Solve 1/5+52/7+24/5+55/7)*(2-frac{5}{11})=

$$\frac { 1 } { 5 } + 5 \frac { 2 } { 7 } + 2 \frac { 4 } { 5 } + 5 \frac { 5 } { 7 } ) \times ( 2 - \frac { 5 } { 11 } ) =$$

Evaluate

$$14$$

Solution Steps

Multiply 5 and 7 to get 35.

$$\frac{1}{5}+\frac{35+2}{7}+\frac{2\times 5+4}{5}+\frac{5\times 7+5}{7}$$

Add 35 and 2 to get 37.

$$\frac{1}{5}+\frac{37}{7}+\frac{2\times 5+4}{5}+\frac{5\times 7+5}{7}$$

Least common multiple of 5 and 7 is 35. Convert \frac{1}{5} and \frac{37}{7} to fractions with denominator 35.

$$\frac{7}{35}+\frac{185}{35}+\frac{2\times 5+4}{5}+\frac{5\times 7+5}{7}$$

Since \frac{7}{35} and \frac{185}{35} have the same denominator, add them by adding their numerators.

$$\frac{7+185}{35}+\frac{2\times 5+4}{5}+\frac{5\times 7+5}{7}$$

Add 7 and 185 to get 192.

$$\frac{192}{35}+\frac{2\times 5+4}{5}+\frac{5\times 7+5}{7}$$

Multiply 2 and 5 to get 10.

$$\frac{192}{35}+\frac{10+4}{5}+\frac{5\times 7+5}{7}$$

Add 10 and 4 to get 14.

$$\frac{192}{35}+\frac{14}{5}+\frac{5\times 7+5}{7}$$

Least common multiple of 35 and 5 is 35. Convert \frac{192}{35} and \frac{14}{5} to fractions with denominator 35.

$$\frac{192}{35}+\frac{98}{35}+\frac{5\times 7+5}{7}$$

Since \frac{192}{35} and \frac{98}{35} have the same denominator, add them by adding their numerators.

$$\frac{192+98}{35}+\frac{5\times 7+5}{7}$$

Add 192 and 98 to get 290.

$$\frac{290}{35}+\frac{5\times 7+5}{7}$$

Reduce the fraction \frac{290}{35} to lowest terms by extracting and canceling out 5.

$$\frac{58}{7}+\frac{5\times 7+5}{7}$$

Multiply 5 and 7 to get 35.

$$\frac{58}{7}+\frac{35+5}{7}$$

Add 35 and 5 to get 40.

$$\frac{58}{7}+\frac{40}{7}$$

Since \frac{58}{7} and \frac{40}{7} have the same denominator, add them by adding their numerators.

$$\frac{58+40}{7}$$

Add 58 and 40 to get 98.

$$\frac{98}{7}$$

Divide 98 by 7 to get 14.

$$14$$

Factor

$$2\times 7$$