Solve 15/8-1/4left(8/9div2/3right)

$$1 \frac{ 5 }{ 8 } - \frac{ 1 }{ 4 } \left( \frac{ 8 }{ 9 } \div \frac{ 2 }{ 3 } \right)$$

Evaluate

$$\frac{31}{24}\approx 1.291666667$$

Solution Steps

Multiply 1 and 8 to get 8.

$$\frac{8+5}{8}-\frac{1}{4}\times \frac{\frac{8}{9}}{\frac{2}{3}}$$

Add 8 and 5 to get 13.

$$\frac{13}{8}-\frac{1}{4}\times \frac{\frac{8}{9}}{\frac{2}{3}}$$

Divide \frac{8}{9} by \frac{2}{3} by multiplying \frac{8}{9} by the reciprocal of \frac{2}{3}.

$$\frac{13}{8}-\frac{1}{4}\times \frac{8}{9}\times \frac{3}{2}$$

Multiply \frac{8}{9} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{8}-\frac{1}{4}\times \frac{8\times 3}{9\times 2}$$

Do the multiplications in the fraction \frac{8\times 3}{9\times 2}.

$$\frac{13}{8}-\frac{1}{4}\times \frac{24}{18}$$

Reduce the fraction \frac{24}{18} to lowest terms by extracting and canceling out 6.

$$\frac{13}{8}-\frac{1}{4}\times \frac{4}{3}$$

Multiply \frac{1}{4} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{8}-\frac{1\times 4}{4\times 3}$$

Cancel out 4 in both numerator and denominator.

$$\frac{13}{8}-\frac{1}{3}$$

Least common multiple of 8 and 3 is 24. Convert \frac{13}{8} and \frac{1}{3} to fractions with denominator 24.

$$\frac{39}{24}-\frac{8}{24}$$

Since \frac{39}{24} and \frac{8}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{39-8}{24}$$

Subtract 8 from 39 to get 31.

$$\frac{31}{24}$$

Factor

$$\frac{31}{2 ^ {3} \cdot 3} = 1\frac{7}{24} = 1.2916666666666667$$