Solve 62/9div0.875-11/3*(7.5-45/6)

$$6 \frac { 2 } { 9 } \div 0.875 - 1 \frac { 1 } { 3 } \times ( 7.5 - 4 \frac { 5 } { 6 } )$$

Evaluate

$$\frac{32}{9}\approx 3.555555556$$

Solution Steps

Express \frac{\frac{6\times 9+2}{9}}{0.875} as a single fraction.

$$\frac{6\times 9+2}{9\times 0.875}-\frac{1\times 3+1}{3}\left(7.5-\frac{4\times 6+5}{6}\right)$$

Multiply 6 and 9 to get 54.

$$\frac{54+2}{9\times 0.875}-\frac{1\times 3+1}{3}\left(7.5-\frac{4\times 6+5}{6}\right)$$

Add 54 and 2 to get 56.

$$\frac{56}{9\times 0.875}-\frac{1\times 3+1}{3}\left(7.5-\frac{4\times 6+5}{6}\right)$$

Multiply 9 and 0.875 to get 7.875.

$$\frac{56}{7.875}-\frac{1\times 3+1}{3}\left(7.5-\frac{4\times 6+5}{6}\right)$$

Expand \frac{56}{7.875} by multiplying both numerator and the denominator by 1000.

$$\frac{56000}{7875}-\frac{1\times 3+1}{3}\left(7.5-\frac{4\times 6+5}{6}\right)$$

Reduce the fraction \frac{56000}{7875} to lowest terms by extracting and canceling out 875.

$$\frac{64}{9}-\frac{1\times 3+1}{3}\left(7.5-\frac{4\times 6+5}{6}\right)$$

Multiply 1 and 3 to get 3.

$$\frac{64}{9}-\frac{3+1}{3}\left(7.5-\frac{4\times 6+5}{6}\right)$$

Add 3 and 1 to get 4.

$$\frac{64}{9}-\frac{4}{3}\left(7.5-\frac{4\times 6+5}{6}\right)$$

Multiply 4 and 6 to get 24.

$$\frac{64}{9}-\frac{4}{3}\left(7.5-\frac{24+5}{6}\right)$$

Add 24 and 5 to get 29.

$$\frac{64}{9}-\frac{4}{3}\left(7.5-\frac{29}{6}\right)$$

Convert decimal number 7.5 to fraction \frac{75}{10}. Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

$$\frac{64}{9}-\frac{4}{3}\left(\frac{15}{2}-\frac{29}{6}\right)$$

Least common multiple of 2 and 6 is 6. Convert \frac{15}{2} and \frac{29}{6} to fractions with denominator 6.

$$\frac{64}{9}-\frac{4}{3}\left(\frac{45}{6}-\frac{29}{6}\right)$$

Since \frac{45}{6} and \frac{29}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{64}{9}-\frac{4}{3}\times \frac{45-29}{6}$$

Subtract 29 from 45 to get 16.

$$\frac{64}{9}-\frac{4}{3}\times \frac{16}{6}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$\frac{64}{9}-\frac{4}{3}\times \frac{8}{3}$$

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

$$\frac{64}{9}-\frac{4\times 8}{3\times 3}$$

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

$$\frac{64}{9}-\frac{32}{9}$$

Since \frac{64}{9} and \frac{32}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{64-32}{9}$$

Subtract 32 from 64 to get 32.

$$\frac{32}{9}$$

Factor

$$\frac{2 ^ {5}}{3 ^ {2}} = 3\frac{5}{9} = 3.5555555555555554$$