Introduction to Algebra
Introduction to Algebra (pre-algebra): In Algebra,we will come across following terms:1) Variables 2) Constant 3) Algebraic expression . This is pre-algebra.
Introduction to Algebra :
Let us fill up the empty gaps.
1) (----) + 3 = 7
2) 3 + ( ----) = 8
3) 8 + 3 = ( ----)
In the first blank you will write 4 , in 2nd you will write 5 and in the 3rd you will write 11. The (---) stands for an unknown number.
Now let us write these problems a little differently.
1) Cost of a pen + $ 3 is equal to $7.
2) After paying the cost of book, Sam is left with $3 from his pocket money of $8.
3) Jill had 8 toffees and her brother gave her 3 more.How many toffees does Jill have now?
In all these cases, we have to find answers, which are not known. They are referred to as unknowns
The mathematics which involves unknowns are called Algebra.
So, in this section I am giving you the Introduction to Algebra.
Literal numbers are generally referred to as variables as there values vary and are not fixed
Example:5 more than a number.
Solution:Here,we do not know the number, so it becomes a variable.
The quantities with fixed numerical values are called constants
Example:5,8,10 etc. are constants.
5 more than a number(a) can be written in mathematical form as "a+5" This is an algebraic expression
| 1) | If two values are equal, we use the "equals" sign | Equal to | = | Example: 2+2=4 |
| 2) | If two values are definitely not equal, we use the "not equal to" sign | Not equal | ≠ | Example : 2+2 ≠ 9 |
| 3) | More than | Addition | + | Example: 7 more than x = x+7 |
| 4) | Less than | Subtraction | - | Example : 5 less than x = x-5 |
| 5) | Decrease | Subtraction | - | Example : x is decreased by 2= x-2 |
| 6) | Increase | Addition | + | Example : x is increased by 3=x+3 |
| 7) | Twice of a number(a) | Two times | x | Example : 2 times a = 2a |
| 8) | Thrice of a number (a) | Three times | x | Example : 3 times a=3a |
| 9) | Double of a number (b) | Two times | x | Example : Double the number b = 2b |
| 10) | One half or Half of a number(b) | Division | Divide with 2 | Example : One half of b= ½ b = b/2 |
| 11) | One third of a number (x) | Division | Divide with 3 | Example : One third of x = ⅓ b= b/3 |
Introduction to Algebra
• Addition of Literals
• Subtraction of Literals
• Multiplication of Literals
• Division of Literals
• Constants and Variables
• Coefficient