Solve 42/23/3frac{8{23}}-217/23+-17/23

$$\frac{ 4 \frac{ 2 }{ 23 } }{ 3 \frac{ 8 }{ 23 } } -2 \frac{ 17 }{ 23 } +-1 \frac{ 7 }{ 23 }$$

Evaluate

$$-\frac{4999}{1771}\approx -2.82269904$$

Solution Steps

Divide \frac{4\times 23+2}{23} by \frac{3\times 23+8}{23} by multiplying \frac{4\times 23+2}{23} by the reciprocal of \frac{3\times 23+8}{23}.

$$\frac{\left(4\times 23+2\right)\times 23}{23\left(3\times 23+8\right)}-\frac{2\times 23+17}{23}-\frac{1\times 23+7}{23}$$

Cancel out 23 in both numerator and denominator.

$$\frac{2+4\times 23}{8+3\times 23}-\frac{2\times 23+17}{23}-\frac{1\times 23+7}{23}$$

Multiply 4 and 23 to get 92.

$$\frac{2+92}{8+3\times 23}-\frac{2\times 23+17}{23}-\frac{1\times 23+7}{23}$$

Add 2 and 92 to get 94.

$$\frac{94}{8+3\times 23}-\frac{2\times 23+17}{23}-\frac{1\times 23+7}{23}$$

Multiply 3 and 23 to get 69.

$$\frac{94}{8+69}-\frac{2\times 23+17}{23}-\frac{1\times 23+7}{23}$$

Add 8 and 69 to get 77.

$$\frac{94}{77}-\frac{2\times 23+17}{23}-\frac{1\times 23+7}{23}$$

Multiply 2 and 23 to get 46.

$$\frac{94}{77}-\frac{46+17}{23}-\frac{1\times 23+7}{23}$$

Add 46 and 17 to get 63.

$$\frac{94}{77}-\frac{63}{23}-\frac{1\times 23+7}{23}$$

Least common multiple of 77 and 23 is 1771. Convert \frac{94}{77} and \frac{63}{23} to fractions with denominator 1771.

$$\frac{2162}{1771}-\frac{4851}{1771}-\frac{1\times 23+7}{23}$$

Since \frac{2162}{1771} and \frac{4851}{1771} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2162-4851}{1771}-\frac{1\times 23+7}{23}$$

Subtract 4851 from 2162 to get -2689.

$$-\frac{2689}{1771}-\frac{1\times 23+7}{23}$$

Multiply 1 and 23 to get 23.

$$-\frac{2689}{1771}-\frac{23+7}{23}$$

Add 23 and 7 to get 30.

$$-\frac{2689}{1771}-\frac{30}{23}$$

Least common multiple of 1771 and 23 is 1771. Convert -\frac{2689}{1771} and \frac{30}{23} to fractions with denominator 1771.

$$-\frac{2689}{1771}-\frac{2310}{1771}$$

Since -\frac{2689}{1771} and \frac{2310}{1771} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2689-2310}{1771}$$

Subtract 2310 from -2689 to get -4999.

$$-\frac{4999}{1771}$$

Factor

$$-\frac{4999}{1771} = -2\frac{1457}{1771} = -2.8226990400903444$$