Solve 12/1+left(frac{12{3.1}-1right)30-10/80*0.5}

$$\frac{ 12 }{ 1+ \left( \frac{ 12 }{ 3.1 } -1 \right) \frac{ 30-10 }{ 80 } \times 0.5 }$$

Evaluate

$$\frac{2976}{337}\approx 8.830860534$$

Solution Steps

Expand \frac{12}{3.1} by multiplying both numerator and the denominator by 10.

$$\frac{12}{1+\left(\frac{120}{31}-1\right)\times \frac{30-10}{80}\times 0.5}$$

Convert 1 to fraction \frac{31}{31}.

$$\frac{12}{1+\left(\frac{120}{31}-\frac{31}{31}\right)\times \frac{30-10}{80}\times 0.5}$$

Since \frac{120}{31} and \frac{31}{31} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{1+\frac{120-31}{31}\times \frac{30-10}{80}\times 0.5}$$

Subtract 31 from 120 to get 89.

$$\frac{12}{1+\frac{89}{31}\times \frac{30-10}{80}\times 0.5}$$

Subtract 10 from 30 to get 20.

$$\frac{12}{1+\frac{89}{31}\times \frac{20}{80}\times 0.5}$$

Reduce the fraction \frac{20}{80} to lowest terms by extracting and canceling out 20.

$$\frac{12}{1+\frac{89}{31}\times \frac{1}{4}\times 0.5}$$

Multiply \frac{89}{31} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{1+\frac{89\times 1}{31\times 4}\times 0.5}$$

Do the multiplications in the fraction \frac{89\times 1}{31\times 4}.

$$\frac{12}{1+\frac{89}{124}\times 0.5}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{12}{1+\frac{89}{124}\times \frac{1}{2}}$$

Multiply \frac{89}{124} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{1+\frac{89\times 1}{124\times 2}}$$

Do the multiplications in the fraction \frac{89\times 1}{124\times 2}.

$$\frac{12}{1+\frac{89}{248}}$$

Convert 1 to fraction \frac{248}{248}.

$$\frac{12}{\frac{248}{248}+\frac{89}{248}}$$

Since \frac{248}{248} and \frac{89}{248} have the same denominator, add them by adding their numerators.

$$\frac{12}{\frac{248+89}{248}}$$

Add 248 and 89 to get 337.

$$\frac{12}{\frac{337}{248}}$$

Divide 12 by \frac{337}{248} by multiplying 12 by the reciprocal of \frac{337}{248}.

$$12\times \frac{248}{337}$$

Express 12\times \frac{248}{337} as a single fraction.

$$\frac{12\times 248}{337}$$

Multiply 12 and 248 to get 2976.

$$\frac{2976}{337}$$

Factor

$$\frac{3 \cdot 31 \cdot 2 ^ {5}}{337} = 8\frac{280}{337} = 8.830860534124628$$