Simplifying Algebraic Fractions Textbook Exercise - Corbettmaths - Free Printable

Let's simplify each of the given fractions step by step. We'll look for common factors in the numerator and denominator and cancel them out.

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1) $\frac{3x}{5x}$

- Both numerator and denominator have a factor of $x$.
- Cancel $x$:
$$
\frac{3x}{5x} = \frac{3}{5}
$$

✔ Answer: $\boxed{\frac{3}{5}}$

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2) $\frac{3x}{6x}$

- Both numerator and denominator have $x$ and a common numerical factor.
- Cancel $x$: $\frac{3}{6}$
- Simplify $\frac{3}{6} = \frac{1}{2}$

✔ Answer: $\boxed{\frac{1}{2}}$

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3) $\frac{3x^2}{6x}$

- Numerator: $3x^2 = 3 \cdot x \cdot x$
- Denominator: $6x = 6 \cdot x = 2 \cdot 3 \cdot x$
- Cancel common factors:
- $3$ cancels
- One $x$ cancels
- Left with: $\frac{x}{2}$

✔ Answer: $\boxed{\frac{x}{2}}$

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4) $\frac{3x^2}{8x}$

- Numerator: $3x^2 = 3 \cdot x \cdot x$
- Denominator: $8x = 8 \cdot x$
- Cancel one $x$: $\frac{3x}{8}$

✔ Answer: $\boxed{\frac{3x}{8}}$

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5) $\frac{3x^2}{7x^2}$

- Both numerator and denominator have $x^2$
- Cancel $x^2$: $\frac{3}{7}$

✔ Answer: $\boxed{\frac{3}{7}}$

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6) $\frac{3\sqrt{x}}{8\sqrt{x}}$

- Both numerator and denominator have $\sqrt{x}$
- Cancel $\sqrt{x}$: $\frac{3}{8}$

✔ Answer: $\boxed{\frac{3}{8}}$

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7) $\frac{3x}{8x^5}$

- Numerator: $3x = 3 \cdot x$
- Denominator: $8x^5 = 8 \cdot x^5$
- Cancel $x$: $\frac{3}{8x^4}$

✔ Answer: $\boxed{\frac{3}{8x^4}}$

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8) $\frac{6x}{8x^5}$

- Numerator: $6x = 2 \cdot 3 \cdot x$
- Denominator: $8x^5 = 2 \cdot 4 \cdot x^5 = 2 \cdot 2^2 \cdot x^5 = 2^3 \cdot x^5$
- Cancel common factors:
- $2$ from numerator and denominator → $6/8 = 3/4$
- Cancel $x$: $x/x^5 = 1/x^4$
- So: $\frac{3}{4x^4}$

✔ Answer: $\boxed{\frac{3}{4x^4}}$

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✔ Final Answers:

1) $\frac{3}{5}$
2) $\frac{1}{2}$
3) $\frac{x}{2}$
4) $\frac{3x}{8}$
5) $\frac{3}{7}$
6) $\frac{3}{8}$
7) $\frac{3}{8x^4}$
8) $\frac{3}{4x^4}$

Let me know if you'd like these explained in more detail!