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

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

Evaluate

$$\frac{127}{42}\approx 3.023809524$$

Solution Steps

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

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

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

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

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

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

Add 10 and 63 to get 73.

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

Express -3\times \frac{73}{35} as a single fraction.

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

Multiply -3 and 73 to get -219.

$$\frac{1}{10}-\left(\frac{-219}{35}+\frac{10}{3}\right)$$

Fraction \frac{-219}{35} can be rewritten as -\frac{219}{35} by extracting the negative sign.

$$\frac{1}{10}-\left(-\frac{219}{35}+\frac{10}{3}\right)$$

Least common multiple of 35 and 3 is 105. Convert -\frac{219}{35} and \frac{10}{3} to fractions with denominator 105.

$$\frac{1}{10}-\left(-\frac{657}{105}+\frac{350}{105}\right)$$

Since -\frac{657}{105} and \frac{350}{105} have the same denominator, add them by adding their numerators.

$$\frac{1}{10}-\frac{-657+350}{105}$$

Add -657 and 350 to get -307.

$$\frac{1}{10}-\left(-\frac{307}{105}\right)$$

The opposite of -\frac{307}{105} is \frac{307}{105}.

$$\frac{1}{10}+\frac{307}{105}$$

Least common multiple of 10 and 105 is 210. Convert \frac{1}{10} and \frac{307}{105} to fractions with denominator 210.

$$\frac{21}{210}+\frac{614}{210}$$

Since \frac{21}{210} and \frac{614}{210} have the same denominator, add them by adding their numerators.

$$\frac{21+614}{210}$$

Add 21 and 614 to get 635.

$$\frac{635}{210}$$

Reduce the fraction \frac{635}{210} to lowest terms by extracting and canceling out 5.

$$\frac{127}{42}$$

Factor

$$\frac{127}{2 \cdot 3 \cdot 7} = 3\frac{1}{42} = 3.0238095238095237$$