Solve 51/3+13/4/6frac{1{4}}

$$\frac{ 5 \frac{ 1 }{ 3 } +1 \frac{ 3 }{ 4 } }{ 6 \frac{ 1 }{ 4 } }$$

Evaluate

$$\frac{17}{15}\approx 1.133333333$$

Solution Steps

Multiply 5 and 3 to get 15.

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

Add 15 and 1 to get 16.

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

Multiply 1 and 4 to get 4.

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

Add 4 and 3 to get 7.

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

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

$$\frac{\frac{64}{12}+\frac{21}{12}}{\frac{6\times 4+1}{4}}$$

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

$$\frac{\frac{64+21}{12}}{\frac{6\times 4+1}{4}}$$

Add 64 and 21 to get 85.

$$\frac{\frac{85}{12}}{\frac{6\times 4+1}{4}}$$

Multiply 6 and 4 to get 24.

$$\frac{\frac{85}{12}}{\frac{24+1}{4}}$$

Add 24 and 1 to get 25.

$$\frac{\frac{85}{12}}{\frac{25}{4}}$$

Divide \frac{85}{12} by \frac{25}{4} by multiplying \frac{85}{12} by the reciprocal of \frac{25}{4}.

$$\frac{85}{12}\times \frac{4}{25}$$

Multiply \frac{85}{12} times \frac{4}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{85\times 4}{12\times 25}$$

Do the multiplications in the fraction \frac{85\times 4}{12\times 25}.

$$\frac{340}{300}$$

Reduce the fraction \frac{340}{300} to lowest terms by extracting and canceling out 20.

$$\frac{17}{15}$$

Factor

$$\frac{17}{3 \cdot 5} = 1\frac{2}{15} = 1.1333333333333333$$