Solve 345/10*1/frac{3{7}+3/4}

$$\frac { \frac { 345 } { 10 } \times 1 } { \frac { 3 } { 7 } + \frac { 3 } { 4 } }$$

Evaluate

$$\frac{322}{11}\approx 29.272727273$$

Solution Steps

Reduce the fraction \frac{345}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{69}{2}\times 1}{\frac{3}{7}+\frac{3}{4}}$$

Multiply \frac{69}{2} and 1 to get \frac{69}{2}.

$$\frac{\frac{69}{2}}{\frac{3}{7}+\frac{3}{4}}$$

Least common multiple of 7 and 4 is 28. Convert \frac{3}{7} and \frac{3}{4} to fractions with denominator 28.

$$\frac{\frac{69}{2}}{\frac{12}{28}+\frac{21}{28}}$$

Since \frac{12}{28} and \frac{21}{28} have the same denominator, add them by adding their numerators.

$$\frac{\frac{69}{2}}{\frac{12+21}{28}}$$

Add 12 and 21 to get 33.

$$\frac{\frac{69}{2}}{\frac{33}{28}}$$

Divide \frac{69}{2} by \frac{33}{28} by multiplying \frac{69}{2} by the reciprocal of \frac{33}{28}.

$$\frac{69}{2}\times \frac{28}{33}$$

Multiply \frac{69}{2} times \frac{28}{33} by multiplying numerator times numerator and denominator times denominator.

$$\frac{69\times 28}{2\times 33}$$

Do the multiplications in the fraction \frac{69\times 28}{2\times 33}.

$$\frac{1932}{66}$$

Reduce the fraction \frac{1932}{66} to lowest terms by extracting and canceling out 6.

$$\frac{322}{11}$$

Factor

$$\frac{2 \cdot 7 \cdot 23}{11} = 29\frac{3}{11} = 29.272727272727273$$