Solve 5(1/2+6)-1/8(3/7+4)

$$5 ( \frac { 1 } { 2 } + 6 ) - \frac { 1 } { 8 } ( \frac { 3 } { 7 } + 4 )$$

Evaluate

$$\frac{1789}{56}\approx 31.946428571$$

Solution Steps

Convert 6 to fraction \frac{12}{2}.

$$5\left(\frac{1}{2}+\frac{12}{2}\right)-\frac{1}{8}\left(\frac{3}{7}+4\right)$$

Since \frac{1}{2} and \frac{12}{2} have the same denominator, add them by adding their numerators.

$$5\times \frac{1+12}{2}-\frac{1}{8}\left(\frac{3}{7}+4\right)$$

Add 1 and 12 to get 13.

$$5\times \frac{13}{2}-\frac{1}{8}\left(\frac{3}{7}+4\right)$$

Express 5\times \frac{13}{2} as a single fraction.

$$\frac{5\times 13}{2}-\frac{1}{8}\left(\frac{3}{7}+4\right)$$

Multiply 5 and 13 to get 65.

$$\frac{65}{2}-\frac{1}{8}\left(\frac{3}{7}+4\right)$$

Convert 4 to fraction \frac{28}{7}.

$$\frac{65}{2}-\frac{1}{8}\left(\frac{3}{7}+\frac{28}{7}\right)$$

Since \frac{3}{7} and \frac{28}{7} have the same denominator, add them by adding their numerators.

$$\frac{65}{2}-\frac{1}{8}\times \frac{3+28}{7}$$

Add 3 and 28 to get 31.

$$\frac{65}{2}-\frac{1}{8}\times \frac{31}{7}$$

Multiply \frac{1}{8} times \frac{31}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{65}{2}-\frac{1\times 31}{8\times 7}$$

Do the multiplications in the fraction \frac{1\times 31}{8\times 7}.

$$\frac{65}{2}-\frac{31}{56}$$

Least common multiple of 2 and 56 is 56. Convert \frac{65}{2} and \frac{31}{56} to fractions with denominator 56.

$$\frac{1820}{56}-\frac{31}{56}$$

Since \frac{1820}{56} and \frac{31}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1820-31}{56}$$

Subtract 31 from 1820 to get 1789.

$$\frac{1789}{56}$$

Factor

$$\frac{1789}{2 ^ {3} \cdot 7} = 31\frac{53}{56} = 31.946428571428573$$