Solve 2/21*127-1/3*(1023/5-3/2*255+4*63-4*15)=

$$\frac { 2 } { 21 } \times 127 - \frac { 1 } { 3 } \times ( \frac { 1023 } { 5 } - \frac { 3 } { 2 } \times 255 + 4 \times 63 - 4 \times 15 ) =$$

Evaluate

$$\frac{1553}{210}\approx 7.395238095$$

Solution Steps

Express \frac{2}{21}\times 127 as a single fraction.

$$\frac{2\times 127}{21}-\frac{1}{3}\left(\frac{1023}{5}-\frac{3}{2}\times 255+4\times 63-4\times 15\right)$$

Multiply 2 and 127 to get 254.

$$\frac{254}{21}-\frac{1}{3}\left(\frac{1023}{5}-\frac{3}{2}\times 255+4\times 63-4\times 15\right)$$

Express \frac{3}{2}\times 255 as a single fraction.

$$\frac{254}{21}-\frac{1}{3}\left(\frac{1023}{5}-\frac{3\times 255}{2}+4\times 63-4\times 15\right)$$

Multiply 3 and 255 to get 765.

$$\frac{254}{21}-\frac{1}{3}\left(\frac{1023}{5}-\frac{765}{2}+4\times 63-4\times 15\right)$$

Least common multiple of 5 and 2 is 10. Convert \frac{1023}{5} and \frac{765}{2} to fractions with denominator 10.

$$\frac{254}{21}-\frac{1}{3}\left(\frac{2046}{10}-\frac{3825}{10}+4\times 63-4\times 15\right)$$

Since \frac{2046}{10} and \frac{3825}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{254}{21}-\frac{1}{3}\left(\frac{2046-3825}{10}+4\times 63-4\times 15\right)$$

Subtract 3825 from 2046 to get -1779.

$$\frac{254}{21}-\frac{1}{3}\left(-\frac{1779}{10}+4\times 63-4\times 15\right)$$

Multiply 4 and 63 to get 252.

$$\frac{254}{21}-\frac{1}{3}\left(-\frac{1779}{10}+252-4\times 15\right)$$

Convert 252 to fraction \frac{2520}{10}.

$$\frac{254}{21}-\frac{1}{3}\left(-\frac{1779}{10}+\frac{2520}{10}-4\times 15\right)$$

Since -\frac{1779}{10} and \frac{2520}{10} have the same denominator, add them by adding their numerators.

$$\frac{254}{21}-\frac{1}{3}\left(\frac{-1779+2520}{10}-4\times 15\right)$$

Add -1779 and 2520 to get 741.

$$\frac{254}{21}-\frac{1}{3}\left(\frac{741}{10}-4\times 15\right)$$

Multiply 4 and 15 to get 60.

$$\frac{254}{21}-\frac{1}{3}\left(\frac{741}{10}-60\right)$$

Convert 60 to fraction \frac{600}{10}.

$$\frac{254}{21}-\frac{1}{3}\left(\frac{741}{10}-\frac{600}{10}\right)$$

Since \frac{741}{10} and \frac{600}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{254}{21}-\frac{1}{3}\times \frac{741-600}{10}$$

Subtract 600 from 741 to get 141.

$$\frac{254}{21}-\frac{1}{3}\times \frac{141}{10}$$

Multiply \frac{1}{3} times \frac{141}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{254}{21}-\frac{1\times 141}{3\times 10}$$

Do the multiplications in the fraction \frac{1\times 141}{3\times 10}.

$$\frac{254}{21}-\frac{141}{30}$$

Reduce the fraction \frac{141}{30} to lowest terms by extracting and canceling out 3.

$$\frac{254}{21}-\frac{47}{10}$$

Least common multiple of 21 and 10 is 210. Convert \frac{254}{21} and \frac{47}{10} to fractions with denominator 210.

$$\frac{2540}{210}-\frac{987}{210}$$

Since \frac{2540}{210} and \frac{987}{210} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2540-987}{210}$$

Subtract 987 from 2540 to get 1553.

$$\frac{1553}{210}$$

Factor

$$\frac{1553}{2 \cdot 3 \cdot 5 \cdot 7} = 7\frac{83}{210} = 7.395238095238096$$