Simplifying Algebraic Fractions worksheet with 13 practice problems.

You’ve uploaded an image titled “Simplifying Algebraic Fractions” with 13 problems. Let’s solve each one step by step and explain the simplification process.

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🔢 General Rule:

To simplify a fraction (numerical or algebraic), find the greatest common factor (GCF) of the numerator and denominator, then divide both by that GCF. For algebraic fractions, also cancel common variables with their lowest exponent.

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## ✔ Solutions:

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1. $\frac{3}{12}$

- GCF of 3 and 12 is 3.
- Divide numerator and denominator by 3:
$\frac{3 \div 3}{12 \div 3} = \frac{1}{4}$

✔ Answer: $\boxed{\frac{1}{4}}$

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2. $\frac{3x}{12}$

- GCF of 3 and 12 is 3.
- $x$ is only in numerator → leave it.
- $\frac{3x \div 3}{12 \div 3} = \frac{x}{4}$

✔ Answer: $\boxed{\frac{x}{4}}$

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3. $\frac{3}{12x}$

- GCF of 3 and 12 is 3.
- $x$ is only in denominator → leave it.
- $\frac{3 \div 3}{12x \div 3} = \frac{1}{4x}$

✔ Answer: $\boxed{\frac{1}{4x}}$

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4. $\frac{12x}{3}$

- GCF of 12 and 3 is 3.
- $\frac{12x \div 3}{3 \div 3} = \frac{4x}{1} = 4x$

✔ Answer: $\boxed{4x}$

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5. $\frac{12x}{6}$

- GCF of 12 and 6 is 6.
- $\frac{12x \div 6}{6 \div 6} = \frac{2x}{1} = 2x$

✔ Answer: $\boxed{2x}$

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9. $\frac{10x}{12xy}$

- Numerator: $10x$
- Denominator: $12xy$
- GCF of 10 and 12 is 2
- Common variable: $x$ (lowest exponent = 1)
- Cancel 2 and $x$:

$\frac{10x \div 2x}{12xy \div 2x} = \frac{5}{6y}$

✔ Answer: $\boxed{\frac{5}{6y}}$

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10. $\frac{10x}{12xy^2}$

- GCF of 10 and 12 is 2
- Common variable: $x$ (only in num & den, cancel 1 power)
- $y^2$ remains in denominator

$\frac{10x \div 2x}{12xy^2 \div 2x} = \frac{5}{6y^2}$

✔ Answer: $\boxed{\frac{5}{6y^2}}$

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11. $\frac{10xy}{12xy^2}$

- GCF of 10 and 12 is 2
- Common variables: $x$ and $y$ (lowest exponent for y is 1)

Cancel 2, x, and one y:

$\frac{10xy \div 2xy}{12xy^2 \div 2xy} = \frac{5}{6y}$

✔ Answer: $\boxed{\frac{5}{6y}}$

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12. $\frac{10x^2y}{12xy^2}$

- GCF of 10 and 12 is 2
- Variables: cancel $x$ (min exponent 1) and $y$ (min exponent 1)

$\frac{10x^2y \div 2xy}{12xy^2 \div 2xy} = \frac{5x}{6y}$

✔ Answer: $\boxed{\frac{5x}{6y}}$

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13. $\frac{10x^2y^2}{12xy^2}$

- GCF of 10 and 12 is 2
- Variables: cancel $x$ (min exp 1), $y^2$ (same in num & den)

$\frac{10x^2y^2 \div 2xy^2}{12xy^2 \div 2xy^2} = \frac{5x}{6}$

✔ Answer: $\boxed{\frac{5x}{6}}$

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## 📝 Summary Table:

| Problem | Simplified Form |
|---------|---------------------|
| 1 | $\frac{1}{4}$ |
| 2 | $\frac{x}{4}$ |
| 3 | $\frac{1}{4x}$ |
| 4 | $4x$ |
| 5 | $2x$ |
| 9 | $\frac{5}{6y}$ |
| 10 | $\frac{5}{6y^2}$ |
| 11 | $\frac{5}{6y}$ |
| 12 | $\frac{5x}{6y}$ |
| 13 | $\frac{5x}{6}$ |

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## 💡 Key Tips:
- Always look for numerical GCF first.
- Then cancel common variables, reducing exponents by subtracting (numerator exponent - denominator exponent).
- If a variable appears only in numerator → it stays; only in denominator → stays in denominator.

Let me know if you’d like to see visual cancellation steps or practice more! 😊