Solve (6/17+3/5text{of}71/2)+13/17

$$( \frac { 6 } { 17 } + \frac { 3 } { 5 } \text { of } 7 \frac { 1 } { 2 } ) + \frac { 13 } { 17 }$$

Evaluate

$$\frac{191}{34}\approx 5.617647059$$

Solution Steps

Multiply 7 and 2 to get 14.

$$\frac{6}{17}+\frac{3}{5}\times \frac{14+1}{2}+\frac{13}{17}$$

Add 14 and 1 to get 15.

$$\frac{6}{17}+\frac{3}{5}\times \frac{15}{2}+\frac{13}{17}$$

Multiply \frac{3}{5} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{17}+\frac{3\times 15}{5\times 2}+\frac{13}{17}$$

Do the multiplications in the fraction \frac{3\times 15}{5\times 2}.

$$\frac{6}{17}+\frac{45}{10}+\frac{13}{17}$$

Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$\frac{6}{17}+\frac{9}{2}+\frac{13}{17}$$

Least common multiple of 17 and 2 is 34. Convert \frac{6}{17} and \frac{9}{2} to fractions with denominator 34.

$$\frac{12}{34}+\frac{153}{34}+\frac{13}{17}$$

Since \frac{12}{34} and \frac{153}{34} have the same denominator, add them by adding their numerators.

$$\frac{12+153}{34}+\frac{13}{17}$$

Add 12 and 153 to get 165.

$$\frac{165}{34}+\frac{13}{17}$$

Least common multiple of 34 and 17 is 34. Convert \frac{165}{34} and \frac{13}{17} to fractions with denominator 34.

$$\frac{165}{34}+\frac{26}{34}$$

Since \frac{165}{34} and \frac{26}{34} have the same denominator, add them by adding their numerators.

$$\frac{165+26}{34}$$

Add 165 and 26 to get 191.

$$\frac{191}{34}$$

Factor

$$\frac{191}{2 \cdot 17} = 5\frac{21}{34} = 5.617647058823529$$