Composition of Functions
Introduction
The Four Rules / Operations of Mathematics which includes Addition, Subtraction, Multiplication and Division can be used to Simplify Algebraic Expressions.
Before making use of the Four Operations of Algebraic Expressions, Let's know Signed Numbers
It is the Basis of Signed Numbers that helps us solve Algebraic Expressions.
Signed Numbers are Negative or Positive Numbers that are expressed in Algebraic Expression.
Ex: -5 , 3, -11 , -2, +19 etc.
Note that any number without a sign, the default sign is Positive (+).
let's say, if I Put Four numbers together like this 6 - 5 - 8 + 2
and I ask to give the Sign of Each numbers
The sign of 6 is Positive (+)
The sign of -5 is Negative (-)
The sign of -8 is Negative (-)
The sign of +2 is Positive (+)
Remember always that the sign of the number is always called first before the Number,and any number without a Sign, the default sign is Positive (+).
Getting these in Mind, Let's observe the sign Rules.
Before making use of the Four Operations of Algebraic Expressions, Let's know Signed Numbers
It is the Basis of Signed Numbers that helps us solve Algebraic Expressions.
Signed Numbers are Negative or Positive Numbers that are expressed in Algebraic Expression.
Ex: -5 , 3, -11 , -2, +19 etc.
Note that any number without a sign, the default sign is Positive (+).
let's say, if I Put Four numbers together like this 6 - 5 - 8 + 2
and I ask to give the Sign of Each numbers
The sign of 6 is Positive (+)
The sign of -5 is Negative (-)
The sign of -8 is Negative (-)
The sign of +2 is Positive (+)
Remember always that the sign of the number is always called first before the Number,and any number without a Sign, the default sign is Positive (+).
Getting these in Mind, Let's observe the sign Rules.
Problems and Solutions
Addition and Subtraction Rules
+ + + = Add the two Numbers and end up in Positive (+)
- + - = Add the two Numbers and end up in Negative (-)
+ + - = Subtract the smaller number from the bigger number and carry the Sign of the Bigger Number
- + + = Subtract the smaller number from the bigger number and carry the Sign of the Bigger Number
Short cut Rule to this
Same Sign, add them and carry that sign.
Opposite Sign, Subtract the smaller number from the Bigger number and Carry the Sign of the Bigger Number.
Example : 1. Simplify 6 + 5
Ans : the 6 is Positive and the 5 is Positive, Therefore, they are same Sign, we add them, this gives us 11. the answer remains like this because, any number without a sign, the sign is Positive.
Example : 2. Simplify -3 - 12
Ans : the -3 is Negative and the -12 is Negative, Therefore, they are same Sign, we add them, this gives us 15 ,because they are negative, the answer becomes -15
Example : 3. Simplify -9 - 5
Ans : the -9 is Negative and the -5 is Negative, Therefore, they are same Sign, we add them, this gives us 14 ,because they are negative, the answer becomes -14
Example : 4. Simplify -3 + 8
Ans : the -3 is Negative and the +8 is Positive, Therefore, they have different Signs, we subtract 3 from 8 , this gives us 5 ,because the bigger number here is 8 and it is Positive, the answer becomes 5 (which is Positive 5)
Example : 5. Simplify 3 - 8
Ans : the 3 is Positive and the -8 is Negative, Therefore, they have different Signs, we subtract 3 from 8 , this gives us 5 ,because the bigger number here is 8 and it is Negative, the answer becomes -5
+ + + = Add the two Numbers and end up in Positive (+)
- + - = Add the two Numbers and end up in Negative (-)
+ + - = Subtract the smaller number from the bigger number and carry the Sign of the Bigger Number
- + + = Subtract the smaller number from the bigger number and carry the Sign of the Bigger Number
Short cut Rule to this
Same Sign, add them and carry that sign.
Opposite Sign, Subtract the smaller number from the Bigger number and Carry the Sign of the Bigger Number.
Example : 1. Simplify 6 + 5
Ans : the 6 is Positive and the 5 is Positive, Therefore, they are same Sign, we add them, this gives us 11. the answer remains like this because, any number without a sign, the sign is Positive.
Example : 2. Simplify -3 - 12
Ans : the -3 is Negative and the -12 is Negative, Therefore, they are same Sign, we add them, this gives us 15 ,because they are negative, the answer becomes -15
Example : 3. Simplify -9 - 5
Ans : the -9 is Negative and the -5 is Negative, Therefore, they are same Sign, we add them, this gives us 14 ,because they are negative, the answer becomes -14
Example : 4. Simplify -3 + 8
Ans : the -3 is Negative and the +8 is Positive, Therefore, they have different Signs, we subtract 3 from 8 , this gives us 5 ,because the bigger number here is 8 and it is Positive, the answer becomes 5 (which is Positive 5)
Example : 5. Simplify 3 - 8
Ans : the 3 is Positive and the -8 is Negative, Therefore, they have different Signs, we subtract 3 from 8 , this gives us 5 ,because the bigger number here is 8 and it is Negative, the answer becomes -5
Note: These Sign Rules will be used Through out your Mathematical Journey until we all depart this world. Practice using your own examples and the examples we provided for you.
Exercise
Write Exercise Here
Self-Practice
Write Self Prace Here.
Answer To Exercise
Write Exercise Answer Here