# Test: Algebraic Fractions - Ambitious

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Question 1:   Simplify: $\frac{3x}{2{y}^{3}}\cdot \frac{6xy}{9{x}^{2}}$
$\frac{1}{{y}^{2}}$
$\frac{x}{{y}^{2}}$
$\frac{3}{{y}^{3}}$
$\frac{3}{{y}^{2}}$
Question 2:   Simplify: $\frac{{a}^{2}}{{b}^{2}}\cdot \frac{2ab}{3a}$
$\frac{2}{3b}$
$\frac{2{a}^{2}}{3{b}^{2}}$
$\frac{2{a}^{2}}{3b}$
$0$
Question 3:   Simplify: $\frac{4{x}^{2}{y}^{2}}{3{z}^{2}}\cdot \frac{5{y}^{2}z}{2xz}\cdot \frac{2x}{{y}^{2}z}$
$\frac{8{x}^{2}{y}^{2}}{3{z}^{2}}$
$\frac{20{x}^{2}{y}^{2}}{3{z}^{3}}$
$\frac{8{z}^{3}{y}^{2}}{3x}$
$\frac{20x{y}^{2}}{3{z}^{2}}$
Question 4:   Simplify: $\frac{x{y}^{2}}{z}÷\frac{{x}^{2}y}{2z}$
$2\frac{x}{y}$
$2y$
$2\frac{y}{x}$
$2x$
Question 5:   Simplify: $\frac{3{p}^{2}q}{4r{s}^{2}}÷\frac{9p{r}^{2}}{12{q}^{2}s}$
$\frac{2{q}^{3}}{3p{r}^{2}}$
$\frac{{q}^{3}}{{r}^{2}}$
$\frac{3q}{sr}$
$\frac{p{q}^{3}}{s{r}^{3}}$
Question 6:   Simplify: $\frac{3x}{2}+\frac{2x}{3}+\frac{5x}{4}$
$2\frac{13}{18}x$
$2\frac{1}{4}x$
$2\frac{17}{18}x$
$3\frac{5}{12}x$
Question 7:   Simplify: $\frac{1}{x}+\frac{2}{3x}+\frac{3}{7x}$
$2\frac{1}{7}x$
$2\frac{1}{7x}$
$2\frac{2}{21x}$
$2\frac{2}{21}x$
Question 8:   Simplify: $3x+\frac{2x+y}{3}-\frac{x-3y}{5}$
$1\frac{1}{3}x-\frac{2}{5}y$
$6x-\frac{2}{5}y$
$3\frac{7}{15}x+\frac{14}{15}y$
$2\frac{5}{8}x-\frac{2}{3}y$
Question 9:   Simplify: $\frac{5x}{6y}-\frac{3y}{2x}$
$\frac{5\left(x-y\right)\left(x+y\right)}{6xy}$
$\frac{5{x}^{2}-9{y}^{2}}{6xy}$
$\frac{7{x}^{2}+3{y}^{2}}{5xy}$
$\frac{7{x}^{2}-3{y}^{2}}{2xy}$
Question 10:   Simplify: $\frac{p-3}{3q}-\frac{3p+2}{2q}+\frac{4p-1}{5q}$
$\frac{-p-2}{q}$
$\frac{7p-1}{30q}$
$\frac{13p+17}{30q}$
$\frac{-11p-66}{30q}$