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
Algebra Page
6th Grade Page
From Addition of Literals to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Oct 10, 24 05:15 PM
Oct 10, 24 10:06 AM
Oct 10, 24 03:19 AM
Oct 09, 24 05:16 PM
Oct 08, 24 10:53 AM
● Literal Numbers - Worksheets
Worksheet on Addition of Literals
Worksheet on Subtraction of Literals
Worksheet on Multiplication of Literals
Worksheet on Division of Literals
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.