Ejercicios mixtos de cálculo con fracciones

Para formar la fracción invertida, no tienes que calcular, basta con intercambiar los dos números (denominador y numerador). Cuanto mayor sea un número, menor será su fracción recíproca (y viceversa).

Solución: $\frac{7}{4}\backslash frac\{7\}\{4\}$

Para formar la fracción invertida, no tienes que calcular, basta con intercambiar los dos números (denominador y numerador). Cuanto mayor sea un número, menor será su fracción recíproca (y viceversa).

Solución: $\frac{13}{27}\backslash frac\{13\}\{27\}$

$\frac{1}{14}+\frac{5}{14}=\frac{1+5}{14}=\frac{6}{14}\backslash frac\{1\}\{14\}+\backslash frac\{5\}\{14\}=\backslash frac\{1+5\}\{14\}=\backslash frac\{6\}\{14\}$

$\frac{6}{14}=\frac{6:2}{14:2}=\frac{3}{7}\backslash frac\{6\}\{14\}=\backslash frac\{6:2\}\{14:2\}=\backslash frac\{3\}\{7\}$

Respuesta: $\frac{3}{7}\backslash frac\{3\}\{7\}$

$\frac{17}{45}+\frac{18}{45}=\frac{17+18}{45}=\frac{35}{45}\backslash frac\{17\}\{45\}+\backslash frac\{18\}\{45\}=\backslash frac\{17+18\}\{45\}=\backslash frac\{35\}\{45\}$

$\frac{35}{45}=\frac{35:5}{45:5}=\frac{7}{9}\backslash frac\{35\}\{45\}=\backslash frac\{35:5\}\{45:5\}=\backslash frac\{7\}\{9\}$

Respuesta: $\frac{7}{9}\backslash frac\{7\}\{9\}$

$\frac{17}{35}-\frac{12}{35}=\frac{17-12}{35}=\frac{5}{35}\backslash frac\{17\}\{35\}-\backslash frac\{12\}\{35\}=\backslash frac\{17-12\}\{35\}=\backslash frac\{5\}\{35\}$

$\frac{5}{35}=\frac{5:5}{35:5}=\frac{1}{7}\backslash frac\{5\}\{35\}=\backslash frac\{5:5\}\{35:5\}=\backslash frac\{1\}\{7\}$

Respuesta: $\frac{1}{7}\backslash frac\{1\}\{7\}$

$\frac{9}{10}-\frac{6}{10}=\frac{9-6}{10}=\frac{3}{10}\backslash frac\{9\}\{10\}-\backslash frac\{6\}\{10\}=\backslash frac\{9-6\}\{10\}=\backslash frac\{3\}\{10\}$

Respuesta: $\frac{3}{10}\backslash frac\{3\}\{10\}$

$\frac{1}{2}+\frac{3}{5}=\frac{5}{10}+\frac{6}{10}=\frac{5+6}{10}=\frac{11}{10}\backslash frac\{1\}\{2\}+\backslash frac\{3\}\{5\}=\backslash frac\{5\}\{10\}+\backslash frac\{6\}\{10\}=\backslash frac\{5+6\}\{10\}=\backslash frac\{11\}\{10\}$

${\displaystyle \frac{3}{4}}+{\displaystyle \frac{2}{5}}={\displaystyle \frac{15}{20}}+{\displaystyle \frac{8}{20}}={\displaystyle \frac{15+8}{20}}={\displaystyle \frac{23}{20}}\backslash dfrac\{3\}\{4\}+\backslash dfrac\{2\}\{5\}=\backslash dfrac\{15\}\{20\}+\backslash dfrac\{8\}\{20\}=\backslash dfrac\{15+8\}\{20\}=\backslash dfrac\{23\}\{20\}$

${\displaystyle \frac{4}{5}}-{\displaystyle \frac{1}{7}}={\displaystyle \frac{28}{35}}-{\displaystyle \frac{5}{35}}={\displaystyle \frac{28-5}{35}}={\displaystyle \frac{23}{35}}\backslash dfrac\{4\}\{5\}-\backslash dfrac\{1\}\{7\}=\backslash dfrac\{28\}\{35\}-\backslash dfrac\{5\}\{35\}=\backslash dfrac\{28-5\}\{35\}=\backslash dfrac\{23\}\{35\}$

