Division of literals obeys all operation of division of numbers.
In arithmetic, we have studied that the division sign ‘÷’ read as ‘by’ between two numbers means that the number on the left of the division sign is to be divided by the number on the right.
For example:
15 ÷ 3 means that the number 15 on the left of the division sign is to be divided by the number 3 on the right of division sign.
In the case of literal numbers also x ÷ y read as ‘x by y’ means that the literal x is to be divided by the literal y and is written as x/y.
Thus 25 divided by a is written as 25/a and y divided by 5 written as y/5. It should be noted that 1/5 of y or y divided by 5 is also written as y/5.
Similarly, x divided by 10 is x/10. Quotient of 5 by z is 5/z.
Examples on Division of Literals:
Write each of the following phrases using numbers, literals and the
basic operations of addition, subtraction, multiplication and
division:
1. Quotient of x by 4 is added to y.
Solution: We have,
Quotient of x by 4 = x/4
Therefore, quotient of x by 4 added to y = x/4 + y
2. Quotient of z by 6 is multiplied by y.
Solution: We have,
Quotient of z by 6 = z/6
Therefore, quotient of z by 6 is multiplied by y = z/6 × y = zy/6
3. Quotient of x by y added to the product of x and y.
Solution: We have,
Question of x by y = x/y
And product of x and y = xy
Therefore, quotient of x by y and to product of x and y = x/y + xy.
4. 100 taken away from the quotient of 5m by 2x.
Solution:
We have,
Quotient of 5m by 2x = 5m/2x.
Therefore, 100 taken away from the quotient of 5m by 2x = 5m/2x  100
5. Product of 4 and a divided by the difference of 5 and a.
Solution: Product of 4 and a = 4a
Difference of 5 and a = (5  a)
Thus, we have 4a ÷ (5  a)
or, 4a/(5  4)
6. Express the share of each child algebraically if x apples were equally distributed among four children.
Solution: Total number of Apple = x
Number of children = 4
Therefore, each children gets x ÷ 4 = x/4 apples.
7. Quotient of x by 2 subtracted from 10 less than x
Solution: We have,
Quotient of x by 2 = x/2
10 less than x = (x  10)
Thus, we have (x  10)  x/2
Properties of Division of Literals
For any literal number a
(i) a ÷ a = 1
(ii) 0 ÷ a = 0
(iii) a ÷ 1 = a
Division of literals is neither commutative nor associative.
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