Solve (197/13-34/9)-(37/13+25/9)

$$( 19 \frac { 7 } { 13 } - 3 \frac { 4 } { 9 } )-( 3 \frac { 7 } { 13 } + 2 \frac { 5 } { 9 } )$$

Evaluate

$$10$$

Solution Steps

Multiply 19 and 13 to get 247.

$$\frac{247+7}{13}-\frac{3\times 9+4}{9}-\left(\frac{3\times 13+7}{13}+\frac{2\times 9+5}{9}\right)$$

Add 247 and 7 to get 254.

$$\frac{254}{13}-\frac{3\times 9+4}{9}-\left(\frac{3\times 13+7}{13}+\frac{2\times 9+5}{9}\right)$$

Multiply 3 and 9 to get 27.

$$\frac{254}{13}-\frac{27+4}{9}-\left(\frac{3\times 13+7}{13}+\frac{2\times 9+5}{9}\right)$$

Add 27 and 4 to get 31.

$$\frac{254}{13}-\frac{31}{9}-\left(\frac{3\times 13+7}{13}+\frac{2\times 9+5}{9}\right)$$

Least common multiple of 13 and 9 is 117. Convert \frac{254}{13} and \frac{31}{9} to fractions with denominator 117.

$$\frac{2286}{117}-\frac{403}{117}-\left(\frac{3\times 13+7}{13}+\frac{2\times 9+5}{9}\right)$$

Since \frac{2286}{117} and \frac{403}{117} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2286-403}{117}-\left(\frac{3\times 13+7}{13}+\frac{2\times 9+5}{9}\right)$$

Subtract 403 from 2286 to get 1883.

$$\frac{1883}{117}-\left(\frac{3\times 13+7}{13}+\frac{2\times 9+5}{9}\right)$$

Multiply 3 and 13 to get 39.

$$\frac{1883}{117}-\left(\frac{39+7}{13}+\frac{2\times 9+5}{9}\right)$$

Add 39 and 7 to get 46.

$$\frac{1883}{117}-\left(\frac{46}{13}+\frac{2\times 9+5}{9}\right)$$

Multiply 2 and 9 to get 18.

$$\frac{1883}{117}-\left(\frac{46}{13}+\frac{18+5}{9}\right)$$

Add 18 and 5 to get 23.

$$\frac{1883}{117}-\left(\frac{46}{13}+\frac{23}{9}\right)$$

Least common multiple of 13 and 9 is 117. Convert \frac{46}{13} and \frac{23}{9} to fractions with denominator 117.

$$\frac{1883}{117}-\left(\frac{414}{117}+\frac{299}{117}\right)$$

Since \frac{414}{117} and \frac{299}{117} have the same denominator, add them by adding their numerators.

$$\frac{1883}{117}-\frac{414+299}{117}$$

Add 414 and 299 to get 713.

$$\frac{1883}{117}-\frac{713}{117}$$

Since \frac{1883}{117} and \frac{713}{117} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1883-713}{117}$$

Subtract 713 from 1883 to get 1170.

$$\frac{1170}{117}$$

Divide 1170 by 117 to get 10.

$$10$$

Factor

$$2\times 5$$