${\displaystyle \frac{4}{5}}-{\displaystyle \frac{1}{7}}={\displaystyle \frac{28}{35}}-{\displaystyle \frac{5}{35}}={\displaystyle \frac{28-5}{35}}={\displaystyle \frac{23}{35}}\backslash dfrac\{4\}\{5\}-\backslash dfrac\{1\}\{7\}=\backslash dfrac\{28\}\{35\}-\backslash dfrac\{5\}\{35\}=\backslash dfrac\{28-5\}\{35\}=\backslash dfrac\{23\}\{35\}$

$={\displaystyle \frac{2}{3}}+{\displaystyle \frac{2}{3}}+{\displaystyle \frac{2}{3}}+{\displaystyle \frac{2}{3}}+{\displaystyle \frac{2}{3}}={\displaystyle \frac{2\cdot 5}{3}}={\displaystyle \frac{10}{3}}=\backslash dfrac\{2\}\{3\}+\backslash dfrac\{2\}\{3\}+\backslash dfrac\{2\}\{3\}+\backslash dfrac\{2\}\{3\}+\backslash dfrac\{2\}\{3\}=\backslash dfrac\{2\backslash cdot5\}\{3\}=\backslash dfrac\{10\}\{3\}$

$={\displaystyle \frac{1}{6}}+{\displaystyle \frac{1}{6}}+{\displaystyle \frac{1}{6}}+{\displaystyle \frac{1}{6}}={\displaystyle \frac{4\cdot 1}{6}}={\displaystyle \frac{4}{6}}=\backslash dfrac\{1\}\{6\}+\backslash dfrac\{1\}\{6\}+\backslash dfrac\{1\}\{6\}+\backslash dfrac\{1\}\{6\}=\backslash dfrac\{4\backslash cdot1\}\{6\}=\backslash dfrac\{4\}\{6\}$

$={\displaystyle \frac{6}{11}}+{\displaystyle \frac{6}{11}}+{\displaystyle \frac{6}{11}}={\displaystyle \frac{3\cdot 6}{11}}={\displaystyle \frac{18}{11}}=\backslash dfrac\{6\}\{11\}+\backslash dfrac\{6\}\{11\}+\backslash dfrac\{6\}\{11\}=\backslash dfrac\{3\backslash cdot6\}\{11\}=\backslash dfrac\{18\}\{11\}$

$={\displaystyle \frac{3}{8}}+{\displaystyle \frac{3}{8}}={\displaystyle \frac{2\cdot 3}{8}}={\displaystyle \frac{6}{8}}=\backslash dfrac\{3\}\{8\}+\backslash dfrac\{3\}\{8\}=\backslash dfrac\{2\backslash cdot3\}\{8\}=\backslash dfrac\{6\}\{8\}$

${\displaystyle \frac{5}{12}}\cdot 7={\displaystyle \frac{5\cdot 7}{12}}={\displaystyle \frac{35}{12}}=2{\displaystyle \frac{11}{12}}\backslash dfrac\{5\}\{12\}\backslash cdot7=\backslash dfrac\{5\backslash cdot7\}\{12\}=\backslash dfrac\{35\}\{12\}=2\backslash dfrac\{11\}\{12\}$

${\displaystyle \frac{2}{9}}\cdot 5={\displaystyle \frac{2\cdot 5}{9}}={\displaystyle \frac{10}{9}}=1{\displaystyle \frac{1}{9}}\backslash dfrac\{2\}\{9\}\backslash cdot5=\backslash dfrac\{2\backslash cdot5\}\{9\}=\backslash dfrac\{10\}\{9\}=1\backslash dfrac\{1\}\{9\}$

