Solve 105-121/2+286/7-19/21+345/21-103frac{4}{24}-72frac{5}{18}

$$105-12 \frac{ 1 }{ 2 } +28 \frac{ 6 }{ 7 } - \frac{ 19 }{ 21 } +34 \frac{ 5 }{ 21 } -103 \frac{ 4 }{ 24 } -72 \frac{ 5 }{ 18 }$$

Evaluate

$$-\frac{2615}{126}\approx -20.753968254$$

Solution Steps

Multiply 12 and 2 to get 24.

$$105-\frac{24+1}{2}+\frac{28\times 7+6}{7}-\frac{19}{21}+\frac{34\times 21+5}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Add 24 and 1 to get 25.

$$105-\frac{25}{2}+\frac{28\times 7+6}{7}-\frac{19}{21}+\frac{34\times 21+5}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Convert 105 to fraction \frac{210}{2}.

$$\frac{210}{2}-\frac{25}{2}+\frac{28\times 7+6}{7}-\frac{19}{21}+\frac{34\times 21+5}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Since \frac{210}{2} and \frac{25}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{210-25}{2}+\frac{28\times 7+6}{7}-\frac{19}{21}+\frac{34\times 21+5}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Subtract 25 from 210 to get 185.

$$\frac{185}{2}+\frac{28\times 7+6}{7}-\frac{19}{21}+\frac{34\times 21+5}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Multiply 28 and 7 to get 196.

$$\frac{185}{2}+\frac{196+6}{7}-\frac{19}{21}+\frac{34\times 21+5}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Add 196 and 6 to get 202.

$$\frac{185}{2}+\frac{202}{7}-\frac{19}{21}+\frac{34\times 21+5}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Least common multiple of 2 and 7 is 14. Convert \frac{185}{2} and \frac{202}{7} to fractions with denominator 14.

$$\frac{1295}{14}+\frac{404}{14}-\frac{19}{21}+\frac{34\times 21+5}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Since \frac{1295}{14} and \frac{404}{14} have the same denominator, add them by adding their numerators.

$$\frac{1295+404}{14}-\frac{19}{21}+\frac{34\times 21+5}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Add 1295 and 404 to get 1699.

$$\frac{1699}{14}-\frac{19}{21}+\frac{34\times 21+5}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Least common multiple of 14 and 21 is 42. Convert \frac{1699}{14} and \frac{19}{21} to fractions with denominator 42.

$$\frac{5097}{42}-\frac{38}{42}+\frac{34\times 21+5}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Since \frac{5097}{42} and \frac{38}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5097-38}{42}+\frac{34\times 21+5}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Subtract 38 from 5097 to get 5059.

$$\frac{5059}{42}+\frac{34\times 21+5}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Multiply 34 and 21 to get 714.

$$\frac{5059}{42}+\frac{714+5}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Add 714 and 5 to get 719.

$$\frac{5059}{42}+\frac{719}{21}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Least common multiple of 42 and 21 is 42. Convert \frac{5059}{42} and \frac{719}{21} to fractions with denominator 42.

$$\frac{5059}{42}+\frac{1438}{42}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Since \frac{5059}{42} and \frac{1438}{42} have the same denominator, add them by adding their numerators.

$$\frac{5059+1438}{42}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Add 5059 and 1438 to get 6497.

$$\frac{6497}{42}-\frac{103\times 24+4}{24}-\frac{72\times 18+5}{18}$$

Multiply 103 and 24 to get 2472.

$$\frac{6497}{42}-\frac{2472+4}{24}-\frac{72\times 18+5}{18}$$

Add 2472 and 4 to get 2476.

$$\frac{6497}{42}-\frac{2476}{24}-\frac{72\times 18+5}{18}$$

Reduce the fraction \frac{2476}{24} to lowest terms by extracting and canceling out 4.

$$\frac{6497}{42}-\frac{619}{6}-\frac{72\times 18+5}{18}$$

Least common multiple of 42 and 6 is 42. Convert \frac{6497}{42} and \frac{619}{6} to fractions with denominator 42.

$$\frac{6497}{42}-\frac{4333}{42}-\frac{72\times 18+5}{18}$$

Since \frac{6497}{42} and \frac{4333}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6497-4333}{42}-\frac{72\times 18+5}{18}$$

Subtract 4333 from 6497 to get 2164.

$$\frac{2164}{42}-\frac{72\times 18+5}{18}$$

Reduce the fraction \frac{2164}{42} to lowest terms by extracting and canceling out 2.

$$\frac{1082}{21}-\frac{72\times 18+5}{18}$$

Multiply 72 and 18 to get 1296.

$$\frac{1082}{21}-\frac{1296+5}{18}$$

Add 1296 and 5 to get 1301.

$$\frac{1082}{21}-\frac{1301}{18}$$

Least common multiple of 21 and 18 is 126. Convert \frac{1082}{21} and \frac{1301}{18} to fractions with denominator 126.

$$\frac{6492}{126}-\frac{9107}{126}$$

Since \frac{6492}{126} and \frac{9107}{126} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6492-9107}{126}$$

Subtract 9107 from 6492 to get -2615.

$$-\frac{2615}{126}$$

Factor

$$-\frac{2615}{126} = -20\frac{95}{126} = -20.753968253968253$$