Question

A_5/8+3/4+---- =9/4
B_1/6+2/3+---- = 2
C_10/5+5/10+---- =4

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Answer 1

~ Primera operación: 

$\frac{5}{8} + \frac{3}{4} + x = \frac{9}{4}$

$\frac{(8:8.5)+(8:4.3)}{8} + x = \frac{9}{4}$

$\frac{5+6}{8} + x = \frac{9}{4}$

$\frac{11}{8} + x = \frac{9}{4}$

$x = \frac{9}{4} - \frac{11}{8}$

$x= \frac{(8:4.9) - (8:8.11)}{8}$

$x= \frac{18-11}{8}$

$\frac{7}{8}$

Comprobamos:

$\frac{5}{8} + \frac{3}{4} + \frac{7}{8} =$

$\frac{(8:8.5)+(8:4.3)+(8:8.7)}{8} =$

$\frac{5+6+7}{8} =$

$\frac{18}{8} = \frac{9}{4} \checkmark$


~ Segunda operación:

$\frac{1}{6} + \frac{2}{3} + x = 2$

$\frac{(6:6.1)+(6:3.2)}{6} + x = 2$

$\frac{1+4}{6} + x = 2$

$\frac{5}{6} + x = 2$

$x = \frac{2}{1} - \frac{5}{6}$

$x = \frac{(6:1.2) - (6:6.5)}{6}$

$x = \frac{12-5}{6}$

$x = \frac{7}{6}$

Comprobamos:

$\frac{1}{6} + \frac{2}{3} + \frac{7}{6} =$

$\frac{(6:6.1) + (6:3.2) + (6:6.7)}{6} =$

$\frac{1+4+7}{6} =$

$\frac{12}{6} = \frac{2}{1} = 2 \checkmark$


~ Tercera operación:

$\frac{10}{5} + \frac{5}{10} + x = 4$

$\frac{(10:5.10)+(10:10.5)}{10} + x = 4$

$\frac{20+5}{10} + x = 4$

$\frac{25}{10} + x = 4$

$x= \frac{4}{1} - \frac{25}{10}$

$x= \frac{(10:1.4) - (10:10.25)}{10}$

$x= \frac{40-25}{10}$

$x= \frac{15}{10}$

Comprobamos:

$\frac{10}{5} + \frac{5}{10} + \frac{15}{10} =$

$\frac{(10:5.10)+(10:10.5) +(10:10.15)}{10} =$

$\frac{20+5+15}{10} =$

$\frac{40}{10} = \frac{4}{1} = 4 \checkmark$