions

Multiplying two fractions is the easiest of any of the operations.## Rule for Multiplication of Fractions

When multiplying fractions, you simply multiply the numerators together and then multiply the denominators together. Simplify the result.## Example

What do you get when you multiply 1/2 and 3/7?

The result of multiplying these two fractions is 3/14.

## Dividing Fractions

Dividing one fraction by another is almost as easy as multiplying two fractions. It even involves multiplying fractions! First, let's look at how division of two fractions may be represented. If we wish to divide 3/5 by 2/3, we could write that as:## Rule for Division of Fractions

When you divide two fractions, you take the reciprocal of the second fraction, or bottom fraction, and multiply. (Taking the reciprocal of a fraction means to flip it over.)