Practice using the Worksheet on Dividing Monomials and improve your algebra basics. You can solve different types of algebraic expressions much easily provided you have a grip on the Division of Monomials Concept. All the Problems in the Dividing Monomials Worksheet are designed with a simple approach so that you will become familiar with the concept step by step. The Free Printable Math Worksheet on Division of Monomials available in PDF Formats can be accessed for free of cost and you can practice regularly.

See More:

- Worksheet on Addition and Subtraction of Polynomials
- Worksheet on Multiplying Monomial and Binomial
- Worksheet on Multiplying Monomial and Polynomial

## Dividing Monomials Worksheet with Answers

**I. Divide the following monomials and write the answer in simplest form:
**(i) (48xy) ÷ (4x)

(ii) (12p

^{6}q

^{4}) ÷ (-6p

^{2}q

^{2})

(iii) (26m

^{2}pn

^{2}) ÷ (-2mn)

(iv) (-96x

^{4}y

^{3}) ÷ (-8x

^{2}y)

(v) (-56b

^{2}x

^{3}y

^{5}) ÷ (4bx

^{2}y

^{2})

(vi) (48ab) ÷ (-4)

(vii) (75m

^{2}n) ÷ (5n)

**Solution:**

(i) Given monomials are 48xy,4x

Now we have to write each term in expanded form and then cancel the terms which are common to both numerator and denominator.

48xy/4x=6 × 8 × x × y/2 × 2 × x

=24y/2

=12y

Therefore, By dividing (48xy) with (4x) we get 12y.

(ii) Given (12p^{6}q^{4}) ÷ (-6p^{2}q^{2})

Now we have to write each term in expanded form and then cancel the terms which are common to both numerator and denominator.

(12p^{6}q^{4}) / (-6p^{2}q^{2})=2 × 6 × p × p ×p ×p × p ×p × q × q × q × q/-6 × p × p × q × q

=-2p^{4}q^{2}

Therefore, By dividing 12p^{6}q^{4} with -6p^{2}q^{2} we get -2p^{4}q^{2}.

(iii) Given (26m^{2}pn^{2}) ÷ (-2mn)

Now we have to write each term in expanded form and then cancel the terms which are common to both numerator and denominator.

26m^{2}pn^{2}/-2mn=2 × 13 × m × m × p × n × n/-2 ×m ×n

=-13mpn

Therefore, By dividing 26m^{2}pn^{2} with -2mn we get -13mpn.

(iv) Given (-96x^{4}y^{3}) ÷ (-8x^{2}y)

Now we have to write each term in expanded form and then cancel the terms which are common to both numerator and denominator.

-96x^{4}y^{3}/8x^{2}y=-12 × 8 × x × x × x × x × y × y × y/8 × x × x ×y

=-12 x^{2}y^{2}

Therefore, By dividing -96x^{4}y^{3} with-8x^{2}y we get -12 x^{2}y^{2}.

(v) Given (-56 b^{2}x^{3}y^{5}) ÷ (4bx^{2}y^{2})

Now we have to write each term in expanded form and then cancel the terms which are common to both numerator and denominator.

-56 b^{2}x^{3}y^{5}/4bx^{2}y^{2}= -4 × 14 × b × b × x × x × x × y × y × y × y × y/4 × b × x × x × y × y

=-14bxy^{3}

Therefore, By dividing -54b^{2}x^{3}y^{5} with 4bx^{2}y^{2} we get -14bxy^{3}.

(vi) Given (48ab) ÷ (-4)

Now we have to write each term in expanded form and then cancel the terms which are common to both numerator and denominator.

48ab/-4=12 × 4 × a × b/-4

=-12ab

Therefore, By dividing 48ab with -4 we get -12ab.

(vii) Given (75m^{2}n) ÷ (5n)

Now we have to write each term in expanded form and then cancel the terms which are common to both numerator and denominator.

75m^{2}n/5n= 15 × 5 × m × m × n/5 × n

=15m^{2}

Therefore, By dividing 75m^{2}n with 5n we get 15m^{2} .

**
II. Divide a monomial by a monomial:
**(i) 60a

^{2}÷ 5a

(ii) 63x

^{2}y

^{2}÷ 7xy

(iii) 48a

^{4}b

^{6}÷ 12a

^{2}b

^{2 }(iv) 108m

^{4}n

^{3}÷ (-18m

^{2}n

^{2})

(v) (-46a

^{4}b

^{5}c

^{2}) ÷ (-23a

^{2}bc)

**Solution:**

(i) Given, 60a^{2} ÷ 5a

Now we have to write each term in expanded form and then cancel the terms which are common to both numerator and denominator.

60a^{2}/5a= 12 × 5 × a × a/5 × a

=12a

Hence, By dividing 60a^{2} with 5a we get 12a.

(ii) Given, 63x^{2}y^{2} ÷ 7xy

Now we have to write each term in expanded form and then cancel the terms which are common to both numerator and denominator.

63x^{2}y^{2}/7xy=7 × 9 × x × x × y× y/7 × x × y

=9xy

Therefore, By dividing 63x^{2}y^{2} with 7xy we get 9xy.

