Basic Algebra: Introduction
Variables, Constants, Coefficients
There are multiple branches of mathematics. The one in which we study numbers is called arithmetic. The branch of mathematics in which we study shapes is called geometry.
Algebra is the branch of mathematics which deals with restoration or completion of broken parts. It has mathematical symbols attached with it. There are multiple advantages of using these symbols or letters.
- It is easy to generalize the rules and formulae when we use letters.
- Letters/Symbols can be used to represent unknown quantities.
- Since letters/symbols represents numbers so operation can be performed on them as numbers.
For example, 10 – = 4
So, the answer would be 6. However, in algebra, we don’t use boxes instead we use to represent these symbols. Mostly the letters used are x, y. But it is not necessary, we can use any letter. So, we write,
10 – X = 4
And solving above, gives that X=6
The benefit of using these letters is that they are easy to write than to draw boxes. When there are multiple unknowns that means instead of drawing several empty boxes, we can use different letters.
Constants and Variables
There are two types of symbols used in algebra: Constant and Variables.
Constants are those symbols which have fixed numerical value.
For example–2, 1, 3, 6, 8, 0, -1/8, 4/6
Example 1:
How many days are there in a week?
Answer: 7
It is fixed value. It represents a constant.
Example 2: What is constant in this expression?
- 3x+ 9
Solution
Yes! It is 9. Because the value 3 that is in multiplication with x is called co-efficient. Hence the only constand we will call would be “9”
Coming over to Variables, it is a quantity which has no fixed value. It can take different values like 1, 2, 3, 4…..etc. Something that can vary or change is variable.
For example, at different times of a day temperature is a variable. A variable is denoted by letters x, y, z, w etc.
Note: A combination of variable and constant is also called a variable.
In the expression 3X + 9, what is a variable?
Yes, it is ‘x’ because it can take any values. 3 is a coefficient and 9 is a variable in above expression.
Example 4: If 3 is constant and x is variable in the following expression. Then what is the expression called?
3 + X
Solution: The combination of constant and variable is also called variable. So, the above expression as a whole is also a variable.
Coefficients:
It is a number multiplied with a variable, for example 4Z means 4 times Z. Here “Z” is variable and 4 is a coefficient. Variables with no number multiplied have coefficient of 1.
As we learn algebra in advanced classes, the use of coefficient plays a very important role in handling and solving system of equations. But let us first build our basic understanding in how we read equations as well as know general terms such as coefficients, number and variables.
Example: In bx + c, “x” is a variable and “b” is the coefficient. Let us look at 5x + 10
Example-
- Write the coefficient of y in 4y – 9
Solution: The coefficient of y is 4.
- Write the coefficient of x in 18x – 12
Solution: The coefficient of x is 18.