Solve 2.9+[(-4/7)-(-31/3)]

$$2.9 + [ ( - \frac { 4 } { 7 } ) - ( - 3 \frac { 1 } { 3 } ) ]$$

Evaluate

$$\frac{1189}{210}\approx 5.661904762$$

Solution Steps

Multiply 3 and 3 to get 9.

$$2.9+-\frac{4}{7}-\left(-\frac{9+1}{3}\right)$$

Add 9 and 1 to get 10.

$$2.9+-\frac{4}{7}-\left(-\frac{10}{3}\right)$$

The opposite of -\frac{10}{3} is \frac{10}{3}.

$$2.9-\frac{4}{7}+\frac{10}{3}$$

Least common multiple of 7 and 3 is 21. Convert -\frac{4}{7} and \frac{10}{3} to fractions with denominator 21.

$$2.9-\frac{12}{21}+\frac{70}{21}$$

Since -\frac{12}{21} and \frac{70}{21} have the same denominator, add them by adding their numerators.

$$2.9+\frac{-12+70}{21}$$

Add -12 and 70 to get 58.

$$2.9+\frac{58}{21}$$

Convert decimal number 2.9 to fraction \frac{29}{10}.

$$\frac{29}{10}+\frac{58}{21}$$

Least common multiple of 10 and 21 is 210. Convert \frac{29}{10} and \frac{58}{21} to fractions with denominator 210.

$$\frac{609}{210}+\frac{580}{210}$$

Since \frac{609}{210} and \frac{580}{210} have the same denominator, add them by adding their numerators.

$$\frac{609+580}{210}$$

Add 609 and 580 to get 1189.

$$\frac{1189}{210}$$

Factor

$$\frac{29 \cdot 41}{2 \cdot 3 \cdot 5 \cdot 7} = 5\frac{139}{210} = 5.661904761904762$$