Purpose of this Lesson
- To perform Addition, Subtraction, Multiplication and Division on Fractions
- To follow the correct order when simplifying Fractions
- To use BODMAS order to figure out problems correctly
Types of Fractions
There are certain types of Fractions which you should know clearly before solving any problem. - Proper Fraction
- Improper Fraction
- Unit Fraction
- Mixed Fraction
| Proper Fraction |
Improper Fraction
|
Unit Fraction
|
Mixed Fraction
|
2/5
|
8/5
|
1/5
|
1 with 4/5
|
3/8
|
3/2
|
1/8
|
2 with 5/8
|
11/12
|
87/56
|
1/98
|
45 with 2/3
|
½
|
9/8
|
1/78
|
75 with 1/2
|
- Proper Fractions – In these Numerator < Denominator
- Improper Fractions – In these Denominator> Numerator
- Unit Fractions – These are a type of Proper Fraction. In terms of Math “The set of Unit Fractions is a subset of the set of Proper Fraction”. Having said so it means that the numerator of a unit fraction is always smaller than the denominator.
- Mixed Fractions – These contain a whole number and a proper fraction.
Now get yourself familiarised by looking at the examples for each type of Fraction. Once you are clear in it move to the section below. If you want to learn about "Number Patterns" click here.
Addition and Subtraction of Fractions
Addition & Subtraction of Fractions are same like we do it for any whole numbers. But you have you follow some ideas. There are two main cases which are as follows
- Denominator of all Fractions are same
| 2/5 + 8/5 =? |
In this case all you have to do is to add only the numerators and keep the denominator same. (Think of one part as one whole cake and that every cake is divided into 5 parts. So you add two + eight = ten pieces. So, how many cakes in total? This is the practical situation. When we perform math, we just communicate in terms of Math shortening words spoken or written. I Hope it’s helpful)
2/5 + 8/5 = 10/5 = 2
Subtraction too follows the same principle.
For example
11/9 - 4/9 = 11-4/9 = 7/9 |
- Denominator of Fractions are different
3/5 + 1/4 =?
|
In this situation simple principle that you have to follow is to change the all the denominators (In this case two, there can be more denominators in complex problems)
To state more clearly: Find the L.C.M (least Common multiple) of the Denominators. Then turn all the Fractions such that they have that L.C.M as their Denominator.
Here is the solution to the problem.
| 3/5 + 1/4 = 12/20 + 5/20 = 17/20 |
Using the same procedure you can solve subtraction problems too. Now get a text book of your choice and solve some Fractional Problems in it. So, you can be confident in your math performance.
Multiplication and Division of Fractions
Example:
2/5 x 3/7 = 2x3/5x7 = 6/35 |
When dividing two numbers you have to multiply one term by another term’s Reciprocal. (Inverse of the number)
Example:
3/4 ÷ 5/4 = 3/4 x 4/5(Reciprocal) = 3x4/4x5 = 3/5 |
Solving Problems with Brackets and “of”
Brackets – The concept is simple. Whenever you see brackets in a problem, first solve the portion inside the brackets.
Of – It means multiplication symbol. For example if it is half of five cakes you know that the answer is two and a half. Let’s solve it mathematically now.
1/2 of 5 = 1/2 x 5 = 5/2 = 2 with 1/2 |
The last part is to solve a complex problem. Here the order of solving is very important. You can use the mnemonic BODMAS for it.
B - Brackets (First solve the parts inside Brackets)
O - Of (Of is the one to solve next)
D - Division
M - Multiplication (Division should be converted to the form of multiplication, so the solution to both can be given in one process)
A - Addition
S - Subtraction (Addition and Subtraction can be solved in one process like multiplication and Division are performed)
Example: (2 ¼ ÷ 3/14) of 2 with 1/7
First convert the mixed fractions to improper as you do whenever solving division and multiplication.
= (9/4 x14/3) x 15/7
= 126/12 x 15/7
= 21/2 x 15/7
= 315/14
= 45/2
= 22½
That's it for this lesson. If you have any doubts feel free to contact me. Don't forget to give your comments below.
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