Solve (1/28+7/14+5/56)+(1+frac{1/12}{1+2})

$$( \frac { 1 } { 28 } + \frac { 7 } { 14 } + \frac { 5 } { 56 } ) + ( \frac { 1 + \frac { 1 } { 12 } } { 1 + 2 } )$$

Evaluate

$$\frac{71}{72}\approx 0.986111111$$

Solution Steps

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$\frac{1}{28}+\frac{1}{2}+\frac{5}{56}+\frac{1+\frac{1}{12}}{1+2}$$

Least common multiple of 28 and 2 is 28. Convert \frac{1}{28} and \frac{1}{2} to fractions with denominator 28.

$$\frac{1}{28}+\frac{14}{28}+\frac{5}{56}+\frac{1+\frac{1}{12}}{1+2}$$

Since \frac{1}{28} and \frac{14}{28} have the same denominator, add them by adding their numerators.

$$\frac{1+14}{28}+\frac{5}{56}+\frac{1+\frac{1}{12}}{1+2}$$

Add 1 and 14 to get 15.

$$\frac{15}{28}+\frac{5}{56}+\frac{1+\frac{1}{12}}{1+2}$$

Least common multiple of 28 and 56 is 56. Convert \frac{15}{28} and \frac{5}{56} to fractions with denominator 56.

$$\frac{30}{56}+\frac{5}{56}+\frac{1+\frac{1}{12}}{1+2}$$

Since \frac{30}{56} and \frac{5}{56} have the same denominator, add them by adding their numerators.

$$\frac{30+5}{56}+\frac{1+\frac{1}{12}}{1+2}$$

Add 30 and 5 to get 35.

$$\frac{35}{56}+\frac{1+\frac{1}{12}}{1+2}$$

Reduce the fraction \frac{35}{56} to lowest terms by extracting and canceling out 7.

$$\frac{5}{8}+\frac{1+\frac{1}{12}}{1+2}$$

Convert 1 to fraction \frac{12}{12}.

$$\frac{5}{8}+\frac{\frac{12}{12}+\frac{1}{12}}{1+2}$$

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

$$\frac{5}{8}+\frac{\frac{12+1}{12}}{1+2}$$

Add 12 and 1 to get 13.

$$\frac{5}{8}+\frac{\frac{13}{12}}{1+2}$$

Add 1 and 2 to get 3.

$$\frac{5}{8}+\frac{\frac{13}{12}}{3}$$

Express \frac{\frac{13}{12}}{3} as a single fraction.

$$\frac{5}{8}+\frac{13}{12\times 3}$$

Multiply 12 and 3 to get 36.

$$\frac{5}{8}+\frac{13}{36}$$

Least common multiple of 8 and 36 is 72. Convert \frac{5}{8} and \frac{13}{36} to fractions with denominator 72.

$$\frac{45}{72}+\frac{26}{72}$$

Since \frac{45}{72} and \frac{26}{72} have the same denominator, add them by adding their numerators.

$$\frac{45+26}{72}$$

Add 45 and 26 to get 71.

$$\frac{71}{72}$$

Factor

$$\frac{71}{2 ^ {3} \cdot 3 ^ {2}} = 0.9861111111111112$$