Let’s simplify each fraction one by one. We’ll cancel out common factors in the numerator and denominator — both numbers and variables.
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1) $\frac{3x}{5x}$
→ The $x$ in top and bottom cancels (as long as $x \ne 0$).
→ So we get: $\frac{3}{5}$
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2) $\frac{3x}{6x}$
→ Cancel $x$: $\frac{3}{6}$
→ Simplify $\frac{3}{6} = \frac{1}{2}$
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3) $\frac{3x^2}{6x}$
→ Numbers: $\frac{3}{6} = \frac{1}{2}$
→ Variables: $\frac{x^2}{x} = x^{2-1} = x$
→ So: $\frac{1}{2} \cdot x = \frac{x}{2}$
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4) $\frac{3x^2}{8x}$
→ Numbers: 3 and 8 have no common factor → stay as is
→ Variables: $\frac{x^2}{x} = x$
→ So: $\frac{3x}{8}$
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5) $\frac{3x^2}{7x^2}$
→ Numbers: 3 and 7 → no simplification
→ Variables: $\frac{x^2}{x^2} = 1$
→ So: $\frac{3}{7}$
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6) $\frac{3\sqrt{x}}{8\sqrt{x}}$
→ As long as $x > 0$, $\sqrt{x}$ cancels out
→ So: $\frac{3}{8}$
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7) $\frac{3x}{8x^5}$
→ Numbers: 3 and 8 → no simplification
→ Variables: $\frac{x}{x^5} = x^{1-5} = x^{-4} = \frac{1}{x^4}$
→ So: $\frac{3}{8x^4}$
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8) $\frac{6x}{8x^5}$
→ Numbers: $\frac{6}{8} = \frac{3}{4}$
→ Variables: $\frac{x}{x^5} = \frac{1}{x^4}$
→ So: $\frac{3}{4x^4}$
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Final Answer:
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) $\frac{3}{4x^4}$
Parent Tip: Review the logic above to help your child master the concept of dividing algebraic fractions worksheet.
