Solve |3/4*2+-1*3+0/sqrt{(frac{3{4})^2+(-1)^2}}|=

$$| \frac { \frac { 3 } { 4 } \times 2 + - 1 \times 3 + 0 } { \sqrt { ( \frac { 3 } { 4 } ) ^ { 2 } + ( - 1 ) ^ { 2 } } } | =$$

Evaluate

$$\frac{6}{5}=1.2$$

Solution Steps

Express \frac{3}{4}\times 2 as a single fraction.

$$|\frac{\frac{3\times 2}{4}-3+0}{\sqrt{\left(\frac{3}{4}\right)^{2}+\left(-1\right)^{2}}}|$$

Multiply 3 and 2 to get 6.

$$|\frac{\frac{6}{4}-3+0}{\sqrt{\left(\frac{3}{4}\right)^{2}+\left(-1\right)^{2}}}|$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$|\frac{\frac{3}{2}-3+0}{\sqrt{\left(\frac{3}{4}\right)^{2}+\left(-1\right)^{2}}}|$$

Convert 3 to fraction \frac{6}{2}.

$$|\frac{\frac{3}{2}-\frac{6}{2}+0}{\sqrt{\left(\frac{3}{4}\right)^{2}+\left(-1\right)^{2}}}|$$

Since \frac{3}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{\frac{3-6}{2}+0}{\sqrt{\left(\frac{3}{4}\right)^{2}+\left(-1\right)^{2}}}|$$

Subtract 6 from 3 to get -3.

$$|\frac{-\frac{3}{2}+0}{\sqrt{\left(\frac{3}{4}\right)^{2}+\left(-1\right)^{2}}}|$$

Add -\frac{3}{2} and 0 to get -\frac{3}{2}.

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

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$|\frac{-\frac{3}{2}}{\sqrt{\frac{9}{16}+\left(-1\right)^{2}}}|$$

Calculate -1 to the power of 2 and get 1.

$$|\frac{-\frac{3}{2}}{\sqrt{\frac{9}{16}+1}}|$$

Convert 1 to fraction \frac{16}{16}.

$$|\frac{-\frac{3}{2}}{\sqrt{\frac{9}{16}+\frac{16}{16}}}|$$

Since \frac{9}{16} and \frac{16}{16} have the same denominator, add them by adding their numerators.

$$|\frac{-\frac{3}{2}}{\sqrt{\frac{9+16}{16}}}|$$

Add 9 and 16 to get 25.

$$|\frac{-\frac{3}{2}}{\sqrt{\frac{25}{16}}}|$$

Rewrite the square root of the division \frac{25}{16} as the division of square roots \frac{\sqrt{25}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$|\frac{-\frac{3}{2}}{\frac{5}{4}}|$$

Divide -\frac{3}{2} by \frac{5}{4} by multiplying -\frac{3}{2} by the reciprocal of \frac{5}{4}.

$$|-\frac{3}{2}\times \frac{4}{5}|$$

Multiply -\frac{3}{2} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$|\frac{-3\times 4}{2\times 5}|$$

Do the multiplications in the fraction \frac{-3\times 4}{2\times 5}.

$$|\frac{-12}{10}|$$

Reduce the fraction \frac{-12}{10} to lowest terms by extracting and canceling out 2.

$$|-\frac{6}{5}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{6}{5} is \frac{6}{5}.

$$\frac{6}{5}$$

Factor

$$\frac{2 \cdot 3}{5} = 1\frac{1}{5} = 1.2$$