Multiplicación y división de fracciones

Para multiplicar dos fracciones, por ejemplo \(\dfrac {3} {5}\cdot \dfrac {2} {7}\) , multiplicaremos numerador por numerador, (numeros de arriba) en este caso 3 y 2, y denominador por denominador, (números  de abajo) en este caso 5 y 7. Por lo tanto \(\dfrac {3} {5}\cdot{\dfrac {2} {7}}=\dfrac {6} {35}\).

Para dividir dos fracciones, por ejemplo \(\dfrac {3} {5}:\dfrac {2} {7}\), cambiamos de posición numerador y denominador de la segunda fracción y la convertimos en una multiplicación \(\dfrac {3} {5}\cdot\dfrac {7} {2}=\dfrac {21} {10}\) .

Aquí os dejo más ejercicios resueltos.

\(\bullet\dfrac {3} {5}.\dfrac {1} {3}\cdot \dfrac {2} {7}\cdot \dfrac {15} {2}=\dfrac {3\cdot 1\cdot\enclose{updiagonalstrike}{2}\cdot\enclose{updiagonalstrike}{3}\cdot\enclose{updiagonalstrike}{5}} {\enclose{updiagonalstrike}{5}\cdot\enclose{updiagonalstrike}{3}\cdot 7\cdot\enclose{updiagonalstrike}{2}}=\boxed{\dfrac {3} {7}}\)

\(\bullet\dfrac {3} {2}:\dfrac {1} {4}:\dfrac {6} {5}=\dfrac {3} {2}\cdot \dfrac {4} {1}\cdot \dfrac {5} {6}=\dfrac {\enclose{updiagonalstrike}{3}\cdot \enclose{updiagonalstrike}{2^{2}}\cdot 5} {\enclose{updiagonalstrike}{2}\cdot\enclose{updiagonalstrike}{2}\cdot\enclose{updiagonalstrike}{3}}=\boxed5\)

\(\bullet\dfrac {16} {25}:\dfrac {12} {35}=\dfrac {16} {25}\cdot \dfrac {35} {12}=\dfrac {2^{4}\cdot \enclose{updiagonalstrike}{5}\cdot 7} {5^{\enclose{updiagonalstrike}{2}}\cdot 2^{2}\cdot 3}=\dfrac {2^{2}\cdot 7} {3\cdot 5}=\boxed{\dfrac {28} {15}}\)

\(\bullet\dfrac {22} {3}\cdot \dfrac {5} {11}:\dfrac {4} {5}=\dfrac {22} {3}\cdot \dfrac {5} {11}\cdot \dfrac {5} {4}=\dfrac {\enclose{updiagonalstrike}{2}\cdot \enclose{updiagonalstrike}{11}\cdot 5\cdot 5} {3\cdot \enclose{updiagonalstrike}{11}\cdot 2^{\enclose{updiagonalstrike}{2}}}=\boxed{\dfrac {25} {6}}\)

\(\bullet\dfrac {6} {35}\cdot \dfrac {25} {9}\cdot \dfrac {12} {5}:\left( \dfrac {6} {7}\cdot \dfrac {5} {4}\right) =\dfrac {6} {35}\cdot \dfrac {25} {9}\cdot \dfrac {12} {5}:\left( \dfrac {\enclose{updiagonalstrike}{2}\cdot 3\cdot 5} {7\cdot 2^{\enclose{updiagonalstrike}{2}}}\right)\)

\(\dfrac {6} {35}\cdot \dfrac {25} {9}\cdot \dfrac {12} {5}:\dfrac {15} {14}=\dfrac {6} {35}\cdot \dfrac {25} {9}\cdot \dfrac {12} {5}\cdot \dfrac {14} {15}=\dfrac {2\cdot\enclose{updiagonalstrike} {3}\cdot\enclose{updiagonalstrike}{ 5^{2}}\cdot\enclose{updiagonalstrike}{3}\cdot 2^{2}\cdot 2\cdot \enclose{updiagonalstrike}{7}} {\enclose{updiagonalstrike}{7}\cdot 5\cdot\enclose{updiagonalstrike}{3^{2}}\cdot\enclose{updiagonalstrike} {5}\cdot\enclose{updiagonalstrike} {3}\cdot\enclose{updiagonalstrike} {5}}=\)

\(=\boxed{\dfrac {16} {15}}\)