13.05 Multiplying and dividing algebraic fractions
Simplify the following expressions:
\dfrac{1}{a} \times \dfrac{1}{b}
\dfrac{a}{3} \times \dfrac{a}{7}
\dfrac{b}{q} \times \dfrac{k}{u}
\dfrac{c}{3} \times \dfrac{d}{2}
\dfrac{9 x}{2} \times \dfrac{5 y}{7}
\dfrac{4 x}{5} \times \dfrac{3 y}{7}
\dfrac{11 s}{7 t} \times \dfrac{3 r}{5 q}
\dfrac{9 u}{7 v} \times \dfrac{8 w}{11 y}
\dfrac{ y}{8} \times \dfrac{5 y}{9}
\dfrac{u}{3 a} \times \dfrac{ v}{5 b}
\dfrac{5 a}{ b} \times \dfrac{3 }{8 }
\dfrac{8 a}{7 y} \times \dfrac{9 b}{5 x}
Complete the following:
\dfrac{⬚}{3a^2}\times\dfrac{7b}{⬚}=\dfrac{14bc}{9a^2 d}The product of two fractions is 1. If one of the fractions is \dfrac{3x}{4yz}, what is the other fraction?
Simplify the following expressions:
\dfrac{3 y}{8} \times \dfrac{4 y}{9}
\dfrac{5 u}{3 a} \times \dfrac{3 v}{5 b}
\dfrac{9 a}{10 b} \times \dfrac{3 b}{8 a}
\dfrac{8 x}{7 y} \times \dfrac{9 y}{5 x}
\dfrac{14 u}{15 v} \times \dfrac{40 v}{24 q}
\dfrac{9 u}{77 v} \times \dfrac{110 v}{24 q}.
\dfrac{x^{2}}{3} \times \dfrac{6}{x}
\dfrac{p^{2}}{q} \times \dfrac{q^{2}}{p}
\dfrac{r^{2}}{n} \times \dfrac{n^{2}}{r}
\dfrac{5 y^{2}}{9} \times 27 y^{2}
\dfrac{5 y}{2} \times 6 y^{5}.
\dfrac{4 m^{2}}{20} \times \dfrac{3 y^{2}}{7 m}
\dfrac{7 a^{2}}{15 b^{2}} \times \dfrac{10 b}{11 a}.
\dfrac{11 a^{2}}{4 b^{2}} \times \dfrac{10 b}{3 a}
\left( - \dfrac{10}{21 x} \right) \times \dfrac{3 x^{2}}{110}
\dfrac{2 n^{2}}{6} \times \dfrac{- 2 y^{2}}{3 n}
Simplify:
Simplify \left(\dfrac{x}{3y}\right)^2\times\dfrac{5x^2}{2y}.
Simplify the following expressions:
\dfrac{r}{3} \div \dfrac{2}{m}
\dfrac{u}{3} \div \dfrac{4}{v}
\dfrac{3 y}{5} \div \dfrac{4 }{7}
\dfrac{2 x}{9} \div \dfrac{7}{5 y}
\dfrac{y^{2}}{4} \div \dfrac{12}{29 y^{6}}
\dfrac{4 u}{11 } \div \dfrac{7 q}{50 y}
\dfrac{- 2 x}{11} \div \dfrac{5y}{3}
\dfrac{9 u}{11 v} \div \dfrac{7 v}{10 u}
\dfrac{- 9 m}{5} \div \dfrac{11 n}{8}
\dfrac{u^{2}}{12} \div \dfrac{v}{11}
\dfrac{u^{2}}{9} \div \dfrac{v}{20}
\dfrac{2 u^{3}}{13 v} \div \dfrac{5 v^{3}}{23 u}
Complete the following:
\dfrac{⬚}{4p^2}\div\frac{2q^2}{3r}=\frac{27r^3}{⬚}A rectangle has an area of \dfrac{5 x^{3} y^{4}}{3 p q} and a length of \dfrac{4 x y}{p}. Find an expression for the width of the rectangle.
Simplify the following expressions:
\dfrac{m}{4} \div \dfrac{m}{3}
\dfrac{m}{28} \div \dfrac{23}{20}
\dfrac{3 y}{6} \div \dfrac{4 y}{7}
\dfrac{3 y^{2}}{4} \div \dfrac{12}{29 y^{6}}
\dfrac{4 u}{35 y} \div \dfrac{14 q}{50 y}
\dfrac{- 2 x}{11} \div \dfrac{2 x}{3}.
\dfrac{9 u}{36 v} \div \dfrac{7 v}{36 u}
\dfrac{- 9 n}{4} \div \dfrac{11 n}{8}.
\dfrac{u^{2}}{12} \div \dfrac{u}{9}
\dfrac{u^{2}}{9} \div \dfrac{u}{6}.
\dfrac{8 u^{3}}{32 v} \div \dfrac{5 v^{3}}{96 u}
\dfrac{3 w^{3}}{7} \div 9 w^{6}
\dfrac{16 u}{17 v} \div \left( - 14 u v \right)
\dfrac{45 x^{2} y z}{10} \div \dfrac{9 y^{2}}{5 x}
\dfrac{35 t^{2} u^{2}}{12 v^{2} w^{2}} \div \dfrac{35 t^{3} u}{12 w^{2} y^{2}}
\dfrac{10 t^{2} u^{3}}{35 v^{3} w^{3}} \div \dfrac{10 t^{3} u^{2}}{20 w^{3} y}
Simplify \left(\dfrac{2x}{y}\right)^4\div\left(\dfrac{z}{3x^2 y}\right)^2.
Simplify \dfrac{3 x y}{12 y} \times \dfrac{4 y^{2}}{3 w x} \div \dfrac{15 w x}{3 w^{2}}.