(iii) Given, 48a^{4}b^{6} ÷ 12a^{2}b^{2}

Now we have to write each term in expanded form and then cancel the terms which are common to both numerator and denominator.

48a^{4}b^{6}/12a^{2}b^{2}= 12 × 4 × a × a × a × a × b × b × b × b × b × b/4 × 3 × a × a × b × b

=4a2b4

Therefore, By dividing 48a^{4}b^{6} with 12a^{2}b^{2} we get 4a2b4.

(iv) Given, 108m^{4}n^{3} ÷ (-18m^{2}n^{2})

Now we have to write each term in expanded form and then cancel the terms which are common to both numerator and denominator.

108m^{4}n^{3}/-18m^{2}n^{2}= 18 × 6 × m × m × m × m × n × n × n/-6 × 3 × m × m × n × n

=-6m2n

Therefore, By dividing 108m^{4}n^{3 } with -18m^{2}n^{2} we get -6m2n.

(v) Given, (-46a^{4}b^{5}c^{2}) ÷ (-23a^{2}bc)

Now we have to write each term in expanded form and then cancel the terms which are common to both numerator and denominator.

-46a^{4}b^{5}c^{2}/-23a^{2}bc= -23 × 2 × a × a × a × a × b × b × b × b × b × c × c/-23 × a × a × b × b × c

=2a2b4c

Hence, By dividing -46a^{4}b^{5}c^{2} with -23a^{2}bc we get 2a2b4c.

**III. Divide first monomial by the second monomial:
**(i) 30xy, 6x

(ii) 75a

^{4}b, 5b

(iii) 48ab

^{4}c, 8b

^{2}c

(iv) 30a

^{5}, (-a

^{2})

(v) 22a

^{2}b

^{5}, 2ab

**Solution:**

(i) Given 30xy, 6x

30xy/6x=5y

Hence, By dividing the first monomial 30xy with the second monomial 6x we get 5y.

(ii) Given 75a^{4}, 5b

75a^{4}b/5b=15a^{4}

Therefore, By dividing the first monomial 75a^{4}b with the second monomial 5b we get 15a^{4}.

(iii) Given 48ab^{4}c, 8b^{2}c

48ab^{4}c/8b^{2}c=6ab^{2}

Therefore, By dividing the first monomial 48ab4c with the second monomial 8b2c we get 6ab^{2}.

(iv) Given 30a^{5}, (-a^{2})

30a^{5}5/-a^{2}=-30a^{3}

Hence, By dividing the first monomial 30a^{5} with the second monomial -a^{2} we get -30a^{3}.

(v) Given 22a^{2}b^{5}, 2ab

22a^{2}b^{5}/ 2ab=11ab^{4}

Therefore, By dividing the first monomial 22a2b5 with the second monomial 2ab we get 11ab^{4}.

**IV. Simplify the division of the monomials
**(i) (-18x

^{8}) ÷ (-9x

^{2})

(ii) (40a

^{4}b

^{8}c

^{4}) ÷ (5a

^{2}b

^{2}c

^{2})

(iii) (14x

^{4}y

^{3}z

^{2}) ÷ (-2x

^{2}yz)

(iv) (81a

^{7}b

^{8}c

^{3}) ÷ (9a

^{4}b

^{3}3c

^{3})

(v) (51x

^{6}y

^{5}z

^{4}) ÷ (-3x

^{4}y

^{2}z)

**Solution:**

(i) Given (-18×8) ÷ (-9x^{2})

-18x^{8}/-9x^{2}=2x^{6}

Hence, By dividing -18x^{8} with -9x^{2} we get 2x^{6}.

(ii) Given (40a^{4}b^{8}c^{4}) ÷ (5a^{2}b^{2}c^{2})

40a^{4}b^{8}c^{4}/5a^{2}b^{2}c^{2}=8a^{2}b^{6}c^{2}

Hence, By dividing 40a^{4}4b^{8}c^{4} with 5a^{2}b^{2}c^{2} we get 8a^{2}b^{6}c^{2}.

(iii) Given (14x^{4}4y^{3}z^{2}) ÷ (-2x^{2}yz)

14x^{4}y^{3}z^{2}/-2x^{2}yz=-7x^{2}y^{2}z

Hence, By dividing 14x^{4}y^{3}z^{2} with -2x^{2}yz we get -7x^{2}y^{2}z.

(iv) Given (81a^{7}b^{8}c^{3}) ÷ (9a^{4}b3c^{3})

81a^{7}b^{8}c^{3}/9a4b3c^{3}=9a^{3}b^{5}

Hence, By dividing 81a^{7}b^{8}c^{3} with 9a4b3c^{3} we get 9a^{3}b^{5}.

(v) Given (51x^{6}y5z4) ÷ (-3x^{4}y^{2}z)

51x^{6}y5z4/-3x^{4}y^{2}z=-17x^{2}2y^{3}z^{3}

Hence, By dividing 51x^{6}y5z4 with -3x^{4}y^{2}z we get -17x^{2}2y^{3}z^{3}.