Solve 1/10-[-3(2/7-(-9/5)+10/3]

$$\frac { 1 } { 10 } - [ - 3 ( \frac { 2 } { 7 } - ( - \frac { 9 } { 5 } ) + \frac { 10 } { 3 } ]$$

Evaluate

$$\frac{229}{14}\approx 16.357142857$$

Solution Steps

The opposite of -\frac{9}{5} is \frac{9}{5}.

$$\frac{1}{10}-\left(-3\left(\frac{2}{7}+\frac{9}{5}+\frac{10}{3}\right)\right)$$

Least common multiple of 7 and 5 is 35. Convert \frac{2}{7} and \frac{9}{5} to fractions with denominator 35.

$$\frac{1}{10}-\left(-3\left(\frac{10}{35}+\frac{63}{35}+\frac{10}{3}\right)\right)$$

Since \frac{10}{35} and \frac{63}{35} have the same denominator, add them by adding their numerators.

$$\frac{1}{10}-\left(-3\left(\frac{10+63}{35}+\frac{10}{3}\right)\right)$$

Add 10 and 63 to get 73.

$$\frac{1}{10}-\left(-3\left(\frac{73}{35}+\frac{10}{3}\right)\right)$$

Least common multiple of 35 and 3 is 105. Convert \frac{73}{35} and \frac{10}{3} to fractions with denominator 105.

$$\frac{1}{10}-\left(-3\left(\frac{219}{105}+\frac{350}{105}\right)\right)$$

Since \frac{219}{105} and \frac{350}{105} have the same denominator, add them by adding their numerators.

$$\frac{1}{10}-\left(-3\times \frac{219+350}{105}\right)$$

Add 219 and 350 to get 569.

$$\frac{1}{10}-\left(-3\times \frac{569}{105}\right)$$

Express -3\times \frac{569}{105} as a single fraction.

$$\frac{1}{10}-\frac{-3\times 569}{105}$$

Multiply -3 and 569 to get -1707.

$$\frac{1}{10}-\frac{-1707}{105}$$

Reduce the fraction \frac{-1707}{105} to lowest terms by extracting and canceling out 3.

$$\frac{1}{10}-\left(-\frac{569}{35}\right)$$

The opposite of -\frac{569}{35} is \frac{569}{35}.

$$\frac{1}{10}+\frac{569}{35}$$

Least common multiple of 10 and 35 is 70. Convert \frac{1}{10} and \frac{569}{35} to fractions with denominator 70.

$$\frac{7}{70}+\frac{1138}{70}$$

Since \frac{7}{70} and \frac{1138}{70} have the same denominator, add them by adding their numerators.

$$\frac{7+1138}{70}$$

Add 7 and 1138 to get 1145.

$$\frac{1145}{70}$$

Reduce the fraction \frac{1145}{70} to lowest terms by extracting and canceling out 5.

$$\frac{229}{14}$$

Factor

$$\frac{229}{2 \cdot 7} = 16\frac{5}{14} = 16.357142857142858$$