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

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

Evaluate

$$\frac{281}{6}\approx 46.833333333$$

Solution Steps

Convert -3 to fraction -\frac{12}{4}.

$$-2\left(-3+5\left(-\frac{12}{4}+\frac{3}{4}\right)\right)-5\left(\frac{4}{3}-2\times 5\times \frac{1}{2}\right)$$

Since -\frac{12}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$-2\left(-3+5\times \frac{-12+3}{4}\right)-5\left(\frac{4}{3}-2\times 5\times \frac{1}{2}\right)$$

Add -12 and 3 to get -9.

$$-2\left(-3+5\left(-\frac{9}{4}\right)\right)-5\left(\frac{4}{3}-2\times 5\times \frac{1}{2}\right)$$

Express 5\left(-\frac{9}{4}\right) as a single fraction.

$$-2\left(-3+\frac{5\left(-9\right)}{4}\right)-5\left(\frac{4}{3}-2\times 5\times \frac{1}{2}\right)$$

Multiply 5 and -9 to get -45.

$$-2\left(-3+\frac{-45}{4}\right)-5\left(\frac{4}{3}-2\times 5\times \frac{1}{2}\right)$$

Fraction \frac{-45}{4} can be rewritten as -\frac{45}{4} by extracting the negative sign.

$$-2\left(-3-\frac{45}{4}\right)-5\left(\frac{4}{3}-2\times 5\times \frac{1}{2}\right)$$

Convert -3 to fraction -\frac{12}{4}.

$$-2\left(-\frac{12}{4}-\frac{45}{4}\right)-5\left(\frac{4}{3}-2\times 5\times \frac{1}{2}\right)$$

Since -\frac{12}{4} and \frac{45}{4} have the same denominator, subtract them by subtracting their numerators.

$$-2\times \frac{-12-45}{4}-5\left(\frac{4}{3}-2\times 5\times \frac{1}{2}\right)$$

Subtract 45 from -12 to get -57.

$$-2\left(-\frac{57}{4}\right)-5\left(\frac{4}{3}-2\times 5\times \frac{1}{2}\right)$$

Express -2\left(-\frac{57}{4}\right) as a single fraction.

$$\frac{-2\left(-57\right)}{4}-5\left(\frac{4}{3}-2\times 5\times \frac{1}{2}\right)$$

Multiply -2 and -57 to get 114.

$$\frac{114}{4}-5\left(\frac{4}{3}-2\times 5\times \frac{1}{2}\right)$$

Reduce the fraction \frac{114}{4} to lowest terms by extracting and canceling out 2.

$$\frac{57}{2}-5\left(\frac{4}{3}-2\times 5\times \frac{1}{2}\right)$$

Multiply 2 and 5 to get 10.

$$\frac{57}{2}-5\left(\frac{4}{3}-10\times \frac{1}{2}\right)$$

Multiply 10 and \frac{1}{2} to get \frac{10}{2}.

$$\frac{57}{2}-5\left(\frac{4}{3}-\frac{10}{2}\right)$$

Divide 10 by 2 to get 5.

$$\frac{57}{2}-5\left(\frac{4}{3}-5\right)$$

Convert 5 to fraction \frac{15}{3}.

$$\frac{57}{2}-5\left(\frac{4}{3}-\frac{15}{3}\right)$$

Since \frac{4}{3} and \frac{15}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{57}{2}-5\times \frac{4-15}{3}$$

Subtract 15 from 4 to get -11.

$$\frac{57}{2}-5\left(-\frac{11}{3}\right)$$

Express 5\left(-\frac{11}{3}\right) as a single fraction.

$$\frac{57}{2}-\frac{5\left(-11\right)}{3}$$

Multiply 5 and -11 to get -55.

$$\frac{57}{2}-\frac{-55}{3}$$

Fraction \frac{-55}{3} can be rewritten as -\frac{55}{3} by extracting the negative sign.

$$\frac{57}{2}-\left(-\frac{55}{3}\right)$$

The opposite of -\frac{55}{3} is \frac{55}{3}.

$$\frac{57}{2}+\frac{55}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{57}{2} and \frac{55}{3} to fractions with denominator 6.

$$\frac{171}{6}+\frac{110}{6}$$

Since \frac{171}{6} and \frac{110}{6} have the same denominator, add them by adding their numerators.

$$\frac{171+110}{6}$$

Add 171 and 110 to get 281.

$$\frac{281}{6}$$

Factor

$$\frac{281}{2 \cdot 3} = 46\frac{5}{6} = 46.833333333333336$$