FRACTION
In mathematics, a fraction is used to represent a part of whole. It depicts the
whole’s equal pieces. The numerator and denominator are the two elements
of a fraction. The Upper part of a fraction is called Numerator , while lower
part of the fraction is called denominator. The numerator specifies the number
of equal parts taken, whereas the denominator specifies the total number of
equal parts in the total.
Types of Fraction
There are different types of fractions
a) proper fraction;
proper fractions are the fraction in which denominator is greater than the
numerator.
examples; 2/5, 1/2, 5/7
b)Improper fractions;
Improper fractions are the fraction in which numerator is greater than the
denominator.
examples; 11/7 , 22/3 ,84/45
c) Equivalent Fractions;
Equivalent fractions are the fractions that represents the same value after
simplification. We can multiply or divide both numerator and denominator of the
fraction with same number
For adding and subtracting we have two fractions
Like fractions
when the denominators of the fraction are same we call it as like fraction
Unlike fraction
When the denominators of the fraction are different we call it as unlike fraction
HOW TO ADD LIKE FRACTIONS?
If the fractions have the same denominator simply add the numerator over same
denominator.
Example
A simple example is when the denominators are already the same or Like fractions
HOW TO ADD UNLIKE FRACTIONS?
To add an unlike fraction (fractions with different denominator) we have two method
a) Making the denominators same and adding the numerator only.
b) Cross multiplying
Method 1 ;
1.Check , if the fractions have the same denominator.
2. If they don't have the same denominator, then convert them to equivalent fractions with
the same denominator.
3. Once they have the same denominator, add in the numerator.
4. Write your answer with the new numerator over the denominator.
5. Note: The denominator may have changed when you converted the fractions to the same
common denominator.
HOW TO ADD FRACTION WHEN THE DENOMINATORS ARE NOT SAME?
Method 1;
1. In the fractions where denominators are different . We convert into like fractions that have common denominator
2. For this we take L C M (Lowest common multiple ) of the denominators
3. And make the denominators same by multiplying and dividing the number to get the denominators same
we must first convert this into like fractions that have common denominators.
Method2;
1. These fractions do not have the same denominator. Before adding the fractions together,
we cross multiply first numerator to second denominator and add with second numerator to first denominator.
2.And then we multiply the denominators.
Example
b) Method 2 ;
Making the denominators same and adding the numerator
Example
Add the Numerators
Now that the denominators are the same, you can add the numerators and put the answer over the same denominator.
HOW TO SUBTRACT THE FRACTIONS WHEN THE DENOMINATORS ARE NOT SAME
a) Method 1: cross multiplying
b)Method 2:
Making the denominators same and subtracting the numerator over the same denominator
Now that the denominators are the same, you can add the numerators and put the answer over the same denominator.
Reducing fractions
Sometimes the answer will need to be reduced. Here is an example:
The initial answer after adding the numerators was 10/15, however this fraction can be further reduced to 2/3 as shown in the last step.
HOW TO ADD MIXED FRACTIONS WITH SAME DENOMINATOR
To add a mixed fraction with same denominator
1.convert the mixed fractions into an improper fraction
2. And add the numerators over the same denominators
HOW TO SUBTRACT THE MIXED FRACTION WITH SAME DENOMINATOR
HOW TO ADD MIXED FRACTIONS WITH DIFFERENT DENOMINATOR
To add the mixed fractions with different denominator
1. Convert the mixed fraction into an improper fraction
2. And convert the improper fraction with different denominator into an equivalent fractions
3.After converting it add the numerators over the same denominators
Now , we got the unlike improper fractions with different denominator. Now you can use cross multiply or making the denominator same for adding the fractions.
HOW TO SUBTRACT THE MIXED FRACTION WITH DIFFERENT DENOMINATOR
Here is an example of subtracting fractions where only one denominator needs to be changed:
Rules for Adding and Subtracting Fractions
Always make sure that the denominators are the same before you add or subtract.
If you multiply the top and the bottom of a fraction by the same number, the value stays the same.
Be sure to practice converting fractions to common denominators. This is the hardest part of adding and subtracting fractions.
You may need to simplify your answer after you are done adding and subtracting. Sometimes the answer can be reduced even though the original fractions could not be reduced.
The same process is used for both adding and subtracting, if you can add fractions, you can subtract them.
If there are mixed numbers that you are adding or subtracting be sure to convert them to improper fractions before you start the process
