Solve 3+2[1/2(1/3+3/2*2)*2+(1/4)^2(-2)]+(-2)(frac{1}{4})

$$3 + 2 [ \frac { 1 } { 2 } ( \frac { 1 } { 3 } + \frac { 3 } { 2 } \cdot 2 ) \cdot 2 + ( \frac { 1 } { 4 } ) ^ { 2 } ( - 2 ) ] + ( - 2 ) ( \frac { 1 } { 4 } )$$

Evaluate

$$\frac{107}{12}\approx 8.916666667$$

Solution Steps

Cancel out 2 and 2.

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

Convert 3 to fraction \frac{9}{3}.

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

Since \frac{1}{3} and \frac{9}{3} have the same denominator, add them by adding their numerators.

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

Add 1 and 9 to get 10.

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

Multiply \frac{1}{2} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 10}{2\times 3}.

$$3+2\left(\frac{10}{6}\times 2+\left(\frac{1}{4}\right)^{2}\left(-2\right)\right)-2\times \frac{1}{4}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

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

Express \frac{5}{3}\times 2 as a single fraction.

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

Multiply 5 and 2 to get 10.

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

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$3+2\left(\frac{10}{3}+\frac{1}{16}\left(-2\right)\right)-2\times \frac{1}{4}$$

Multiply \frac{1}{16} and -2 to get \frac{-2}{16}.

$$3+2\left(\frac{10}{3}+\frac{-2}{16}\right)-2\times \frac{1}{4}$$

Reduce the fraction \frac{-2}{16} to lowest terms by extracting and canceling out 2.

$$3+2\left(\frac{10}{3}-\frac{1}{8}\right)-2\times \frac{1}{4}$$

Least common multiple of 3 and 8 is 24. Convert \frac{10}{3} and \frac{1}{8} to fractions with denominator 24.

$$3+2\left(\frac{80}{24}-\frac{3}{24}\right)-2\times \frac{1}{4}$$

Since \frac{80}{24} and \frac{3}{24} have the same denominator, subtract them by subtracting their numerators.

$$3+2\times \frac{80-3}{24}-2\times \frac{1}{4}$$

Subtract 3 from 80 to get 77.

$$3+2\times \frac{77}{24}-2\times \frac{1}{4}$$

Express 2\times \frac{77}{24} as a single fraction.

$$3+\frac{2\times 77}{24}-2\times \frac{1}{4}$$

Multiply 2 and 77 to get 154.

$$3+\frac{154}{24}-2\times \frac{1}{4}$$

Reduce the fraction \frac{154}{24} to lowest terms by extracting and canceling out 2.

$$3+\frac{77}{12}-2\times \frac{1}{4}$$

Convert 3 to fraction \frac{36}{12}.

$$\frac{36}{12}+\frac{77}{12}-2\times \frac{1}{4}$$

Since \frac{36}{12} and \frac{77}{12} have the same denominator, add them by adding their numerators.

$$\frac{36+77}{12}-2\times \frac{1}{4}$$

Add 36 and 77 to get 113.

$$\frac{113}{12}-2\times \frac{1}{4}$$

Multiply -2 and \frac{1}{4} to get \frac{-2}{4}.

$$\frac{113}{12}+\frac{-2}{4}$$

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

$$\frac{113}{12}-\frac{1}{2}$$

Least common multiple of 12 and 2 is 12. Convert \frac{113}{12} and \frac{1}{2} to fractions with denominator 12.

$$\frac{113}{12}-\frac{6}{12}$$

Since \frac{113}{12} and \frac{6}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{113-6}{12}$$

Subtract 6 from 113 to get 107.

$$\frac{107}{12}$$

Factor

$$\frac{107}{2 ^ {2} \cdot 3} = 8\frac{11}{12} = 8.916666666666666$$