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

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

Evaluate

$$\frac{7}{10}=0.7$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{7}{2} and \frac{7}{5} to fractions with denominator 10.

$$\frac{1}{2}\left(\frac{35}{10}+\frac{14}{10}-\frac{14}{4}\right)$$

Since \frac{35}{10} and \frac{14}{10} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}\left(\frac{35+14}{10}-\frac{14}{4}\right)$$

Add 35 and 14 to get 49.

$$\frac{1}{2}\left(\frac{49}{10}-\frac{14}{4}\right)$$

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

$$\frac{1}{2}\left(\frac{49}{10}-\frac{7}{2}\right)$$

Least common multiple of 10 and 2 is 10. Convert \frac{49}{10} and \frac{7}{2} to fractions with denominator 10.

$$\frac{1}{2}\left(\frac{49}{10}-\frac{35}{10}\right)$$

Since \frac{49}{10} and \frac{35}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{49-35}{10}$$

Subtract 35 from 49 to get 14.

$$\frac{1}{2}\times \frac{14}{10}$$

Reduce the fraction \frac{14}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}\times \frac{7}{5}$$

Multiply \frac{1}{2} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 7}{2\times 5}$$

Do the multiplications in the fraction \frac{1\times 7}{2\times 5}.

$$\frac{7}{10}$$

Factor

$$\frac{7}{2 \cdot 5} = 0.7$$