# Test: Algebraic Fractions - Normal

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Question 1:   Simplify: $\frac{9{t}^{3}}{27{t}^{5}}$
$\frac{1}{3{t}^{2}}$
$3\frac{1}{t}$
$\frac{1}{6t}$
$\frac{1}{18{t}^{2}}$
Question 2:   Simplify $\frac{2x}{3y}\cdot \frac{3y}{2x}$
$\frac{2x}{3y}$
$\frac{3y}{2x}$
$\frac{2}{3}$
$1$
Question 3:   Write $\frac{a}{b}+\frac{b}{a}$ as a single fraction
$\frac{{a}^{2}+{b}^{2}}{ab}$
$\frac{a+b}{b+a}$
$\frac{\left(a+b\right)\left(a-b\right)}{ab}$
$\frac{a+b}{ab}$
Question 4:   Simplify: $\frac{{x}^{2}}{{y}^{3}}\cdot \frac{{y}^{2}}{{x}^{3}}$
$\frac{2x}{3y}$
$\frac{x}{y}$
$\frac{1}{xy}$
$\frac{y}{x}$
Question 5:   Simplify: $\frac{{t}^{2}}{s}:\frac{t}{{s}^{2}}$
$\frac{s}{t}$
$\frac{1}{ts}$
$ts$
$\frac{t}{s}$
Question 6:   Simplify: $\frac{pq}{{r}^{2}s}\cdot \frac{{p}^{2}r}{qs}$
$\frac{{p}^{3}{q}^{2}r}{{s}^{2}}$
$\frac{{p}^{3}r}{{r}^{2}s}$
$\frac{{p}^{2}{r}^{2}}{{r}^{2}{s}^{2}}$
$\frac{{p}^{3}}{r{s}^{2}}$
Question 7:   Simplify: $\frac{1}{x}+\frac{2}{x}+\frac{3}{x}$
$\frac{1}{x}$
$\frac{6}{x}$
$\frac{9}{x}$
$\frac{6}{{x}^{3}}$
Question 8:   Simplify: $\frac{x}{2}+\frac{x}{3}+\frac{x}{4}$
$\frac{5x}{9}$
$1\frac{7}{12}x$
$\frac{x}{3}$
$1\frac{1}{12}x$
Question 9:   Simplify: $\frac{2}{x}+\frac{3}{4}x$
$\frac{3{x}^{2}-8}{x}$
$\frac{3{x}^{2}+8}{4x}$
$\frac{2+3x}{4x}$
$\frac{x\left(3x-8\right)}{4}$
Question 10:   Simplify: $x+\frac{x+y}{2}-\frac{x+y}{3}$
$\frac{7x-3y}{6}$
$\frac{2x+2y}{3}$
$\frac{7x+y}{6}$
$\frac{5x+3y}{6}$