Solve (3)(1/3+(1/4+1/9)-7/5)=

$$( 3 ) ( \frac { 1 } { 3 } + ( \frac { 1 } { 4 } + \frac { 1 } { 9 } ) - \frac { 7 } { 5 } ) =$$

Evaluate

$$-\frac{127}{60}\approx -2.116666667$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$3\left(\frac{4}{12}+\frac{3}{12}+\frac{1}{9}-\frac{7}{5}\right)$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$3\left(\frac{4+3}{12}+\frac{1}{9}-\frac{7}{5}\right)$$

Add 4 and 3 to get 7.

$$3\left(\frac{7}{12}+\frac{1}{9}-\frac{7}{5}\right)$$

Least common multiple of 12 and 9 is 36. Convert \frac{7}{12} and \frac{1}{9} to fractions with denominator 36.

$$3\left(\frac{21}{36}+\frac{4}{36}-\frac{7}{5}\right)$$

Since \frac{21}{36} and \frac{4}{36} have the same denominator, add them by adding their numerators.

$$3\left(\frac{21+4}{36}-\frac{7}{5}\right)$$

Add 21 and 4 to get 25.

$$3\left(\frac{25}{36}-\frac{7}{5}\right)$$

Least common multiple of 36 and 5 is 180. Convert \frac{25}{36} and \frac{7}{5} to fractions with denominator 180.

$$3\left(\frac{125}{180}-\frac{252}{180}\right)$$

Since \frac{125}{180} and \frac{252}{180} have the same denominator, subtract them by subtracting their numerators.

$$3\times \frac{125-252}{180}$$

Subtract 252 from 125 to get -127.

$$3\left(-\frac{127}{180}\right)$$

Express 3\left(-\frac{127}{180}\right) as a single fraction.

$$\frac{3\left(-127\right)}{180}$$

Multiply 3 and -127 to get -381.

$$\frac{-381}{180}$$

Reduce the fraction \frac{-381}{180} to lowest terms by extracting and canceling out 3.

$$-\frac{127}{60}$$

Factor

$$-\frac{127}{60} = -2\frac{7}{60} = -2.1166666666666667$$