Solve 15215/3015-14/26*(4/7+1/21)

$$\frac { 15215 } { 3015 } - \frac { 14 } { 26 } \cdot ( \frac { 4 } { 7 } + \frac { 1 } { 21 } )$$

Evaluate

$$\frac{2842}{603}\approx 4.713101161$$

Solution Steps

Reduce the fraction \frac{15215}{3015} to lowest terms by extracting and canceling out 5.

$$\frac{3043}{603}-\frac{14}{26}\left(\frac{4}{7}+\frac{1}{21}\right)$$

Reduce the fraction \frac{14}{26} to lowest terms by extracting and canceling out 2.

$$\frac{3043}{603}-\frac{7}{13}\left(\frac{4}{7}+\frac{1}{21}\right)$$

Least common multiple of 7 and 21 is 21. Convert \frac{4}{7} and \frac{1}{21} to fractions with denominator 21.

$$\frac{3043}{603}-\frac{7}{13}\left(\frac{12}{21}+\frac{1}{21}\right)$$

Since \frac{12}{21} and \frac{1}{21} have the same denominator, add them by adding their numerators.

$$\frac{3043}{603}-\frac{7}{13}\times \frac{12+1}{21}$$

Add 12 and 1 to get 13.

$$\frac{3043}{603}-\frac{7}{13}\times \frac{13}{21}$$

Multiply \frac{7}{13} times \frac{13}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3043}{603}-\frac{7\times 13}{13\times 21}$$

Cancel out 13 in both numerator and denominator.

$$\frac{3043}{603}-\frac{7}{21}$$

Reduce the fraction \frac{7}{21} to lowest terms by extracting and canceling out 7.

$$\frac{3043}{603}-\frac{1}{3}$$

Least common multiple of 603 and 3 is 603. Convert \frac{3043}{603} and \frac{1}{3} to fractions with denominator 603.

$$\frac{3043}{603}-\frac{201}{603}$$

Since \frac{3043}{603} and \frac{201}{603} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3043-201}{603}$$

Subtract 201 from 3043 to get 2842.

$$\frac{2842}{603}$$

Factor

$$\frac{2 \cdot 7 ^ {2} \cdot 29}{3 ^ {2} \cdot 67} = 4\frac{430}{603} = 4.7131011608623545$$