Solve 32/7-41/3+65/7

$$3 \frac{ 2 }{ 7 } -4 \frac{ 1 }{ 3 } +6 \frac{ 5 }{ 7 }$$

Evaluate

$$\frac{17}{3}\approx 5.666666667$$

Solution Steps

Multiply 3 and 7 to get 21.

$$\frac{21+2}{7}-\frac{4\times 3+1}{3}+\frac{6\times 7+5}{7}$$

Add 21 and 2 to get 23.

$$\frac{23}{7}-\frac{4\times 3+1}{3}+\frac{6\times 7+5}{7}$$

Multiply 4 and 3 to get 12.

$$\frac{23}{7}-\frac{12+1}{3}+\frac{6\times 7+5}{7}$$

Add 12 and 1 to get 13.

$$\frac{23}{7}-\frac{13}{3}+\frac{6\times 7+5}{7}$$

Least common multiple of 7 and 3 is 21. Convert \frac{23}{7} and \frac{13}{3} to fractions with denominator 21.

$$\frac{69}{21}-\frac{91}{21}+\frac{6\times 7+5}{7}$$

Since \frac{69}{21} and \frac{91}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{69-91}{21}+\frac{6\times 7+5}{7}$$

Subtract 91 from 69 to get -22.

$$-\frac{22}{21}+\frac{6\times 7+5}{7}$$

Multiply 6 and 7 to get 42.

$$-\frac{22}{21}+\frac{42+5}{7}$$

Add 42 and 5 to get 47.

$$-\frac{22}{21}+\frac{47}{7}$$

Least common multiple of 21 and 7 is 21. Convert -\frac{22}{21} and \frac{47}{7} to fractions with denominator 21.

$$-\frac{22}{21}+\frac{141}{21}$$

Since -\frac{22}{21} and \frac{141}{21} have the same denominator, add them by adding their numerators.

$$\frac{-22+141}{21}$$

Add -22 and 141 to get 119.

$$\frac{119}{21}$$

Reduce the fraction \frac{119}{21} to lowest terms by extracting and canceling out 7.

$$\frac{17}{3}$$

Factor

$$\frac{17}{3} = 5\frac{2}{3} = 5.666666666666667$$