Solve |3/5-7/3|-5/3

$$| \frac { 3 } { 5 } - \frac { 7 } { 3 } | - \frac { 5 } { 3 }$$

Evaluate

$$\frac{1}{15}\approx 0.066666667$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{7}{3} to fractions with denominator 15.

$$|\frac{9}{15}-\frac{35}{15}|-\frac{5}{3}$$

Since \frac{9}{15} and \frac{35}{15} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{9-35}{15}|-\frac{5}{3}$$

Subtract 35 from 9 to get -26.

$$|-\frac{26}{15}|-\frac{5}{3}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{26}{15} is \frac{26}{15}.

$$\frac{26}{15}-\frac{5}{3}$$

Least common multiple of 15 and 3 is 15. Convert \frac{26}{15} and \frac{5}{3} to fractions with denominator 15.

$$\frac{26}{15}-\frac{25}{15}$$

Since \frac{26}{15} and \frac{25}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{26-25}{15}$$

Subtract 25 from 26 to get 1.

$$\frac{1}{15}$$

Factor

$$\frac{1}{3 \cdot 5} = 0.06666666666666667$$