Solve 15/16*[1div(2/3+1/2)]

$$\frac { 15 } { 16 } \times [ 1 \div ( \frac { 2 } { 3 } + \frac { 1 } { 2 } ) ]$$

Evaluate

$$\frac{45}{56}\approx 0.803571429$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{15}{16}\times \frac{1}{\frac{4}{6}+\frac{3}{6}}$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{15}{16}\times \frac{1}{\frac{4+3}{6}}$$

Add 4 and 3 to get 7.

$$\frac{15}{16}\times \frac{1}{\frac{7}{6}}$$

Divide 1 by \frac{7}{6} by multiplying 1 by the reciprocal of \frac{7}{6}.

$$\frac{15}{16}\times 1\times \frac{6}{7}$$

Multiply 1 and \frac{6}{7} to get \frac{6}{7}.

$$\frac{15}{16}\times \frac{6}{7}$$

Multiply \frac{15}{16} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\times 6}{16\times 7}$$

Do the multiplications in the fraction \frac{15\times 6}{16\times 7}.

$$\frac{90}{112}$$

Reduce the fraction \frac{90}{112} to lowest terms by extracting and canceling out 2.

$$\frac{45}{56}$$

Factor

$$\frac{3 ^ {2} \cdot 5}{2 ^ {3} \cdot 7} = 0.8035714285714286$$