${\displaystyle \frac{7}{11}}\cdot 2={\displaystyle \frac{7\cdot 2}{11}}={\displaystyle \frac{14}{11}}=1{\displaystyle \frac{3}{11}}\backslash dfrac\{7\}\{11\}\backslash cdot2=\backslash dfrac\{7\backslash cdot2\}\{11\}=\backslash dfrac\{14\}\{11\}=1\backslash dfrac\{3\}\{11\}$

${\displaystyle \frac{3}{4}}\cdot 4={\displaystyle \frac{3\cdot 4}{4}}={\displaystyle \frac{12}{4}}=3\backslash dfrac\{3\}\{4\}\backslash cdot4=\backslash dfrac\{3\backslash cdot4\}\{4\}=\backslash dfrac\{12\}\{4\}=3$

${\displaystyle \frac{3}{4}}\cdot {\displaystyle \frac{5}{6}}={\displaystyle \frac{3\cdot 5}{4\cdot 6}}={\displaystyle \frac{15}{24}}={\displaystyle \frac{5}{8}}\backslash dfrac\{3\}\{4\}\backslash cdot\backslash dfrac\{5\}\{6\}=\backslash dfrac\{3\backslash cdot5\}\{4\backslash cdot6\}=\backslash dfrac\{15\}\{24\}=\backslash dfrac\{5\}\{8\}$

${\displaystyle \frac{2}{7}}\cdot {\displaystyle \frac{5}{4}}={\displaystyle \frac{2\cdot 5}{7\cdot 4}}={\displaystyle \frac{10}{28}}={\displaystyle \frac{5}{14}}\backslash dfrac\{2\}\{7\}\; \backslash cdot\; \backslash dfrac\{5\}\{4\}=\backslash dfrac\{2\backslash cdot5\}\{7\backslash cdot4\}=\backslash dfrac\{10\}\{28\}=\backslash dfrac\{5\}\{14\}$

${\displaystyle \frac{3}{16}}\cdot {\displaystyle \frac{1}{2}}={\displaystyle \frac{3\cdot 1}{16\cdot 2}}={\displaystyle \frac{2}{32}}\backslash dfrac\{3\}\{16\}\backslash cdot\; \backslash dfrac\{1\}\{2\}=\backslash dfrac\{3\; \backslash cdot1\}\{16\backslash cdot2\}=\backslash dfrac\{2\}\{32\}$

${\displaystyle \frac{5}{8}}\cdot {\displaystyle \frac{2}{3}}={\displaystyle \frac{5\cdot 2}{8\cdot 3}}={\displaystyle \frac{10}{24}}={\displaystyle \frac{5}{12}}\backslash dfrac\{5\}\{8\}\; \backslash cdot\; \backslash dfrac\{2\}\{3\}=\backslash dfrac\{5\backslash cdot\; 2\}\{8\backslash cdot\; 3\}=\backslash dfrac\{10\}\{24\}=\backslash dfrac\{5\}\{12\}$

${\displaystyle \frac{1}{8}}\backslash dfrac\{1\}\{8\}$

${\displaystyle \frac{4}{8}}:4={\displaystyle \frac{4}{8}}\cdot {\displaystyle \frac{1}{4}}={\displaystyle \frac{4\cdot 1}{8\cdot 4}}={\displaystyle \frac{4}{32}}\backslash dfrac\{4\}\{8\}:4=\backslash dfrac\{4\}\{8\}\backslash cdot\backslash dfrac\{1\}\{4\}=\backslash dfrac\{4\backslash cdot1\}\{8\backslash cdot4\}=\backslash dfrac\{4\}\{32\}$

${\displaystyle \frac{6}{7}}:8={\displaystyle \frac{6}{7}}\cdot {\displaystyle \frac{1}{8}}={\displaystyle \frac{6\cdot 1}{7\cdot 8}}={\displaystyle \frac{6}{56}}\backslash dfrac\{6\}\{7\}:8=\backslash dfrac\{6\}\{7\}\backslash cdot\backslash dfrac\{1\}\{8\}=\backslash dfrac\{6\backslash cdot1\}\{7\backslash cdot8\}=\backslash dfrac\{6\}\{56\}$