Solve 4/5div(5/6*3/5)-11/2

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

Evaluate

$$\frac{1}{10}=0.1$$

Solution Steps

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

$$\frac{\frac{4}{5}}{\frac{5\times 3}{6\times 5}}-\frac{1\times 2+1}{2}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{4}{5}}{\frac{3}{6}}-\frac{1\times 2+1}{2}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

Divide \frac{4}{5} by \frac{1}{2} by multiplying \frac{4}{5} by the reciprocal of \frac{1}{2}.

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

Express \frac{4}{5}\times 2 as a single fraction.

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

Multiply 4 and 2 to get 8.

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

Multiply 1 and 2 to get 2.

$$\frac{8}{5}-\frac{2+1}{2}$$

Add 2 and 1 to get 3.

$$\frac{8}{5}-\frac{3}{2}$$

Least common multiple of 5 and 2 is 10. Convert \frac{8}{5} and \frac{3}{2} to fractions with denominator 10.

$$\frac{16}{10}-\frac{15}{10}$$

Since \frac{16}{10} and \frac{15}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-15}{10}$$

Subtract 15 from 16 to get 1.

$$\frac{1}{10}$$

Factor

$$\frac{1}{2 \cdot 5} = 0.1$$