Addition of literals obey all properties of addition of numbers. Suppose we are asked to find the sum of two numbers, say 3 and 5. The sum of 3 and 5 is denoted by 3 + 5. Exactly in the same way, the sum of the literal y and a number 7 is denoted by y + 7 and is read as ‘y plus 7’. y + 7 can also be read as ‘7 more than y or increase y by 7’.
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.
Let us consider an algebraic entity ‘m’ and we want to add 25 to it. We write this operation as m + 25, just as we do for arithmetical quantities. We may also add one quantity m to another quantity n and this process is represented by m + n. The sum of m and 25 is written as m + 25.
Sum of two literal numbers m and n is written as m + n.
The sum of m and m is written as m + m = 2m.
Sum of m, n and 5 is written as = m + n + 5.
Properties of Addition of Literals:
Since literals are used to represent numbers. Here, we list the properties of addition of literals.
Commutativity: For any two literals a and b, we have
a + b = b + a
2 + x = x + 2
Associativity: For any three literals a, b and c, we have
(a + b) + c = a + (b + c)
(3 + x) + y = 3 + (x + y)
Identity: For any literals a, we have
a + 0 = a = 0 + a
5 + 0 = 5 = 0 + 5
Here ‘0’ is known as the additive identity.
Problems on Addition of Literals
Write each of the following phrases using numbers, literals and the basic operation of addition :
(i) The sum of x and 3.
Answer: x + 3
(ii) The sum of 10 and z.
Answer: 10 + z
(iii) The sum of x and y.
Answer: x + y
(iv) 3 more than a number x.
Answer: x + 3
(v) 100 more than a number p.
Answer: p + 100
(vi) x added to 9.
Answer: x + 9
(vii) m added to 50.
Answer: m + 50
(viii) Increase x by 4.
Answer: x + 4
(ix) Increase z by 10.
Answer: z + 10
(x) The sum of x and 5 added to y.
Answer: (x + 5) + y
(xi) The sum of m and 25 added to n.
Answer: (m + 25) + n
(xii) The sum of x and y added to z.
Answer: (x + y) + z
(xiii) The sum of a and b added to 5.
Answer: (a + b) + 5
(xiv) x added to the sum of y and 4.
Answer: x + (y + 4)
(xv) 5 added to the sum of a and b.
Answer: 5 + (a + b)
(xvi) a added to the sum of y and z.
Answer: a + (y + z)
Properties of Multiplication of Literals
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