Practice worksheet for simplifying expressions by dividing monomials, featuring 22 problems with algebraic terms and a QR code in the top right corner.

Sure! Let’s solve each of these dividing monomials problems step by step. The key rules to remember are:

- Divide the coefficients (numbers) normally.
- For variables with exponents, subtract the exponents when dividing:
$ \frac{x^a}{x^b} = x^{a-b} $
- If a variable appears in the numerator but not the denominator (or vice versa), it remains as is (with exponent 1 or -1, which we write as just the variable or its reciprocal).
- Cancel common variables and simplify signs.

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Let’s go one by one:

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1) $ 4x^2y^3 \div 2y = \frac{4x^2y^3}{2y} $

- Coefficients: $ \frac{4}{2} = 2 $
- $ x^2 $ → no x in denominator → stays $ x^2 $
- $ y^3 \div y = y^{3-1} = y^2 $

✔ Answer: $ 2x^2y^2 $

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2) $ \frac{-28x^2y^2z}{4yz} $

- Coefficients: $ \frac{-28}{4} = -7 $
- $ x^2 $ → no x in denominator → stays $ x^2 $
- $ y^2 \div y = y^{2-1} = y $
- $ z \div z = z^{1-1} = z^0 = 1 $ → cancels out

✔ Answer: $ -7x^2y $

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3) $ \frac{27xzy}{-3yz} $

Note: $ xzy = xyz $, same as $ xyz $

- Coefficients: $ \frac{27}{-3} = -9 $
- $ x $ → no x in denominator → stays $ x $
- $ y \div y = 1 $
- $ z \div z = 1 $

✔ Answer: $ -9x $

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4) $ -30xz^2 \div 3xz^2 = \frac{-30xz^2}{3xz^2} $

- Coefficients: $ \frac{-30}{3} = -10 $
- $ x \div x = 1 $
- $ z^2 \div z^2 = 1 $

✔ Answer: $ -10 $

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5) $ \frac{-12x^2y^3z}{2yz} $

- Coefficients: $ \frac{-12}{2} = -6 $
- $ x^2 $ → no x in denominator → stays $ x^2 $
- $ y^3 \div y = y^2 $
- $ z \div z = 1 $

✔ Answer: $ -6x^2y^2 $

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6) $ -24x^2y^3 \div 3y = \frac{-24x^2y^3}{3y} $

- Coefficients: $ \frac{-24}{3} = -8 $
- $ x^2 $ → stays
- $ y^3 \div y = y^2 $

✔ Answer: $ -8x^2y^2 $

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7) $ \frac{-14xzy}{-2yz} $

- Coefficients: $ \frac{-14}{-2} = 7 $
- $ x $ → stays
- $ y \div y = 1 $
- $ z \div z = 1 $

✔ Answer: $ 7x $

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8) $ -8xz^2 \div 4xz^2 = \frac{-8xz^2}{4xz^2} $

- Coefficients: $ \frac{-8}{4} = -2 $
- $ x \div x = 1 $
- $ z^2 \div z^2 = 1 $

✔ Answer: $ -2 $

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9) $ \frac{-9xzy}{-3yz} $

- Coefficients: $ \frac{-9}{-3} = 3 $
- $ x $ → stays
- $ y \div y = 1 $
- $ z \div z = 1 $

✔ Answer: $ 3x $

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10) $ -8xz^2 \div 2xz^2 = \frac{-8xz^2}{2xz^2} $

- Coefficients: $ \frac{-8}{2} = -4 $
- $ x \div x = 1 $
- $ z^2 \div z^2 = 1 $

✔ Answer: $ -4 $

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11) $ 6xz^2 \div 3xz^2 = \frac{6xz^2}{3xz^2} $

- Coefficients: $ \frac{6}{3} = 2 $
- $ x \div x = 1 $
- $ z^2 \div z^2 = 1 $

✔ Answer: $ 2 $

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12) $ \frac{-8x^2y^3z}{2yz} $

- Coefficients: $ \frac{-8}{2} = -4 $
- $ x^2 $ → stays
- $ y^3 \div y = y^2 $
- $ z \div z = 1 $

✔ Answer: $ -4x^2y^2 $

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13) $ \frac{-24xzy}{-4yz} $

- Coefficients: $ \frac{-24}{-4} = 6 $
- $ x $ → stays
- $ y \div y = 1 $
- $ z \div z = 1 $

✔ Answer: $ 6x $

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14) $ \frac{32x^2y^2z}{4yz} $

- Coefficients: $ \frac{32}{4} = 8 $
- $ x^2 $ → stays
- $ y^2 \div y = y $
- $ z \div z = 1 $

✔ Answer: $ 8x^2y $

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15) $ -32xz^2 \div 4xz^2 = \frac{-32xz^2}{4xz^2} $

- Coefficients: $ \frac{-32}{4} = -8 $
- $ x \div x = 1 $
- $ z^2 \div z^2 = 1 $

✔ Answer: $ -8 $

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16) $ -8x^2y^3 \div 4y = \frac{-8x^2y^3}{4y} $

- Coefficients: $ \frac{-8}{4} = -2 $
- $ x^2 $ → stays
- $ y^3 \div y = y^2 $

✔ Answer: $ -2x^2y^2 $

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17) $ 24xz^2 \div 4xz^2 = \frac{24xz^2}{4xz^2} $

- Coefficients: $ \frac{24}{4} = 6 $
- $ x \div x = 1 $
- $ z^2 \div z^2 = 1 $

✔ Answer: $ 6 $

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18) $ \frac{14xzy}{-2yz} $

- Coefficients: $ \frac{14}{-2} = -7 $
- $ x $ → stays
- $ y \div y = 1 $
- $ z \div z = 1 $

✔ Answer: $ -7x $

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19) $ -9xz^2 \div 3xz^2 = \frac{-9xz^2}{3xz^2} $

- Coefficients: $ \frac{-9}{3} = -3 $
- $ x \div x = 1 $
- $ z^2 \div z^2 = 1 $

✔ Answer: $ -3 $

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20) $ 12xz^2 \div 3xz^2 = \frac{12xz^2}{3xz^2} $

- Coefficients: $ \frac{12}{3} = 4 $
- $ x \div x = 1 $
- $ z^2 \div z^2 = 1 $

✔ Answer: $ 4 $

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21) $ 27xz^2 \div 3xz^2 = \frac{27xz^2}{3xz^2} $

- Coefficients: $ \frac{27}{3} = 9 $
- $ x \div x = 1 $
- $ z^2 \div z^2 = 1 $

✔ Answer: $ 9 $

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22) $ \frac{-16x^2y^3z}{2yz} $

- Coefficients: $ \frac{-16}{2} = -8 $
- $ x^2 $ → stays
- $ y^3 \div y = y^2 $
- $ z \div z = 1 $

✔ Answer: $ -8x^2y^2 $

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## ✔ Final Answers Summary:

1) $ 2x^2y^2 $
2) $ -7x^2y $
3) $ -9x $
4) $ -10 $
5) $ -6x^2y^2 $
6) $ -8x^2y^2 $
7) $ 7x $
8) $ -2 $
9) $ 3x $
10) $ -4 $
11) $ 2 $
12) $ -4x^2y^2 $
13) $ 6x $
14) $ 8x^2y $
15) $ -8 $
16) $ -2x^2y^2 $
17) $ 6 $
18) $ -7x $
19) $ -3 $
20) $ 4 $
21) $ 9 $
22) $ -8x^2y^2 $

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