Solve 6.1/2*(61/12)^2-0.2*(61/12)^3+2.7*61/12

$$\frac { 6.1 } { 2 } \times ( \frac { 61 } { 12 } ) ^ { 2 } - 0.2 \times ( \frac { 61 } { 12 } ) ^ { 3 } + 2.7 \times \frac { 61 } { 12 }$$

Evaluate

$$\frac{286273}{4320}\approx 66.266898148$$

Solution Steps

Expand \frac{6.1}{2} by multiplying both numerator and the denominator by 10.

$$\frac{61}{20}\times \left(\frac{61}{12}\right)^{2}-0.2\times \left(\frac{61}{12}\right)^{3}+2.7\times \frac{61}{12}$$

Calculate \frac{61}{12} to the power of 2 and get \frac{3721}{144}.

$$\frac{61}{20}\times \frac{3721}{144}-0.2\times \left(\frac{61}{12}\right)^{3}+2.7\times \frac{61}{12}$$

Multiply \frac{61}{20} times \frac{3721}{144} by multiplying numerator times numerator and denominator times denominator.

$$\frac{61\times 3721}{20\times 144}-0.2\times \left(\frac{61}{12}\right)^{3}+2.7\times \frac{61}{12}$$

Do the multiplications in the fraction \frac{61\times 3721}{20\times 144}.

$$\frac{226981}{2880}-0.2\times \left(\frac{61}{12}\right)^{3}+2.7\times \frac{61}{12}$$

Calculate \frac{61}{12} to the power of 3 and get \frac{226981}{1728}.

$$\frac{226981}{2880}-0.2\times \frac{226981}{1728}+2.7\times \frac{61}{12}$$

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{226981}{2880}-\frac{1}{5}\times \frac{226981}{1728}+2.7\times \frac{61}{12}$$

Multiply \frac{1}{5} times \frac{226981}{1728} by multiplying numerator times numerator and denominator times denominator.

$$\frac{226981}{2880}-\frac{1\times 226981}{5\times 1728}+2.7\times \frac{61}{12}$$

Do the multiplications in the fraction \frac{1\times 226981}{5\times 1728}.

$$\frac{226981}{2880}-\frac{226981}{8640}+2.7\times \frac{61}{12}$$

Least common multiple of 2880 and 8640 is 8640. Convert \frac{226981}{2880} and \frac{226981}{8640} to fractions with denominator 8640.

$$\frac{680943}{8640}-\frac{226981}{8640}+2.7\times \frac{61}{12}$$

Since \frac{680943}{8640} and \frac{226981}{8640} have the same denominator, subtract them by subtracting their numerators.

$$\frac{680943-226981}{8640}+2.7\times \frac{61}{12}$$

Subtract 226981 from 680943 to get 453962.

$$\frac{453962}{8640}+2.7\times \frac{61}{12}$$

Reduce the fraction \frac{453962}{8640} to lowest terms by extracting and canceling out 2.

$$\frac{226981}{4320}+2.7\times \frac{61}{12}$$

Convert decimal number 2.7 to fraction \frac{27}{10}.

$$\frac{226981}{4320}+\frac{27}{10}\times \frac{61}{12}$$

Multiply \frac{27}{10} times \frac{61}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{226981}{4320}+\frac{27\times 61}{10\times 12}$$

Do the multiplications in the fraction \frac{27\times 61}{10\times 12}.

$$\frac{226981}{4320}+\frac{1647}{120}$$

Reduce the fraction \frac{1647}{120} to lowest terms by extracting and canceling out 3.

$$\frac{226981}{4320}+\frac{549}{40}$$

Least common multiple of 4320 and 40 is 4320. Convert \frac{226981}{4320} and \frac{549}{40} to fractions with denominator 4320.

$$\frac{226981}{4320}+\frac{59292}{4320}$$

Since \frac{226981}{4320} and \frac{59292}{4320} have the same denominator, add them by adding their numerators.

$$\frac{226981+59292}{4320}$$

Add 226981 and 59292 to get 286273.

$$\frac{286273}{4320}$$

Factor

$$\frac{13 \cdot 61 \cdot 19 ^ {2}}{5 \cdot 2 ^ {5} \cdot 3 ^ {3}} = 66\frac{1153}{4320} = 66.26689814814814$$