a) $\dfrac{2}{45}-\dfrac{11}{21}+\dfrac{5}{14}$
b) $\dfrac{4}{7} \cdot \dfrac{21}{9}$
c) $\dfrac{3}{2} \div \dfrac{6}{18}$
d) $\left(-\dfrac{5}{4}\right)^{2} \div \dfrac{15}{2}-\dfrac{1}{2}$
SOLUCIÓN.
a)
$\dfrac{2}{45}-\dfrac{11}{21}+\dfrac{5}{14} \quad \overset{\text{m.c.m}(45,21,14)=630}{=} \quad \dfrac{2 \cdot 630 \div 45}{630}+\dfrac{(-11)\cdot 630 \div 21}{630}+\dfrac{5 \cdot 630\div 14}{630}$
$=\dfrac{28}{630}+\dfrac{(-330)}{630+\dfrac{225}{630}}$
$=\dfrac{28+(-330)+225}{630}$
$=\dfrac{-77}{630}$
$=-\dfrac{77}{630}$
$\quad \overset{\text{m.c.d.}(77,630)=7}{=}\quad -\dfrac{11}{90}$
b)
$\dfrac{4}{7} \cdot \dfrac{21}{9}$
$=\dfrac{4 \cdot 21}{7 \cdot 9}$
$=\dfrac{21 \cdot 4}{7 \cdot 9}$
$=\dfrac{21}{7}\cdot \dfrac{4}{9}$
$=3\cdot \dfrac{4}{9}$
$=\dfrac{3\cdot 4}{9}$
$=\dfrac{4\cdot 3}{9}$
$=4 \cdot \dfrac{3}{9}$
$=4 \cdot \dfrac{1}{3}$
$=\dfrac{4}{3}$
c)
$\dfrac{3}{2} \div \dfrac{6}{18}$
$ \overset{\frac{6}{18}=\frac{1}{3}}{=} \quad \dfrac{3}{2} \div \dfrac{1}{3}$
$=\dfrac{3}{2} \cdot \text{inverso} \left( \dfrac{1}{3} \right)$
$=\dfrac{3}{2} \cdot 3$
$=\dfrac{3 \cdot 3}{2}$
$=\dfrac{9}{2}$
d)
$\left(-\dfrac{5}{4}\right)^{2} \div \dfrac{15}{2}-\dfrac{1}{2}$
$=\dfrac{25}{16} \div \dfrac{15}{2}-\dfrac{1}{2}$
$=\dfrac{25}{16} \cdot \text{inverso}\left( \dfrac{15}{2}\right)-\dfrac{1}{2}$
$=\dfrac{25}{16} \cdot \dfrac{2}{15}-\dfrac{1}{2}$
$=\dfrac{25 \cdot 2}{16 \cdot 15} -\dfrac{1}{2}$
$=\dfrac{2 \cdot 25}{16 \cdot 15} -\dfrac{1}{2}$
$=\dfrac{2}{16}\cdot \dfrac{25}{15} -\dfrac{1}{2}$
$=\dfrac{1}{8}\cdot \dfrac{5}{3} -\dfrac{1}{2}$
$=\dfrac{1\cdot 5}{8 \cdot 3} -\dfrac{1}{2}$
$=\dfrac{5}{24} -\dfrac{1}{2}$
$=\dfrac{5}{24} -\dfrac{12}{24}$
$=\dfrac{5}{24} +\dfrac{(-12)}{24}$
$=\dfrac{5+(-12)}{24}$
$=\dfrac{(-7)}{24}$
$=-\dfrac{7}{24}$
$\square$
[autoría]
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