Solve |1/2-4/3|*21/5

$$| \frac { 1 } { 2 } - \frac { 4 } { 3 } | \times \frac { 21 } { 5 }$$

Evaluate

$$\frac{7}{2}=3.5$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$|\frac{3}{6}-\frac{8}{6}|\times \frac{21}{5}$$

Since \frac{3}{6} and \frac{8}{6} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{3-8}{6}|\times \frac{21}{5}$$

Subtract 8 from 3 to get -5.

$$|-\frac{5}{6}|\times \frac{21}{5}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{5}{6} is \frac{5}{6}.

$$\frac{5}{6}\times \frac{21}{5}$$

Multiply \frac{5}{6} times \frac{21}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 21}{6\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{21}{6}$$

Reduce the fraction \frac{21}{6} to lowest terms by extracting and canceling out 3.

$$\frac{7}{2}$$

Factor

$$\frac{7}{2} = 3\frac{1}{2} = 3.5$$