Solve 13div17/8*(3/4+3/7)

$$13 \div \frac{ 17 }{ 8 } \times ( \frac{ 3 }{ 4 } + \frac{ 3 }{ 7 } )$$

Evaluate

$$\frac{858}{119}\approx 7.210084034$$

Solution Steps

Divide 13 by \frac{17}{8} by multiplying 13 by the reciprocal of \frac{17}{8}.

$$13\times \frac{8}{17}\left(\frac{3}{4}+\frac{3}{7}\right)$$

Express 13\times \frac{8}{17} as a single fraction.

$$\frac{13\times 8}{17}\left(\frac{3}{4}+\frac{3}{7}\right)$$

Multiply 13 and 8 to get 104.

$$\frac{104}{17}\left(\frac{3}{4}+\frac{3}{7}\right)$$

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

$$\frac{104}{17}\left(\frac{21}{28}+\frac{12}{28}\right)$$

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

$$\frac{104}{17}\times \frac{21+12}{28}$$

Add 21 and 12 to get 33.

$$\frac{104}{17}\times \frac{33}{28}$$

Multiply \frac{104}{17} times \frac{33}{28} by multiplying numerator times numerator and denominator times denominator.

$$\frac{104\times 33}{17\times 28}$$

Do the multiplications in the fraction \frac{104\times 33}{17\times 28}.

$$\frac{3432}{476}$$

Reduce the fraction \frac{3432}{476} to lowest terms by extracting and canceling out 4.

$$\frac{858}{119}$$

Factor

$$\frac{2 \cdot 3 \cdot 11 \cdot 13}{7 \cdot 17} = 7\frac{25}{119} = 7.2100840336134455$$