Solve [51/3+13/4]:61/14=

$$[ 5 \frac { 1 } { 3 } + 1 \frac { 3 } { 4 } ] : 6 \frac { 1 } { 14 } =$$

Evaluate

$$\frac{7}{6}\approx 1.166666667$$

Solution Steps

Multiply 5 and 3 to get 15.

$$\frac{\frac{15+1}{3}+\frac{1\times 4+3}{4}}{\frac{6\times 14+1}{14}}$$

Add 15 and 1 to get 16.

$$\frac{\frac{16}{3}+\frac{1\times 4+3}{4}}{\frac{6\times 14+1}{14}}$$

Multiply 1 and 4 to get 4.

$$\frac{\frac{16}{3}+\frac{4+3}{4}}{\frac{6\times 14+1}{14}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{16}{3}+\frac{7}{4}}{\frac{6\times 14+1}{14}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{16}{3} and \frac{7}{4} to fractions with denominator 12.

$$\frac{\frac{64}{12}+\frac{21}{12}}{\frac{6\times 14+1}{14}}$$

Since \frac{64}{12} and \frac{21}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{64+21}{12}}{\frac{6\times 14+1}{14}}$$

Add 64 and 21 to get 85.

$$\frac{\frac{85}{12}}{\frac{6\times 14+1}{14}}$$

Multiply 6 and 14 to get 84.

$$\frac{\frac{85}{12}}{\frac{84+1}{14}}$$

Add 84 and 1 to get 85.

$$\frac{\frac{85}{12}}{\frac{85}{14}}$$

Divide \frac{85}{12} by \frac{85}{14} by multiplying \frac{85}{12} by the reciprocal of \frac{85}{14}.

$$\frac{85}{12}\times \frac{14}{85}$$

Multiply \frac{85}{12} times \frac{14}{85} by multiplying numerator times numerator and denominator times denominator.

$$\frac{85\times 14}{12\times 85}$$

Cancel out 85 in both numerator and denominator.

$$\frac{14}{12}$$

Reduce the fraction \frac{14}{12} to lowest terms by extracting and canceling out 2.

$$\frac{7}{6}$$

Factor

$$\frac{7}{2 \cdot 3} = 1\frac{1}{6} = 1.1666666666666667$$