Solve 29.5[20:(13-3.3)+1]*4:8}:6+(15-12:6)

$$29.5 [ 20 : ( 13 - 3.3 ) + 1 ] \cdot 4 : 8 \} : 6 + ( 15 - 12 : 6 )$$

Evaluate

$$\frac{17523}{388}\approx 45.162371134$$

Solution Steps

Subtract 3.3 from 13 to get 9.7.

$$\frac{29.5\left(\frac{20}{9.7}+1\right)\times 4}{8}$$

Expand \frac{20}{9.7} by multiplying both numerator and the denominator by 10.

$$\frac{29.5\left(\frac{200}{97}+1\right)\times 4}{8}$$

Convert 1 to fraction \frac{97}{97}.

$$\frac{29.5\left(\frac{200}{97}+\frac{97}{97}\right)\times 4}{8}$$

Since \frac{200}{97} and \frac{97}{97} have the same denominator, add them by adding their numerators.

$$\frac{29.5\times \frac{200+97}{97}\times 4}{8}$$

Add 200 and 97 to get 297.

$$\frac{29.5\times \frac{297}{97}\times 4}{8}$$

Convert decimal number 29.5 to fraction \frac{295}{10}. Reduce the fraction \frac{295}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{59}{2}\times \frac{297}{97}\times 4}{8}$$

Multiply \frac{59}{2} times \frac{297}{97} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{59\times 297}{2\times 97}\times 4}{8}$$

Do the multiplications in the fraction \frac{59\times 297}{2\times 97}.

$$\frac{\frac{17523}{194}\times 4}{8}$$

Express \frac{17523}{194}\times 4 as a single fraction.

$$\frac{\frac{17523\times 4}{194}}{8}$$

Multiply 17523 and 4 to get 70092.

$$\frac{\frac{70092}{194}}{8}$$

Reduce the fraction \frac{70092}{194} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{35046}{97}}{8}$$

Express \frac{\frac{35046}{97}}{8} as a single fraction.

$$\frac{35046}{97\times 8}$$

Multiply 97 and 8 to get 776.

$$\frac{35046}{776}$$

Reduce the fraction \frac{35046}{776} to lowest terms by extracting and canceling out 2.

$$\frac{17523}{388}$$

Factor

$$\frac{11 \cdot 59 \cdot 3 ^ {3}}{97 \cdot 2 ^ {2}} = 45\frac{63}{388} = 45.16237113402062$$