Solve (5/4-3/8*4/9)-4/5*frac{2}{1}

$$( \frac { 5 } { 4 } - \frac { 3 } { 8 } \cdot \frac { 4 } { 9 } ) - \frac { 4 } { 5 } \cdot \frac { 2 } { 1 }$$

Evaluate

$$-\frac{31}{60}\approx -0.516666667$$

Solution Steps

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

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

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

$$\frac{5}{4}-\frac{12}{72}-\frac{4}{5}\times \frac{2}{1}$$

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

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

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

$$\frac{15}{12}-\frac{2}{12}-\frac{4}{5}\times \frac{2}{1}$$

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

$$\frac{15-2}{12}-\frac{4}{5}\times \frac{2}{1}$$

Subtract 2 from 15 to get 13.

$$\frac{13}{12}-\frac{4}{5}\times \frac{2}{1}$$

Anything divided by one gives itself.

$$\frac{13}{12}-\frac{4}{5}\times 2$$

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

$$\frac{13}{12}-\frac{4\times 2}{5}$$

Multiply 4 and 2 to get 8.

$$\frac{13}{12}-\frac{8}{5}$$

Least common multiple of 12 and 5 is 60. Convert \frac{13}{12} and \frac{8}{5} to fractions with denominator 60.

$$\frac{65}{60}-\frac{96}{60}$$

Since \frac{65}{60} and \frac{96}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65-96}{60}$$

Subtract 96 from 65 to get -31.

$$-\frac{31}{60}$$

Factor

$$-\frac{31}{60} = -0.5166666666666667$$