Solve -1div2/3-[sqrt{25}-(-1/3*5/2)-sqrt{64}]=

$$- 1 \div \frac { 2 } { 3 } - [ \sqrt { 25 } - ( - \frac { 1 } { 3 } \cdot \frac { 5 } { 2 } ) - \sqrt { 64 } ] =$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Divide -1 by \frac{2}{3} by multiplying -1 by the reciprocal of \frac{2}{3}.

$$-\frac{3}{2}-\left(\sqrt{25}-\left(-\frac{1}{3}\times \frac{5}{2}\right)-\sqrt{64}\right)$$

Calculate the square root of 25 and get 5.

$$-\frac{3}{2}-\left(5-\left(-\frac{1}{3}\times \frac{5}{2}\right)-\sqrt{64}\right)$$

Multiply -\frac{1}{3} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{3}{2}-\left(5-\frac{-5}{3\times 2}-\sqrt{64}\right)$$

Do the multiplications in the fraction \frac{-5}{3\times 2}.

$$-\frac{3}{2}-\left(5-\frac{-5}{6}-\sqrt{64}\right)$$

Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$-\frac{3}{2}-\left(5-\left(-\frac{5}{6}\right)-\sqrt{64}\right)$$

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

$$-\frac{3}{2}-\left(5+\frac{5}{6}-\sqrt{64}\right)$$

Convert 5 to fraction \frac{30}{6}.

$$-\frac{3}{2}-\left(\frac{30}{6}+\frac{5}{6}-\sqrt{64}\right)$$

Since \frac{30}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$-\frac{3}{2}-\left(\frac{30+5}{6}-\sqrt{64}\right)$$

Add 30 and 5 to get 35.

$$-\frac{3}{2}-\left(\frac{35}{6}-\sqrt{64}\right)$$

Calculate the square root of 64 and get 8.

$$-\frac{3}{2}-\left(\frac{35}{6}-8\right)$$

Convert 8 to fraction \frac{48}{6}.

$$-\frac{3}{2}-\left(\frac{35}{6}-\frac{48}{6}\right)$$

Since \frac{35}{6} and \frac{48}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{2}-\frac{35-48}{6}$$

Subtract 48 from 35 to get -13.

$$-\frac{3}{2}-\left(-\frac{13}{6}\right)$$

The opposite of -\frac{13}{6} is \frac{13}{6}.

$$-\frac{3}{2}+\frac{13}{6}$$

Least common multiple of 2 and 6 is 6. Convert -\frac{3}{2} and \frac{13}{6} to fractions with denominator 6.

$$-\frac{9}{6}+\frac{13}{6}$$

Since -\frac{9}{6} and \frac{13}{6} have the same denominator, add them by adding their numerators.

$$\frac{-9+13}{6}$$

Add -9 and 13 to get 4.

$$\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$