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
external image vinculum.gifvinculum = "divide by"
5 denominator 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 498203-child-with-three-quarters-of-a-circle-learning-about-fractions-and-portions--toddler-art-series.jpg

There are 3 different types of fractions:
  • Proper Fractions Numerator < Denominator
    Proper fractions have the nominator part smaller than the denominator part,
    for example external image F1by2.gif,external image F2by5.gif or external image F19by20.gif .
  • Improper Fractions Numerator > Denominator or Numerator = Denominator,
    Improper fractions have the nominator part greater or equal to the denominator part,
    for exampleexternal image F5by5.gifor external image F7by2.gif.
  • Mixed Fractions
    Mixed fractions have a whole number plus a fraction, for example 2external image F1by5.gifor 123 external image F19by20.gif.
Play this fraction game

Equivalent fractions


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.

external image Pie1to2.gif external image Pie2to4.gif external image Pie4to8.gifexternal image F1by2.gifexternal image F2by4.gifexternal image F4by8.gif


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


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 by the 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.

external image fig12.gif

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.

external image fig13.gif

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.
external image fig1.gif


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

external image fig4.gifprod3501_dt.jpg

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:
external image fig5.gif

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.)
external image fig7.gif