Solve 1+4/5(-5/2)+2div3/2-2(1/3-frac{3}{4})

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

Evaluate

$$\frac{7}{6}\approx 1.166666667$$

Solution Steps

Multiply \frac{4}{5} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{4\left(-5\right)}{5\times 2}.

$$1+\frac{-20}{10}+\frac{2}{\frac{3}{2}}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Divide -20 by 10 to get -2.

$$1-2+\frac{2}{\frac{3}{2}}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Subtract 2 from 1 to get -1.

$$-1+\frac{2}{\frac{3}{2}}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

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

$$-1+2\times \frac{2}{3}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Express 2\times \frac{2}{3} as a single fraction.

$$-1+\frac{2\times 2}{3}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Multiply 2 and 2 to get 4.

$$-1+\frac{4}{3}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Convert -1 to fraction -\frac{3}{3}.

$$-\frac{3}{3}+\frac{4}{3}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Since -\frac{3}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$\frac{-3+4}{3}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Add -3 and 4 to get 1.

$$\frac{1}{3}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{1}{3}-2\left(\frac{4}{12}-\frac{9}{12}\right)$$

Since \frac{4}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}-2\times \frac{4-9}{12}$$

Subtract 9 from 4 to get -5.

$$\frac{1}{3}-2\left(-\frac{5}{12}\right)$$

Express 2\left(-\frac{5}{12}\right) as a single fraction.

$$\frac{1}{3}-\frac{2\left(-5\right)}{12}$$

Multiply 2 and -5 to get -10.

$$\frac{1}{3}-\frac{-10}{12}$$

Reduce the fraction \frac{-10}{12} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}-\left(-\frac{5}{6}\right)$$

The opposite of -\frac{5}{6} is \frac{5}{6}.

$$\frac{1}{3}+\frac{5}{6}$$

Least common multiple of 3 and 6 is 6. Convert \frac{1}{3} and \frac{5}{6} to fractions with denominator 6.

$$\frac{2}{6}+\frac{5}{6}$$

Since \frac{2}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{2+5}{6}$$

Add 2 and 5 to get 7.

$$\frac{7}{6}$$

Factor

$$\frac{7}{2 \cdot 3} = 1\frac{1}{6} = 1.1666666666666667$$