Solve 1/2+2/3*8/7-11/2

$$\frac { 1 } { 2 } + \frac { 2 } { 3 } \times \frac { 8 } { 7 } - 1 \frac { 1 } { 2 }$$

Evaluate

$$-\frac{5}{21}\approx -0.238095238$$

Solution Steps

Multiply \frac{2}{3} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{2\times 8}{3\times 7}-\frac{1\times 2+1}{2}$$

Do the multiplications in the fraction \frac{2\times 8}{3\times 7}.

$$\frac{1}{2}+\frac{16}{21}-\frac{1\times 2+1}{2}$$

Least common multiple of 2 and 21 is 42. Convert \frac{1}{2} and \frac{16}{21} to fractions with denominator 42.

$$\frac{21}{42}+\frac{32}{42}-\frac{1\times 2+1}{2}$$

Since \frac{21}{42} and \frac{32}{42} have the same denominator, add them by adding their numerators.

$$\frac{21+32}{42}-\frac{1\times 2+1}{2}$$

Add 21 and 32 to get 53.

$$\frac{53}{42}-\frac{1\times 2+1}{2}$$

Multiply 1 and 2 to get 2.

$$\frac{53}{42}-\frac{2+1}{2}$$

Add 2 and 1 to get 3.

$$\frac{53}{42}-\frac{3}{2}$$

Least common multiple of 42 and 2 is 42. Convert \frac{53}{42} and \frac{3}{2} to fractions with denominator 42.

$$\frac{53}{42}-\frac{63}{42}$$

Since \frac{53}{42} and \frac{63}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{53-63}{42}$$

Subtract 63 from 53 to get -10.

$$\frac{-10}{42}$$

Reduce the fraction \frac{-10}{42} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{21}$$

Factor

$$-\frac{5}{21} = -0.23809523809523808$$