Solve (-1/3*(5)^3+3*(25)-8(5))-(-64/3+48-32)

$$( - \frac { 1 } { 3 } \cdot ( 5 ) ^ { 3 } + 3 \cdot ( 25 ) - 8 ( 5 ) ) - ( - \frac { 64 } { 3 } + 48 - 32 )$$

Evaluate

$$-\frac{4}{3}\approx -1.333333333$$

Solution Steps

Calculate 5 to the power of 3 and get 125.

$$-\frac{1}{3}\times 125+3\times 25-8\times 5-\left(-\frac{64}{3}+48-32\right)$$

Express -\frac{1}{3}\times 125 as a single fraction.

$$\frac{-125}{3}+3\times 25-8\times 5-\left(-\frac{64}{3}+48-32\right)$$

Fraction \frac{-125}{3} can be rewritten as -\frac{125}{3} by extracting the negative sign.

$$-\frac{125}{3}+3\times 25-8\times 5-\left(-\frac{64}{3}+48-32\right)$$

Multiply 3 and 25 to get 75.

$$-\frac{125}{3}+75-8\times 5-\left(-\frac{64}{3}+48-32\right)$$

Convert 75 to fraction \frac{225}{3}.

$$-\frac{125}{3}+\frac{225}{3}-8\times 5-\left(-\frac{64}{3}+48-32\right)$$

Since -\frac{125}{3} and \frac{225}{3} have the same denominator, add them by adding their numerators.

$$\frac{-125+225}{3}-8\times 5-\left(-\frac{64}{3}+48-32\right)$$

Add -125 and 225 to get 100.

$$\frac{100}{3}-8\times 5-\left(-\frac{64}{3}+48-32\right)$$

Multiply 8 and 5 to get 40.

$$\frac{100}{3}-40-\left(-\frac{64}{3}+48-32\right)$$

Convert 40 to fraction \frac{120}{3}.

$$\frac{100}{3}-\frac{120}{3}-\left(-\frac{64}{3}+48-32\right)$$

Since \frac{100}{3} and \frac{120}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{100-120}{3}-\left(-\frac{64}{3}+48-32\right)$$

Subtract 120 from 100 to get -20.

$$-\frac{20}{3}-\left(-\frac{64}{3}+48-32\right)$$

Convert 48 to fraction \frac{144}{3}.

$$-\frac{20}{3}-\left(-\frac{64}{3}+\frac{144}{3}-32\right)$$

Since -\frac{64}{3} and \frac{144}{3} have the same denominator, add them by adding their numerators.

$$-\frac{20}{3}-\left(\frac{-64+144}{3}-32\right)$$

Add -64 and 144 to get 80.

$$-\frac{20}{3}-\left(\frac{80}{3}-32\right)$$

Convert 32 to fraction \frac{96}{3}.

$$-\frac{20}{3}-\left(\frac{80}{3}-\frac{96}{3}\right)$$

Since \frac{80}{3} and \frac{96}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{20}{3}-\frac{80-96}{3}$$

Subtract 96 from 80 to get -16.

$$-\frac{20}{3}-\left(-\frac{16}{3}\right)$$

The opposite of -\frac{16}{3} is \frac{16}{3}.

$$-\frac{20}{3}+\frac{16}{3}$$

Since -\frac{20}{3} and \frac{16}{3} have the same denominator, add them by adding their numerators.

$$\frac{-20+16}{3}$$

Add -20 and 16 to get -4.

$$-\frac{4}{3}$$

Factor

$$-\frac{4}{3} = -1\frac{1}{3} = -1.3333333333333333$$