Solve (5/6+3/8):29/7}:[(3/8+frac{5}{6}):frac{3}{4}]=x:[(2-frac{4}{7}):frac{5}{4}]

$$( \frac { 5 } { 6 } + \frac { 3 } { 8 } ) : \frac { 29 } { 7 } \} : [ ( \frac { 3 } { 8 } + \frac { 5 } { 6 } ) : \frac { 3 } { 4 } ] = x : [ ( 2 - \frac { 4 } { 7 } ) : \frac { 5 } { 4 } ]$$

Evaluate

$$\frac{7}{24}\approx 0.291666667$$

Solution Steps

Least common multiple of 6 and 8 is 24. Convert \frac{5}{6} and \frac{3}{8} to fractions with denominator 24.

$$\frac{\frac{20}{24}+\frac{9}{24}}{\frac{29}{7}}$$

Since \frac{20}{24} and \frac{9}{24} have the same denominator, add them by adding their numerators.

$$\frac{\frac{20+9}{24}}{\frac{29}{7}}$$

Add 20 and 9 to get 29.

$$\frac{\frac{29}{24}}{\frac{29}{7}}$$

Divide \frac{29}{24} by \frac{29}{7} by multiplying \frac{29}{24} by the reciprocal of \frac{29}{7}.

$$\frac{29}{24}\times \frac{7}{29}$$

Multiply \frac{29}{24} times \frac{7}{29} by multiplying numerator times numerator and denominator times denominator.

$$\frac{29\times 7}{24\times 29}$$

Cancel out 29 in both numerator and denominator.

$$\frac{7}{24}$$

Factor

$$\frac{7}{2 ^ {3} \cdot 3} = 0.2916666666666667$$