Worksheet on Dividing Monomials

Practice the questions given in the worksheet on dividing monomials. The questions are based on dividing the term of the monomial by the term of the monomial and then simplify.

Note: When we divide two monomials we need to divide their coefficients and then divide their variables. In case of exponents with the same base we need to subtract their powers since we know that division is related to subtraction.

1. Divide a monomial by a monomial:

(i) 27x² ÷ 9x

(ii) 14m²n² ÷ 7mn

(iii) 15a⁴b³ ÷ 12a²b

(iv) 48m²n ÷ (-12mn²)

(v) (-76a²b³c) ÷ (-19abc)

(vi) 24m²n⁴ ÷ 6m²n

(vii) 27x⁴ ÷ (–x²)

(viii) abz² ÷ (-az)

(ix) (-35m⁶) ÷ 7m³

(x) m^3n³ ÷ m²n

2. Simplify the division of the monomials:

(i) (3a³) ÷ (a²)

(ii) (4x²y²z³) ÷ (xy²z²)

(iii) (12p⁶q⁶r⁶) ÷ (-3p⁴q²r)

(iv) (-x⁵z⁹) ÷ (-xz³)

(v) (15a⁵b⁷c⁴) ÷ (5a²b²c²)

(vi) (-16m³n²) ÷ (-4mn²)

(vii) (-48x⁹) ÷ (-8x³)

(viii) (35m¹¹) ÷ (7m⁷)

(ix) (63p⁷q⁸r³) ÷ (9p⁵q⁵r³)

(x) (7x²yz) ÷ (-7x²yz)

3. Divide first monomial by the second monomial:

(i) 14ab, 2b

(ii) 45x²z, 3z

(iii) 12ax⁴y, 6x⁴

(iv) 15u⁷, (-u⁵)

(v) 18mn⁴, 3mn

(vi) 56a⁴b³, 7a²b

(vii) 102a³bc, 2bc

(viii) (-80w⁴yz), 10w³z

(ix) 48x²y⁴, (-8xy)

(x) 45a³b², 9ab²

4. Divide the following monomials and write the answer in simplest form:

(i) (36ab) ÷ (-9b)

(ii) (28p⁴q³) ÷ (-4p³q)

(iii) (16p²ba²) ÷ (-2ab)

(iv) (-50a³b³) ÷ (-5a³b)

(v) (-36a⁴m⁵n⁶) ÷ (4a³m²n²)

(vi) (16m) ÷ (-4)

(vii) (20a²) ÷ (5a)

(viii) (30y²) ÷ (-10y²)

(ix) (14x³y³) ÷ (2x²)

(x) (50m²n⁴) ÷ (2mn²)

Answers for the worksheet on dividing monomials are given below to check the exact answers of the above questions on division of monomials.

Answers:

1. (i) 3x

(ii) 2mn

(iii)(5a²b²)/4

(iv) -(4m)/n

(v) 4ab²

(vi) 4n³

(vii) -27x

(viii) -bz

(ix) -5m³

(x) mn²

2. (i) 3a

(ii) 4xz

(iii) -4p²q⁴r⁵

(iv) x⁴z⁶

(v) 3a³b⁵c²

(vi) 4m²

(vii) 6x⁶

(viii) 5m⁴

(ix) 7p²q³

(x) -1

3. (i) 7a

(ii) 15x²

(iii) 2ay

(iv) -15u²

(v) 6n³

(vi) 8a²b²

(vii) 51a³

(viii) -8wy

(ix) -6xy³

(x) 5a²

4. (i) -4a

(ii) -7pq²

(iii) -8p²a

(iv) 10b²

(v) -9am³n⁴

(vi) -4m

(vii) 4a

(viii) -3

(ix) 7xy³

(x) 25mn²

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