Algebra is the branch of mathematics that deals with operations on numbers. These operations can be multiplication, division, subtraction or addition. In algebra numbers represented as variables are used. In addition to that there are mathematical statements termed as expressions that include numbers along with one or more variables. In algebra equations are used. Equations are statements showing equality of two expressions or numbers.
Example 1: Explain the addition, subtraction in algebra with the help of suitable illustration.
(a) Addition: Addition means increasing a number by an amount equal to the other number. For example, add 3 to 2. Here 3 is added in 2. That means 2 is increased by an amount equal to 3. Thus on increasing 2 by an amount equal to 3 we get 5. Thus 2 + 3 = 5.
(b) Subtraction: Subtraction means decreasing a number by an amount equal to the other number. For example, subtract 4 from 6. This means 6 is decreased by an amount equal to 4. Thus on decreasing 6 by an amount equal to 4 we get 2. Thus 6 – 4 = 2.
Example 2: Explain the equation 3y – 4x = 7 in words.
Solution: An equation represents the equality of two numbers or expression. On the left hand side we have two variables y and x. Left hand side of the given equation represents a quantity obtained by subtracting four times variable x from three times variable y. This quantity obtained on the left hand side is equal to the number on the right hand side of the equation that is 7.