Multiplication of Literals
In this section we will discuss about multiplication of literals
In arithmetic, we have studied multiplication as the repeated addition. For example, 2 + 2 + 2 + 2 is called 4 times 2 and is written as 4 x 3. Similarly, if a is literal, then a + a + a + a is 4 times a and is written 4 x a , this is Multiplication - Literals.
Sometimes, the sign of multiplication is confused with letter x. To avoid such confusion, we omit the sign of multiplication between a number and a literal or between two literals. Thus, when there is no sign between a literal and a number or between two literals, it is understood that the two are multiplied.
Thus, a + a + a + a = 4 x a = 4a
Similarly, the product of literals x and y is written as xy.
It should be noted that the product of the type a x 4 is not written as a4
. Conventionally, we write it as 4a
Properties of Multiplication of Literals :
As mentioned earlier that literals are used to represent numbers. Therefore, multiplications of variables obey all properties of multiplication of tables. Here, we list the properties of multiplication of variables.
For any two literals a and b, we have , ab = ba i.e. , the multiplication of variables is commutative.
For any three literals a, b and c, we have, (ab)c = a (bc) i.e. the multiplication of variables is associative.
For any literal a, we have, b x 1 = b = 1 x b. Here ‘1’ is known as the multiplication identity.
Distributive of multiplication over addition:
For any three literals a, b and c, we have (i) a (b + c) = ab + ac (ii) (b + c)a = ba + ca
Write each of the following phrases using numbers, literals and the basic operations of addition, subtraction and multiplication:
(i) 4 times x
(ii) The product of 4 and y
(iii) Multiply x by 7
(iv) a times c
(v) 3 times y added to z
3y + z
(vi) 4 times the sum of a and b
4( a + b)
(vii) 5 times x is subtracted from z
z - 5x
(viii) 8 times d
(ix) a times c added to 3
ac + 3
(x) 5 times t subtracted from s
s - 5t
Introduction to Algebra
• Addition of Literals
• Subtraction of Literals
• Multiplication of Literals
• Division of Literals
• Constants and Variables