Solve 1/2-4/9+2+34/7-1+23/2

$$\frac { 1 } { 2 } - \frac { 4 } { 9 } + 2 + \frac { 34 } { 7 } - 1 + \frac { 23 } { 2 }$$

Evaluate

$$\frac{1097}{63}\approx 17.412698413$$

Solution Steps

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{4}{9} to fractions with denominator 18.

$$\frac{9}{18}-\frac{8}{18}+2+\frac{34}{7}-1+\frac{23}{2}$$

Since \frac{9}{18} and \frac{8}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-8}{18}+2+\frac{34}{7}-1+\frac{23}{2}$$

Subtract 8 from 9 to get 1.

$$\frac{1}{18}+2+\frac{34}{7}-1+\frac{23}{2}$$

Convert 2 to fraction \frac{36}{18}.

$$\frac{1}{18}+\frac{36}{18}+\frac{34}{7}-1+\frac{23}{2}$$

Since \frac{1}{18} and \frac{36}{18} have the same denominator, add them by adding their numerators.

$$\frac{1+36}{18}+\frac{34}{7}-1+\frac{23}{2}$$

Add 1 and 36 to get 37.

$$\frac{37}{18}+\frac{34}{7}-1+\frac{23}{2}$$

Least common multiple of 18 and 7 is 126. Convert \frac{37}{18} and \frac{34}{7} to fractions with denominator 126.

$$\frac{259}{126}+\frac{612}{126}-1+\frac{23}{2}$$

Since \frac{259}{126} and \frac{612}{126} have the same denominator, add them by adding their numerators.

$$\frac{259+612}{126}-1+\frac{23}{2}$$

Add 259 and 612 to get 871.

$$\frac{871}{126}-1+\frac{23}{2}$$

Convert 1 to fraction \frac{126}{126}.

$$\frac{871}{126}-\frac{126}{126}+\frac{23}{2}$$

Since \frac{871}{126} and \frac{126}{126} have the same denominator, subtract them by subtracting their numerators.

$$\frac{871-126}{126}+\frac{23}{2}$$

Subtract 126 from 871 to get 745.

$$\frac{745}{126}+\frac{23}{2}$$

Least common multiple of 126 and 2 is 126. Convert \frac{745}{126} and \frac{23}{2} to fractions with denominator 126.

$$\frac{745}{126}+\frac{1449}{126}$$

Since \frac{745}{126} and \frac{1449}{126} have the same denominator, add them by adding their numerators.

$$\frac{745+1449}{126}$$

Add 745 and 1449 to get 2194.

$$\frac{2194}{126}$$

Reduce the fraction \frac{2194}{126} to lowest terms by extracting and canceling out 2.

$$\frac{1097}{63}$$

Factor

$$\frac{1097}{3 ^ {2} \cdot 7} = 17\frac{26}{63} = 17.41269841269841$$