Solve |2/3+8-6/5|3/10

$$| \frac { 2 } { 3 } + 8 - \frac { 6 } { 5 } | \frac { 3 } { 10 }$$

Evaluate

$$\frac{56}{25}=2.24$$

Solution Steps

Convert 8 to fraction \frac{24}{3}.

$$|\frac{2}{3}+\frac{24}{3}-\frac{6}{5}|\times \frac{3}{10}$$

Since \frac{2}{3} and \frac{24}{3} have the same denominator, add them by adding their numerators.

$$|\frac{2+24}{3}-\frac{6}{5}|\times \frac{3}{10}$$

Add 2 and 24 to get 26.

$$|\frac{26}{3}-\frac{6}{5}|\times \frac{3}{10}$$

Least common multiple of 3 and 5 is 15. Convert \frac{26}{3} and \frac{6}{5} to fractions with denominator 15.

$$|\frac{130}{15}-\frac{18}{15}|\times \frac{3}{10}$$

Since \frac{130}{15} and \frac{18}{15} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{130-18}{15}|\times \frac{3}{10}$$

Subtract 18 from 130 to get 112.

$$|\frac{112}{15}|\times \frac{3}{10}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{112}{15} is \frac{112}{15}.

$$\frac{112}{15}\times \frac{3}{10}$$

Multiply \frac{112}{15} times \frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{112\times 3}{15\times 10}$$

Do the multiplications in the fraction \frac{112\times 3}{15\times 10}.

$$\frac{336}{150}$$

Reduce the fraction \frac{336}{150} to lowest terms by extracting and canceling out 6.

$$\frac{56}{25}$$

Factor

$$\frac{2 ^ {3} \cdot 7}{5 ^ {2}} = 2\frac{6}{25} = 2.24$$