Solve (|-24/37|:|-3/74|-2^2*3^2/10):|-11/30|-|-11,9|

$$( | - \frac { 24 } { 37 } | : | - \frac { 3 } { 74 } | - \frac { 2 ^ { 2 } \cdot 3 ^ { 2 } } { 10 } ) : | - 1 \frac { 1 } { 30 } | - | - 11,9 |$$

Evaluate

$$0,1$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{24}{37} is \frac{24}{37}.

$$\frac{\frac{\frac{24}{37}}{|-\frac{3}{74}|}-\frac{2^{2}\times 3^{2}}{10}}{|-\frac{1\times 30+1}{30}|}-|-11,9|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{3}{74} is \frac{3}{74}.

$$\frac{\frac{\frac{24}{37}}{\frac{3}{74}}-\frac{2^{2}\times 3^{2}}{10}}{|-\frac{1\times 30+1}{30}|}-|-11,9|$$

Divide \frac{24}{37} by \frac{3}{74} by multiplying \frac{24}{37} by the reciprocal of \frac{3}{74}.

$$\frac{\frac{24}{37}\times \frac{74}{3}-\frac{2^{2}\times 3^{2}}{10}}{|-\frac{1\times 30+1}{30}|}-|-11,9|$$

Multiply \frac{24}{37} times \frac{74}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{24\times 74}{37\times 3}-\frac{2^{2}\times 3^{2}}{10}}{|-\frac{1\times 30+1}{30}|}-|-11,9|$$

Do the multiplications in the fraction \frac{24\times 74}{37\times 3}.

$$\frac{\frac{1776}{111}-\frac{2^{2}\times 3^{2}}{10}}{|-\frac{1\times 30+1}{30}|}-|-11,9|$$

Divide 1776 by 111 to get 16.

$$\frac{16-\frac{2^{2}\times 3^{2}}{10}}{|-\frac{1\times 30+1}{30}|}-|-11,9|$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16-\frac{4\times 3^{2}}{10}}{|-\frac{1\times 30+1}{30}|}-|-11,9|$$

Calculate 3 to the power of 2 and get 9.

$$\frac{16-\frac{4\times 9}{10}}{|-\frac{1\times 30+1}{30}|}-|-11,9|$$

Multiply 4 and 9 to get 36.

$$\frac{16-\frac{36}{10}}{|-\frac{1\times 30+1}{30}|}-|-11,9|$$

Reduce the fraction \frac{36}{10} to lowest terms by extracting and canceling out 2.

$$\frac{16-\frac{18}{5}}{|-\frac{1\times 30+1}{30}|}-|-11,9|$$

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

$$\frac{\frac{80}{5}-\frac{18}{5}}{|-\frac{1\times 30+1}{30}|}-|-11,9|$$

Since \frac{80}{5} and \frac{18}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{80-18}{5}}{|-\frac{1\times 30+1}{30}|}-|-11,9|$$

Subtract 18 from 80 to get 62.

$$\frac{\frac{62}{5}}{|-\frac{1\times 30+1}{30}|}-|-11,9|$$

Multiply 1 and 30 to get 30.

$$\frac{\frac{62}{5}}{|-\frac{30+1}{30}|}-|-11,9|$$

Add 30 and 1 to get 31.

$$\frac{\frac{62}{5}}{|-\frac{31}{30}|}-|-11,9|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{31}{30} is \frac{31}{30}.

$$\frac{\frac{62}{5}}{\frac{31}{30}}-|-11,9|$$

Divide \frac{62}{5} by \frac{31}{30} by multiplying \frac{62}{5} by the reciprocal of \frac{31}{30}.

$$\frac{62}{5}\times \frac{30}{31}-|-11,9|$$

Multiply \frac{62}{5} times \frac{30}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{62\times 30}{5\times 31}-|-11,9|$$

Do the multiplications in the fraction \frac{62\times 30}{5\times 31}.

$$\frac{1860}{155}-|-11,9|$$

Divide 1860 by 155 to get 12.

$$12-|-11,9|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -11,9 is 11,9.

$$12-11,9$$

Subtract 11,9 from 12 to get 0,1.

$$0,1$$

Factor

$$\frac{1}{2 \cdot 5} = 0.1$$