Solve 1/2left(7/3+7/5-14/4right)

$$\frac{ 1 }{ 2 } \left( \frac{ 7 }{ 3 } + \frac{ 7 }{ 5 } - \frac{ 14 }{ 4 } \right)$$

Evaluate

$$\frac{7}{60}\approx 0.116666667$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{7}{3} and \frac{7}{5} to fractions with denominator 15.

$$\frac{1}{2}\left(\frac{35}{15}+\frac{21}{15}-\frac{14}{4}\right)$$

Since \frac{35}{15} and \frac{21}{15} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}\left(\frac{35+21}{15}-\frac{14}{4}\right)$$

Add 35 and 21 to get 56.

$$\frac{1}{2}\left(\frac{56}{15}-\frac{14}{4}\right)$$

Reduce the fraction \frac{14}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}\left(\frac{56}{15}-\frac{7}{2}\right)$$

Least common multiple of 15 and 2 is 30. Convert \frac{56}{15} and \frac{7}{2} to fractions with denominator 30.

$$\frac{1}{2}\left(\frac{112}{30}-\frac{105}{30}\right)$$

Since \frac{112}{30} and \frac{105}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{112-105}{30}$$

Subtract 105 from 112 to get 7.

$$\frac{1}{2}\times \frac{7}{30}$$

Multiply \frac{1}{2} times \frac{7}{30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 7}{2\times 30}$$

Do the multiplications in the fraction \frac{1\times 7}{2\times 30}.

$$\frac{7}{60}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3 \cdot 5} = 0.11666666666666667$$