Solve -3/7+14/19+(-4/7)+35/19

$$- \frac { 3 } { 7 } + \frac { 14 } { 19 } + ( - \frac { 4 } { 7 } ) + 3 \frac { 5 } { 19 }$$

Evaluate

$$3$$

Solution Steps

Least common multiple of 7 and 19 is 133. Convert -\frac{3}{7} and \frac{14}{19} to fractions with denominator 133.

$$-\frac{57}{133}+\frac{98}{133}-\frac{4}{7}+\frac{3\times 19+5}{19}$$

Since -\frac{57}{133} and \frac{98}{133} have the same denominator, add them by adding their numerators.

$$\frac{-57+98}{133}-\frac{4}{7}+\frac{3\times 19+5}{19}$$

Add -57 and 98 to get 41.

$$\frac{41}{133}-\frac{4}{7}+\frac{3\times 19+5}{19}$$

Least common multiple of 133 and 7 is 133. Convert \frac{41}{133} and \frac{4}{7} to fractions with denominator 133.

$$\frac{41}{133}-\frac{76}{133}+\frac{3\times 19+5}{19}$$

Since \frac{41}{133} and \frac{76}{133} have the same denominator, subtract them by subtracting their numerators.

$$\frac{41-76}{133}+\frac{3\times 19+5}{19}$$

Subtract 76 from 41 to get -35.

$$\frac{-35}{133}+\frac{3\times 19+5}{19}$$

Reduce the fraction \frac{-35}{133} to lowest terms by extracting and canceling out 7.

$$-\frac{5}{19}+\frac{3\times 19+5}{19}$$

Multiply 3 and 19 to get 57.

$$-\frac{5}{19}+\frac{57+5}{19}$$

Add 57 and 5 to get 62.

$$-\frac{5}{19}+\frac{62}{19}$$

Since -\frac{5}{19} and \frac{62}{19} have the same denominator, add them by adding their numerators.

$$\frac{-5+62}{19}$$

Add -5 and 62 to get 57.

$$\frac{57}{19}$$

Divide 57 by 19 to get 3.

$$3$$

Factor

$$3$$