Dividing Monomials - Algebra Worksheets - Free Printable

You've uploaded an image showing a math worksheet on dividing monomials. The example at the top explains the process:

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✔ Example Breakdown:

> Divide:
> \(\frac{(6x^2y)}{(2x^2y)}\)

Step 1: Divide the coefficients.
→ \( \frac{6}{2} = 3 \)

Step 2: Divide the variables by subtracting exponents.
→ For \(x\): \(x^{2-2} = x^0 = 1\)
→ For \(y\): \(y^{1-1} = y^0 = 1\)

So, \(3 \cdot 1 \cdot 1 = 3\)

✔ Answer: 3

*(Note: The worksheet says “Answer: 2xy” — that appears to be a mistake! It should be 3. We’ll use correct math for the rest.)*

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Now let’s solve all 10 problems using the same method:

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🧮 Problem 1:

\(\frac{6x^2y}{2x^2y}\)
→ Coefficients: \(6 ÷ 2 = 3\)
→ \(x^{2-2} = x^0 = 1\)
→ \(y^{1-1} = y^0 = 1\)
✔ Answer: 3

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🧮 Problem 2:

\(\frac{4x^3y^6}{2x^3y^5}\)
→ Coefficients: \(4 ÷ 2 = 2\)
→ \(x^{3-3} = x^0 = 1\)
→ \(y^{6-5} = y^1 = y\)
✔ Answer: 2y

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🧮 Problem 3:

\(\frac{5x^4y^3}{15x^2y}\)
→ Coefficients: \(5 ÷ 15 = \frac{1}{3}\)
→ \(x^{4-2} = x^2\)
→ \(y^{3-1} = y^2\)
✔ Answer: \(\frac{1}{3}x^2y^2\)

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🧮 Problem 4:

\(\frac{6x^2y}{3x^2}\)
→ Coefficients: \(6 ÷ 3 = 2\)
→ \(x^{2-2} = x^0 = 1\)
→ \(y^{1-0} = y\) (since denominator has no y, exponent is 0)
✔ Answer: 2y

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🧮 Problem 5:

\(\frac{9x^3y^5}{3x^2y}\)
→ Coefficients: \(9 ÷ 3 = 3\)
→ \(x^{3-2} = x^1 = x\)
→ \(y^{5-1} = y^4\)
✔ Answer: 3xy⁴

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🧮 Problem 6:

\(\frac{8x^3y^7}{2y^7}\)
→ Coefficients: \(8 ÷ 2 = 4\)
→ \(x^{3-0} = x^3\) (no x in denominator → exponent 0)
→ \(y^{7-7} = y^0 = 1\)
✔ Answer: 4x³

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🧮 Problem 7:

\(\frac{12x^2y^3}{4xy^2}\)
→ Coefficients: \(12 ÷ 4 = 3\)
→ \(x^{2-1} = x^1 = x\)
→ \(y^{3-2} = y^1 = y\)
✔ Answer: 3xy

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🧮 Problem 8:

\(\frac{18xy^2}{9xy^2}\)
→ Coefficients: \(18 ÷ 9 = 2\)
→ \(x^{1-1} = x^0 = 1\)
→ \(y^{2-2} = y^0 = 1\)
✔ Answer: 2

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🧮 Problem 9:

\(\frac{4x^3y^2}{4x^2y}\)
→ Coefficients: \(4 ÷ 4 = 1\)
→ \(x^{3-2} = x^1 = x\)
→ \(y^{2-1} = y^1 = y\)
✔ Answer: xy

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🧮 Problem 10:

\(\frac{x^3y^3}{x^2y^3}\)
→ Coefficients: \(1 ÷ 1 = 1\)
→ \(x^{3-2} = x^1 = x\)
→ \(y^{3-3} = y^0 = 1\)
✔ Answer: x

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## ✔ Final Answers:

1. 3
2. 2y
3. \(\frac{1}{3}x^2y^2\)
4. 2y
5. 3xy⁴
6. 4x³
7. 3xy
8. 2
9. xy
10. x

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## 💡 Key Rules Used:

- Divide coefficients (numbers) normally.
- For variables, subtract exponents: \(\frac{x^a}{x^b} = x^{a-b}\)
- Any variable with exponent 0 becomes 1 (so you can omit it).
- If a variable doesn’t appear in the denominator, treat its exponent as 0.

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