Solve (79/120+7/8)+(13/120-23/40)

$$( \frac { 79 } { 120 } + \frac { 7 } { 8 } ) + ( \frac { 13 } { 120 } - \frac { 23 } { 40 } )$$

Evaluate

$$\frac{16}{15}\approx 1.066666667$$

Solution Steps

Least common multiple of 120 and 8 is 120. Convert \frac{79}{120} and \frac{7}{8} to fractions with denominator 120.

$$\frac{79}{120}+\frac{105}{120}+\frac{13}{120}-\frac{23}{40}$$

Since \frac{79}{120} and \frac{105}{120} have the same denominator, add them by adding their numerators.

$$\frac{79+105}{120}+\frac{13}{120}-\frac{23}{40}$$

Add 79 and 105 to get 184.

$$\frac{184}{120}+\frac{13}{120}-\frac{23}{40}$$

Since \frac{184}{120} and \frac{13}{120} have the same denominator, add them by adding their numerators.

$$\frac{184+13}{120}-\frac{23}{40}$$

Add 184 and 13 to get 197.

$$\frac{197}{120}-\frac{23}{40}$$

Least common multiple of 120 and 40 is 120. Convert \frac{197}{120} and \frac{23}{40} to fractions with denominator 120.

$$\frac{197}{120}-\frac{69}{120}$$

Since \frac{197}{120} and \frac{69}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{197-69}{120}$$

Subtract 69 from 197 to get 128.

$$\frac{128}{120}$$

Reduce the fraction \frac{128}{120} to lowest terms by extracting and canceling out 8.

$$\frac{16}{15}$$

Factor

$$\frac{2 ^ {4}}{3 \cdot 5} = 1\frac{1}{15} = 1.0666666666666667$$