DIVISION OF A MONOMIAL BY A MONOMIAL

About "Division of a monomial by a monomial"

Division of a monomial by a monomial :

Here we are going to see how to divide a monomial by another monomial.

1)  Division of monomials are also monomials.

2)  Coefficient of the answer

= Coefficient of the first monomial by (Coefficient of the second monomial)

3)  Laws of exponents a^m / aⁿ  =  a^m-n s useful, in finding the division of the terms.

4)  The division of a and b can be represented as: a/b, a ÷ b, a divided by b.

Let us look into some examples based on the above concept.

Example 1 :

Simplify 5a²b²c²  ÷  15abc

Solution :

5a²b²c²  ÷  15abc  =  5a²b²c² /15abc

By dividing 5 and 15, we get 3 in the denominator.

By dividing a² by a, we get a in the numerator.

By dividing b² by b, we get b in the numerator.

By dividing c² by c, we get c in the numerator.

Hence the answer is abc/3

Example 2 :

Simplify 16x⁴ ÷ 32x

Solution :

16x⁴ ÷ 32x  =  16x⁴ /32x

By dividing 16 and 32, we get 2 in the denominator.

By dividing x⁴ by x, we get x³ in the numerator.

Hence the answer is x³/2

Example 3 :

Simplify -42y³ ÷ 7y²

Solution :

-42y³ ÷ 7y²  =  -42y³ / 7y²

By dividing 42 by 7, we get 6 in the numerator.

By dividing y³ by y², we get y in the numerator.

Hence the answer is -6y

Example 4 :

Simplify 30 a³b³c³ ÷ 45 abc

Solution :

30 a³b³c³ ÷ 45 abc  =  30 a³b³c³ /45 abc

by simplifying 30 and 45, we get 2 in the numerator and 3 in the denominator.

By dividing a³ by a, we get a² in the numerator.

By dividing b³ by b, we get b² in the numerator.

By dividing c³ by c, we get c² in the numerator.

Hence the answer is (2/3) a²  b² c²

Example 5 :

Simplify 72 l⁴m⁵n⁸  ÷  (-8l²m²n³)

Solution :

72 l⁴m⁵n⁸  ÷  (-8l²m²n³)  =  72 l⁴m⁵n⁸ /(-8l²m²n³)

by simplifying 72 and -8, we get 9 in the numerator.

By dividing l⁴ by l², we get l² in the numerator.

By dividing m⁵ by m², we get m³ in the numerator.

By dividing n⁸ by n³, we get n⁵ in the numerator.

Hence the answer is 9 l²  m² n²

Example 6 :

Simplify 25x³y²  ÷  15x²y

Solution :

25x³y²  ÷  15x²y  =  25x³y² /15x²y

by simplifying 25 and 15, we get 5 in the numerator and 3 in the denominator.

By dividing x³ by x², we get x in the numerator.

By dividing y² by y, we get y in the numerator.

Hence the answer is (5/3)xy

Example 7 :

Simplify (7m² - 6m)  ÷  m

Solution :

(7m² - 6m)  ÷  m  =  (7m² - 6m)/m

  =  (7m²/m) - (6m/m)

  =  7m - 6

Hence the answer is 7m - 6.

After having gone through the stuff given above, we hope that the students would have understood "Division of a monomial by a monomial". 

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