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[apunts-espa-matematiques.git] / ng-aritmetica-fraccions-operacions.conTeXt

\startsection[title={Operacions amb fraccions}]

\startsubject[title={Preguntes}]

\startexercici[reference=exercici:operacions-amb-fraccions-1, title={suma i resta}] Opereu:
\startitemize[a, columns, three]
\item \startformula \frac{2}{7} + \frac{6}{7} - \frac{1}{7} \stopformula
\item \startformula \frac{5}{8} + \frac{9}{8} \stopformula
\item \startformula \frac{1}{4} + 5 - \frac{1}{4} \stopformula
\item \startformula \frac{3}{5} - \frac{2}{5} + \frac{11}{5} \stopformula
\item \startformula \frac{2}{3} + \frac{1}{4} \stopformula
\item \startformula 5 + \frac{4}{5} \stopformula
\item \startformula \frac{2}{3} + \frac{5}{8} - \frac{1}{9} \stopformula
\item \startformula 10 - \frac{1}{6} + \frac{6}{8} \stopformula
\item \startformula \frac{3}{10} + \frac{7}{12} \stopformula
\stopitemize
\stopexercici

\startexercici[reference=exercici:operacions-amb-fraccions-2, title={multiplicació i divisió}] Opereu:
\startitemize[a, columns, three]
\item \startformula 3 \cdot \frac{5}{3} \stopformula
\item \startformula \frac{3}{4} \cdot \frac{2}{5} \stopformula
\column
\item \startformula \frac{1}{3} \cdot \frac{3}{4} \div \frac{1}{5} \stopformula
\item \startformula 5 \div \frac{7}{10} \cdot 7 \div \frac{2}{5} \stopformula
\column
\item \startformula \frac{1}{2} \cdot \frac{1}{2} \stopformula
\item \startformula \frac{3}{2} \div \frac{2}{3} \div \frac{5}{4} \stopformula
\column
\item \startformula \frac{2}{3} \colon \frac{2}{5} \stopformula
\item \startformula \frac{3}{4} \colon \frac{1}{2} \cdot 6 \stopformula
\item \startformula \frac{2}{3} \colon \frac{3}{4} \cdot \frac{1}{2} \stopformula
\stopitemize
\stopexercici

\startexercici[reference=exercici:operacions-amb-fraccions-3, title={operacions combinades}] Opereu:
\startitemize[a, columns]
\item \startformula \frac{3}{4} + \frac{2}{5} \cdot \frac{1}{2} \stopformula
\item \startformula \frac{2}{5} \div \frac{3}{5} - \frac{1}{4} \stopformula
\item \startformula \left( 2 + \frac{3}{5} \right) \div \frac{4}{3} \stopformula
\item \startformula \frac{2}{3} - \frac{5}{6}\cdot 8 \stopformula
\item \startformula 4 + \frac{3}{5} - \left(2 - \frac{1}{2}\right) \stopformula
\item \startformula 4 \cdot \left(\frac{5}{6} - \frac{1}{4} + \frac{4}{9}\right) \stopformula
\item \startformula \frac{5}{6} - \left(\frac{1}{5} + \frac{1}{3}\right) \stopformula
\item \startformula \frac{5}{6} \div \left( \frac{2}{5} - \frac{1}{10}\right) \stopformula
\item \startformula 4 \cdot \frac{2}{3} \cdot \left(\frac{2}{4} \div \frac{8}{10}\right) \stopformula
\item \startformula \frac{3}{4} + \frac{1}{2} \cdot \frac{4}{10} \stopformula
\item \startformula \frac{10}{12} - \left(\frac{1}{10} + \frac{3}{8}\right) \stopformula
\item \startformula \left(\frac{1}{2} + 2\right) \cdot \left(2 - \frac{1}{4}\right) \stopformula
\item \startformula \left(\frac{3}{4} + \frac{1}{4}\right) \div \left(\frac{5}{6} - \frac{1}{3}\right) \stopformula
\item \startformula 5 + 10 - \frac{1}{10} + 25 \stopformula
\item \startformula \frac{1}{3} + \frac{1}{2} - \frac{2}{5} \stopformula
\item \startformula \left(\frac{1}{2} + \frac{2}{10}\right) \cdot \frac{2}{6} \stopformula
\item \startformula 5 + \frac{1}{3} \cdot \frac{5}{3} \stopformula
\item \startformula \left( 5 + \frac{1}{3} \right) \cdot \frac{5}{3} \stopformula
\stopitemize
\stopexercici

