Solve 1/3(4*-25/32-1)+2/5(2*-25/32+5)-5

$$\frac { 1 } { 3 } ( 4 \times \frac { - 25 } { 32 } - 1 ) + \frac { 2 } { 5 } ( 2 \times \frac { - 25 } { 32 } + 5 ) - 5$$

Evaluate

$$-5$$

Solution Steps

Fraction \frac{-25}{32} can be rewritten as -\frac{25}{32} by extracting the negative sign.

$$\frac{1}{3}\left(4\left(-\frac{25}{32}\right)-1\right)+\frac{2}{5}\left(2\times \frac{-25}{32}+5\right)-5$$

Express 4\left(-\frac{25}{32}\right) as a single fraction.

$$\frac{1}{3}\left(\frac{4\left(-25\right)}{32}-1\right)+\frac{2}{5}\left(2\times \frac{-25}{32}+5\right)-5$$

Multiply 4 and -25 to get -100.

$$\frac{1}{3}\left(\frac{-100}{32}-1\right)+\frac{2}{5}\left(2\times \frac{-25}{32}+5\right)-5$$

Reduce the fraction \frac{-100}{32} to lowest terms by extracting and canceling out 4.

$$\frac{1}{3}\left(-\frac{25}{8}-1\right)+\frac{2}{5}\left(2\times \frac{-25}{32}+5\right)-5$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{1}{3}\left(-\frac{25}{8}-\frac{8}{8}\right)+\frac{2}{5}\left(2\times \frac{-25}{32}+5\right)-5$$

Since -\frac{25}{8} and \frac{8}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}\times \frac{-25-8}{8}+\frac{2}{5}\left(2\times \frac{-25}{32}+5\right)-5$$

Subtract 8 from -25 to get -33.

$$\frac{1}{3}\left(-\frac{33}{8}\right)+\frac{2}{5}\left(2\times \frac{-25}{32}+5\right)-5$$

Multiply \frac{1}{3} times -\frac{33}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-33\right)}{3\times 8}+\frac{2}{5}\left(2\times \frac{-25}{32}+5\right)-5$$

Do the multiplications in the fraction \frac{1\left(-33\right)}{3\times 8}.

$$\frac{-33}{24}+\frac{2}{5}\left(2\times \frac{-25}{32}+5\right)-5$$

Reduce the fraction \frac{-33}{24} to lowest terms by extracting and canceling out 3.

$$-\frac{11}{8}+\frac{2}{5}\left(2\times \frac{-25}{32}+5\right)-5$$

Fraction \frac{-25}{32} can be rewritten as -\frac{25}{32} by extracting the negative sign.

$$-\frac{11}{8}+\frac{2}{5}\left(2\left(-\frac{25}{32}\right)+5\right)-5$$

Express 2\left(-\frac{25}{32}\right) as a single fraction.

$$-\frac{11}{8}+\frac{2}{5}\left(\frac{2\left(-25\right)}{32}+5\right)-5$$

Multiply 2 and -25 to get -50.

$$-\frac{11}{8}+\frac{2}{5}\left(\frac{-50}{32}+5\right)-5$$

Reduce the fraction \frac{-50}{32} to lowest terms by extracting and canceling out 2.

$$-\frac{11}{8}+\frac{2}{5}\left(-\frac{25}{16}+5\right)-5$$

Convert 5 to fraction \frac{80}{16}.

$$-\frac{11}{8}+\frac{2}{5}\left(-\frac{25}{16}+\frac{80}{16}\right)-5$$

Since -\frac{25}{16} and \frac{80}{16} have the same denominator, add them by adding their numerators.

$$-\frac{11}{8}+\frac{2}{5}\times \frac{-25+80}{16}-5$$

Add -25 and 80 to get 55.

$$-\frac{11}{8}+\frac{2}{5}\times \frac{55}{16}-5$$

Multiply \frac{2}{5} times \frac{55}{16} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{11}{8}+\frac{2\times 55}{5\times 16}-5$$

Do the multiplications in the fraction \frac{2\times 55}{5\times 16}.

$$-\frac{11}{8}+\frac{110}{80}-5$$

Reduce the fraction \frac{110}{80} to lowest terms by extracting and canceling out 10.

$$-\frac{11}{8}+\frac{11}{8}-5$$

Add -\frac{11}{8} and \frac{11}{8} to get 0.

$$-5$$

Factor

$$-5$$