Solve 2/7+3/2*15/2-5/10-frac{1}{2}

$$\frac { 2 } { 7 } + \frac { 3 } { 2 } \times \frac { 15 } { 2 } - \frac { 5 } { 10 } - \frac { 1 } { 2 }$$

Evaluate

$$\frac{295}{28}\approx 10.535714286$$

Solution Steps

Multiply \frac{3}{2} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{7}+\frac{3\times 15}{2\times 2}-\frac{5}{10}-\frac{1}{2}$$

Do the multiplications in the fraction \frac{3\times 15}{2\times 2}.

$$\frac{2}{7}+\frac{45}{4}-\frac{5}{10}-\frac{1}{2}$$

Least common multiple of 7 and 4 is 28. Convert \frac{2}{7} and \frac{45}{4} to fractions with denominator 28.

$$\frac{8}{28}+\frac{315}{28}-\frac{5}{10}-\frac{1}{2}$$

Since \frac{8}{28} and \frac{315}{28} have the same denominator, add them by adding their numerators.

$$\frac{8+315}{28}-\frac{5}{10}-\frac{1}{2}$$

Add 8 and 315 to get 323.

$$\frac{323}{28}-\frac{5}{10}-\frac{1}{2}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{323}{28}-\frac{1}{2}-\frac{1}{2}$$

Least common multiple of 28 and 2 is 28. Convert \frac{323}{28} and \frac{1}{2} to fractions with denominator 28.

$$\frac{323}{28}-\frac{14}{28}-\frac{1}{2}$$

Since \frac{323}{28} and \frac{14}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{323-14}{28}-\frac{1}{2}$$

Subtract 14 from 323 to get 309.

$$\frac{309}{28}-\frac{1}{2}$$

Least common multiple of 28 and 2 is 28. Convert \frac{309}{28} and \frac{1}{2} to fractions with denominator 28.

$$\frac{309}{28}-\frac{14}{28}$$

Since \frac{309}{28} and \frac{14}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{309-14}{28}$$

Subtract 14 from 309 to get 295.

$$\frac{295}{28}$$

Factor

$$\frac{5 \cdot 59}{2 ^ {2} \cdot 7} = 10\frac{15}{28} = 10.535714285714286$$