Question

HALLAR EL VALOR DE LAS SIGUIENTES OPERACIONES Y EXPRÉSELO COMO UN ENTERO O FRACCIÓN SIMPLIFICADA:
((7-6.35)÷6.5+9.9)/((1.2÷36+1.2÷0.25-1 5/16)÷169/24)
3(6-1.333…)+6(1.333…)-16.666…
3/(1+2/0.5)-2/(1+3/0.5)+(54/3+1.666…)/(9+2.666…)

Answer 1

El resultado de las expresiones son:

1. ((7-6.35)÷6.5+9.9)/((1.2÷36+1.2÷0.25-1 5/16)÷169/24) = 187/3380

2.  3*(6-1.333…)+6(1.333…)-16.666… = 16/3

3. 3/(1+2/0.5)-2/(1+3/0.5)+(54/3+1.666…)/(9+2.666…) = 73/62

Tenemos las expresiones:

1. ((7-6.35)÷6.5+9.9)/((1.2÷36+1.2÷0.25-1 5/16)÷169/24)  

Modificamos:

6.35 = 635/100 = 127/20

6.5= 13/2

9.9 = 99/10

1.2 = 6/5

0.25 = 1/4

Entonces:

= $((7-\frac{127}{20}) \div \frac{13}{2}+\frac{99}{10})\div((\frac{6}{5}\div36+\frac{6}{5}\div\frac{1}{4}-\frac{15}{16})\div \frac{169}{24})$

= $((\frac{140-127}{20}) \div \frac{13}{2}+\frac{99}{10})\div(\frac{6}{5*36}+\frac{24}{5}-\frac{15}{16} )\div \frac{169}{24})$

= $(\frac{13}{20} \div \frac{13}{2}+\frac{99}{10})\div(\frac{6}{180}+\frac{24}{5}-\frac{15}{16} )\div \frac{169}{24})$

= $(\frac{13*2}{20*13}+\frac{99}{10})\div(\frac{24+3456+675}{720}\div \frac{169}{24})$

$=(\frac{26}{260}+\frac{99}{10})\div(\frac{2805}{720}\div \frac{169}{24})$

$=(\frac{1}{10}+\frac{99}{10})\div(\frac{2805}{720}\div \frac{169}{24})$

$=(\frac{99+1}{10})\div(\frac{2805*24}{720*169})$

$=(\frac{100}{10})\div(\frac{67320}{121680})$

$=(10 \div(\frac{6732}{12168})$

$=\frac{6732}{10*12168} = \frac{6732}{121680} = \frac{1683}{30420} = \frac{561}{10140} = \frac{187}{3380}$

2. 3*(6-1.333…)+6(1.333…)-16.666…

1.3333... = 4/3

16/3 = 50/3

Entonces:

= $3*(6-\frac{4}{3}) + 6*\frac{4}{3} - \frac{50}{3}$

= $3*(\frac{18-4}{3}) + \frac{24}{3} - \frac{50}{3}$

= $3*(\frac{14}{3}) + \frac{24}{3} - \frac{50}{3}$

= $\frac{42}{3} + \frac{24}{3} - \frac{50}{3}$

= $\frac{42+24-50}{3} = \frac{16}{3}$

3. 3/(1+2/0.5)-2/(1+3/0.5)+(54/3+1.666…)/(9+2.666…)

0.5 = 1/2

1.6666 = 5/3

2.6666 = 8/3

$3 \div (1+2\div \frac{1}{2} )-2\div (1+3\div \frac{1}{2})+(\frac{54}{3}+\frac{5}{3}) \div(9+\frac{8}{3})$

$= 3 \div (1+\frac{1}{4} )-2\div (1+\frac{1}{6})+(\frac{54}{3}+\frac{5}{3}) \div(9+\frac{8}{3})$

$= 3 \div (\frac{4+1}{4} )-2\div (\frac{6+1}{6})+(\frac{59}{3}) \div(9+\frac{27+8}{3})$

$= 3 \div (\frac{5}{4} )-2\div (\frac{7}{6})+(\frac{59}{3}) \div(9+\frac{35}{3})$

$= \frac{5}{12}-\frac{7}{12}+(\frac{59}{3}) \div(\frac{27+35}{3})$

$= \frac{5}{12}-\frac{7}{12}+(\frac{59}{3}) \div(\frac{62}{3})$

$= \frac{5}{12}-\frac{7}{12}+\frac{59}{62}$

$= \frac{5}{12}-\frac{7}{12}+\frac{59}{62}= \frac{155-217+354}{372} = \frac{292}{372} = \frac{146}{186}=\frac{73}{62}$