Solve 5/6div2/3-4/9*3/8

$$\frac{ 5 }{ 6 } \div \frac{ 2 }{ 3 } - \frac{ 4 }{ 9 } \times \frac{ 3 }{ 8 }$$

Evaluate

$$\frac{13}{12}\approx 1.083333333$$

Solution Steps

Divide \frac{5}{6} by \frac{2}{3} by multiplying \frac{5}{6} by the reciprocal of \frac{2}{3}.

$$\frac{5}{6}\times \frac{3}{2}-\frac{4}{9}\times \frac{3}{8}$$

Multiply \frac{5}{6} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 3}{6\times 2}-\frac{4}{9}\times \frac{3}{8}$$

Do the multiplications in the fraction \frac{5\times 3}{6\times 2}.

$$\frac{15}{12}-\frac{4}{9}\times \frac{3}{8}$$

Reduce the fraction \frac{15}{12} to lowest terms by extracting and canceling out 3.

$$\frac{5}{4}-\frac{4}{9}\times \frac{3}{8}$$

Multiply \frac{4}{9} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{4}-\frac{4\times 3}{9\times 8}$$

Do the multiplications in the fraction \frac{4\times 3}{9\times 8}.

$$\frac{5}{4}-\frac{12}{72}$$

Reduce the fraction \frac{12}{72} to lowest terms by extracting and canceling out 12.

$$\frac{5}{4}-\frac{1}{6}$$

Least common multiple of 4 and 6 is 12. Convert \frac{5}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{15}{12}-\frac{2}{12}$$

Since \frac{15}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-2}{12}$$

Subtract 2 from 15 to get 13.

$$\frac{13}{12}$$

Factor

$$\frac{13}{2 ^ {2} \cdot 3} = 1\frac{1}{12} = 1.0833333333333333$$