Addition of Literals(variables) follow all the properties of addition of numbers.
Suppose we are asked to find the sum of two numbers, say 3 and 4. The sum of 3 and 4 is denoted by 3 + 4. Exactly in the same way, the sum of the literal x and a number 8 is denoted by x + 8 and is read ‘x plus 8’, which can also be read as ‘8 more than x,’ or ‘increase x by 8’.
Similarly, y more than a literal x is written as x + y. We can also read x + y as the sum of x and y.
(x + y) + z means that the sum of literals x and y is added to the literal z whereas x + ( y + z) means that the literal x is added to the sum of literals y and z.
properties of Addition of Literals
Since literals are used to represent numbers. Therefore, addition of variables obeys all properties of addition of numbers. Here, we list the properties of addition of variables.
Commutativity : For any addition of two literals a and b, we have a + b = b + a
Associativity : For any three literals a, b and c, we have (a + b) + c = a + (b + c)
Identity : For any literal a, we have a + 0 = a = 0 + a, where 0 is known as additive identity
Illustration : Write each of the following phrases using numbers, literals and the basic operation of addition:
(i) The sum of y and 2. Solution: y + 2
(ii) 4 more than a number y. Solution: y +4
(iii) x added to 8. Solution: x + 8
(iv) Increase x by 5 Solution: x + 5
(v) The sum of x and 6 added to z Solution: (x + 6) + z
(vi) y added to the sum of z and 4 Solution: y + (z + 4)