Page 205 - Math_Genius_V1.0_C8_Flipbook

E:\Working\Focus_Learning\Math_Genius-8\Open_Files\11_Chapter_8\Chapter_8
\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

Division of Algebraic Expressions

We have learnt multiplication of algebraic expressions. Now, we will learn the division of algebraic
expressions. Division is essentially the reverse of multiplication. Let’s see how.

We know that 8 multiplied by 9 equals 72, so dividing 72 by 9 gives us 8, or dividing 72 by 8 gives
us 9.
We follow the same rule for the division of algebraic expressions.

2
Since, 4x(x + 2) = 4x + 8x
2
Therefore, (4x + 8x) ÷ 4x = x + 2
2
And (4x + 8x) ÷ (x + 2) = 4x
Now, let us learn how to divide one expression by another in detail. To start, we’ll focus on dividing
one monomial by another monomial.

Dividing a Monomial by another Monomial

To divide a monomial by another monomial, we should follow these steps:

Step 1: Find the quotient of the numerical coefficients.

Step 2: Find the quotient of the variables using the laws of exponents and powers.
Step 3: Find the product of the resultant obtained in steps 1 and 2.

3 2
Example 14: Divide 45a b by 9ab.
3 2
Solution: We have, 45a b ÷ 9ab
So, the quotient of the numerical coefficient is 45 ÷ 9 = 5

ab  a m 
32
Quotient of the variables = = a 31 b ⋅ 21 Q = a mn
−
−
−
ab   a n  
2
= a b
3 2
2
Thus, 45a b ÷ 9ab = 5a b.
Alternative Method:
a
5
a
45ab 3 × 3 × × a ××× b × b
32
=
9ab 3 × 3 × a × b
2
= 5a b
Dividing a Binomial by a Monomial
To divide a binomial by a monomial, we should follow these steps:
ab a b
+
Step 1: Write the binomial (a + b) and monomial c as = + .
c c c
Step 2: Then follow the same steps as we used for dividing a monomial by another monomial.
Example 15: Divide (42x – 63) by 7.

42x − 63 42x 63
Solution: We have, (42x – 63) ÷ 7 = = − = 6x − 9
7 7 7

203 Algebraic Expressions