Solve 3/10(1/4)-1/2|frac{1/2|}{-3frac{5}{6}}

$$\frac { 3 } { 10 } ( \frac { 1 } { 4 } ) - \frac { \frac { 1 } { 2 } | \frac { 1 } { 2 } | } { - 3 \frac { 5 } { 6 } }$$

Evaluate

$$\frac{129}{920}\approx 0.140217391$$

Solution Steps

Multiply \frac{3}{10} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 1}{10\times 4}-\frac{\frac{1}{2}|\frac{1}{2}|}{-\frac{3\times 6+5}{6}}$$

Do the multiplications in the fraction \frac{3\times 1}{10\times 4}.

$$\frac{3}{40}-\frac{\frac{1}{2}|\frac{1}{2}|}{-\frac{3\times 6+5}{6}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{1}{2} is \frac{1}{2}.

$$\frac{3}{40}-\frac{\frac{1}{2}\times \frac{1}{2}}{-\frac{3\times 6+5}{6}}$$

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

$$\frac{3}{40}-\frac{\frac{1\times 1}{2\times 2}}{-\frac{3\times 6+5}{6}}$$

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

$$\frac{3}{40}-\frac{\frac{1}{4}}{-\frac{3\times 6+5}{6}}$$

Multiply 3 and 6 to get 18.

$$\frac{3}{40}-\frac{\frac{1}{4}}{-\frac{18+5}{6}}$$

Add 18 and 5 to get 23.

$$\frac{3}{40}-\frac{\frac{1}{4}}{-\frac{23}{6}}$$

Divide \frac{1}{4} by -\frac{23}{6} by multiplying \frac{1}{4} by the reciprocal of -\frac{23}{6}.

$$\frac{3}{40}-\frac{1}{4}\left(-\frac{6}{23}\right)$$

Multiply \frac{1}{4} times -\frac{6}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{40}-\frac{1\left(-6\right)}{4\times 23}$$

Do the multiplications in the fraction \frac{1\left(-6\right)}{4\times 23}.

$$\frac{3}{40}-\frac{-6}{92}$$

Reduce the fraction \frac{-6}{92} to lowest terms by extracting and canceling out 2.

$$\frac{3}{40}-\left(-\frac{3}{46}\right)$$

The opposite of -\frac{3}{46} is \frac{3}{46}.

$$\frac{3}{40}+\frac{3}{46}$$

Least common multiple of 40 and 46 is 920. Convert \frac{3}{40} and \frac{3}{46} to fractions with denominator 920.

$$\frac{69}{920}+\frac{60}{920}$$

Since \frac{69}{920} and \frac{60}{920} have the same denominator, add them by adding their numerators.

$$\frac{69+60}{920}$$

Add 69 and 60 to get 129.

$$\frac{129}{920}$$

Factor

$$\frac{3 \cdot 43}{2 ^ {3} \cdot 5 \cdot 23} = 0.14021739130434782$$