\startexercici[reference=exercici:operacions-amb-fraccions-4, title={operacions combinades}] Opereu i {\em simpliqueu} els resultats
\startitemize[a, columns]
\item \startformula \frac{2}{3}\colon \left( \frac{4}{5} - \frac{2}{8}\right) - \frac{1}{20} \stopformula
\item \startformula \frac{2}{5} \div \frac{5}{4} \cdot \frac{5}{6} + \frac{2}{7} \stopformula
\item \startformula \frac{2}{3} \div \left( \frac{5}{3} \div \left( \frac{2}{5} + \frac{5}{9} \right)\right) + 2\stopformula
\item \startformula \frac{5}{8} + \left(\frac{2}{5} - \frac{1}{5} \cdot \frac{2}{30}\right) \colon 5 \stopformula
\item \startformula \left( \frac{5}{8} + \frac{2}{4} \right) - \left( \frac{3}{4} - \frac{1}{8} \right) \stopformula
\item \startformula \frac{9}{12} - \frac{2}{5} \colon \frac{5}{3} + \frac{2}{5} \stopformula
%\column
\item \startformula \frac{5}{10} \cdot \left(\frac{3}{10} + \frac{5}{10}\right) \colon \frac{7}{10} \stopformula
\item \startformula \left(\frac{12}{24} + \frac{4}{10}\right) \colon \left(\frac{5}{6} \cdot \left(\frac{8}{10} - \frac{1}{100}\right)\right) \stopformula
\item \startformula \frac{3}{4} - \frac{1}{4} + \frac{5}{7}\cdot \frac{5}{7} \stopformula
\item \startformula \left(\frac{2}{4} + 4\right) - \frac{1}{100} \stopformula
\item \startformula \frac{2}{5} + \frac{1}{2} \cdot \frac{3}{20} \colon 10 \stopformula
\item \startformula 5 \cdot \left(\frac{3}{5} \div \frac{5}{20}\right) \colon 20 \stopformula
\stopitemize
\stopexercici

\stopsubject

\page[yes]
\startsubject[title={Solucions}]

Les solucions estan simplificades.

\startitemize[1][distance=0.5cm]
\sym{\in[exercici:operacions-amb-fraccions-1]} \startitemize[a, text] \item $1$, \item $7/4$, \item $5$, \item $12/5$, \item $11/12$, \item $29/5$, \item $85/72$, \item $127/12$, \item $53/60$ \stopitemize

\sym{\in[exercici:operacions-amb-fraccions-2]} \startitemize[a, text] \item $5$, \item $3/10$, \item $5/4$, \item $125$, \item $1/4$, \item $9/5$, \item $5/3$, \item $9$, \item $3/4$ \stopitemize

\sym{\in[exercici:operacions-amb-fraccions-3]} \startitemize[a, text] \item $19/20$, \item $5/12$, \item $39/20$, \item $-6$, \item $31/10$, \item $37/9$, \item $3/10$, \item $25/9$, \item $5/3$, \item $19/20$, \item $43/120$, \item $35/8$, \item $2$, \item $399/100$, \item $13/30$, \item $7/30$, \item $50/9$, \item $80/9$ \stopitemize

\sym{\in[exercici:operacions-amb-fraccions-4]} \startitemize[a, text] \item $1/2$ \item $58/105$ \item $536/225$ \item $2107/3000$ \item $1/2$ \item $91/100$ \item $7/10$ \item $108/79$ \item $99/98$ \item $449/100$ \item $163/400$ \item $3/5$ \stopitemize
\stopitemize

\stopsubject

\stopsection