Solve (3,24:9/7-31/5:11/3):(-0,9)

$$( 3,24 : \frac { 9 } { 7 } - 3 \frac { 1 } { 5 } : 1 \frac { 1 } { 3 } ) : ( - 0,9 )$$

Evaluate

$$-\frac{2}{15}\approx -0,133333333$$

Solution Steps

Divide 3,24 by \frac{9}{7} by multiplying 3,24 by the reciprocal of \frac{9}{7}.

$$\frac{3,24\times \frac{7}{9}-\frac{\frac{3\times 5+1}{5}}{\frac{1\times 3+1}{3}}}{-0,9}$$

Convert decimal number 3,24 to fraction \frac{324}{100}. Reduce the fraction \frac{324}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{81}{25}\times \frac{7}{9}-\frac{\frac{3\times 5+1}{5}}{\frac{1\times 3+1}{3}}}{-0,9}$$

Multiply \frac{81}{25} times \frac{7}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{81\times 7}{25\times 9}-\frac{\frac{3\times 5+1}{5}}{\frac{1\times 3+1}{3}}}{-0,9}$$

Do the multiplications in the fraction \frac{81\times 7}{25\times 9}.

$$\frac{\frac{567}{225}-\frac{\frac{3\times 5+1}{5}}{\frac{1\times 3+1}{3}}}{-0,9}$$

Reduce the fraction \frac{567}{225} to lowest terms by extracting and canceling out 9.

$$\frac{\frac{63}{25}-\frac{\frac{3\times 5+1}{5}}{\frac{1\times 3+1}{3}}}{-0,9}$$

Divide \frac{3\times 5+1}{5} by \frac{1\times 3+1}{3} by multiplying \frac{3\times 5+1}{5} by the reciprocal of \frac{1\times 3+1}{3}.

$$\frac{\frac{63}{25}-\frac{\left(3\times 5+1\right)\times 3}{5\left(1\times 3+1\right)}}{-0,9}$$

Multiply 3 and 5 to get 15.

$$\frac{\frac{63}{25}-\frac{\left(15+1\right)\times 3}{5\left(1\times 3+1\right)}}{-0,9}$$

Add 15 and 1 to get 16.

$$\frac{\frac{63}{25}-\frac{16\times 3}{5\left(1\times 3+1\right)}}{-0,9}$$

Multiply 16 and 3 to get 48.

$$\frac{\frac{63}{25}-\frac{48}{5\left(1\times 3+1\right)}}{-0,9}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{63}{25}-\frac{48}{5\left(3+1\right)}}{-0,9}$$

Add 3 and 1 to get 4.

$$\frac{\frac{63}{25}-\frac{48}{5\times 4}}{-0,9}$$

Multiply 5 and 4 to get 20.

$$\frac{\frac{63}{25}-\frac{48}{20}}{-0,9}$$

Reduce the fraction \frac{48}{20} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{63}{25}-\frac{12}{5}}{-0,9}$$

Least common multiple of 25 and 5 is 25. Convert \frac{63}{25} and \frac{12}{5} to fractions with denominator 25.

$$\frac{\frac{63}{25}-\frac{60}{25}}{-0,9}$$

Since \frac{63}{25} and \frac{60}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{63-60}{25}}{-0,9}$$

Subtract 60 from 63 to get 3.

$$\frac{\frac{3}{25}}{-0,9}$$

Express \frac{\frac{3}{25}}{-0,9} as a single fraction.

$$\frac{3}{25\left(-0,9\right)}$$

Multiply 25 and -0,9 to get -22,5.

$$\frac{3}{-22,5}$$

Expand \frac{3}{-22,5} by multiplying both numerator and the denominator by 10.

$$\frac{30}{-225}$$

Reduce the fraction \frac{30}{-225} to lowest terms by extracting and canceling out 15.

$$-\frac{2}{15}$$

Factor

$$-\frac{2}{15} = -0.13333333333333333$$