Equality

UNIT−4

ALGEBRA

Situation

Mala: Sir, my brother said he was studying algebra. What is algebra?

Sir: To put it simply, algebraconsists of the use of numbers and letters to state and solve problems.

Arun: Does that mean addition and subtraction of letters? How do we do that?

Sir: To prepare for that, let’s first learn a few things using numbers.

Equality

Whenever we add, subtract, multiply or divide two numbers, the answer we get is always another number. For example when we add 4 and 2, we get the number 6. We write this as 4 + 2 = 6. Similarly, 10 − 4 = 6 , 12 ÷ 2 = 6, 6 × 1 = 6.

Now, let us think about this in another way.

Suppose that, by performing a mathematical operation on two numbers, we have obtained the number 10. Let us find pairs of such numbers.

They could be (5 + 5), (17 − 7), (5 × 2), (20 ÷ 2) etc.

When we want to say a number obtained by adding 5 and 5, it is easier to express it by using brackets like this: (5 + 5).

(17 − 7) means a number obtained by subtracting 7 from 17.

(5 × 2) means a number obtained by multiplying 5 by 2.

(20 ÷ 2) means a number obtained by dividing 20 by 2.

Arrangement of numbers like (5 + 5), (17 − 7), (5 × 2) and (20 ÷ 2) are called expressions. The value of each of these expressions is 10, which means all these expressions are equal to each other.

Hence, we can also write this as,

(5 + 5) = (17 − 7) = (5 × 2) = (20 ÷ 2)

An expression such as (5 + 5) = (17 − 7) or (5 + 5) = (20 ÷ 2) is called an ‘equality’.

5 + 2 = 7, 8 × 1 = 8 are also equalities.