Solve 7.5-2/3-(1/3+2.5)

$$7.5 - \frac { 2 } { 3 } - ( \frac { 1 } { 3 } + 2.5 )$$

Evaluate

$$4$$

Solution Steps

Convert decimal number 7.5 to fraction \frac{75}{10}. Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

$$\frac{15}{2}-\frac{2}{3}-\left(\frac{1}{3}+2.5\right)$$

Least common multiple of 2 and 3 is 6. Convert \frac{15}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{45}{6}-\frac{4}{6}-\left(\frac{1}{3}+2.5\right)$$

Since \frac{45}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{45-4}{6}-\left(\frac{1}{3}+2.5\right)$$

Subtract 4 from 45 to get 41.

$$\frac{41}{6}-\left(\frac{1}{3}+2.5\right)$$

Convert decimal number 2.5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$\frac{41}{6}-\left(\frac{1}{3}+\frac{5}{2}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{5}{2} to fractions with denominator 6.

$$\frac{41}{6}-\left(\frac{2}{6}+\frac{15}{6}\right)$$

Since \frac{2}{6} and \frac{15}{6} have the same denominator, add them by adding their numerators.

$$\frac{41}{6}-\frac{2+15}{6}$$

Add 2 and 15 to get 17.

$$\frac{41}{6}-\frac{17}{6}$$

Since \frac{41}{6} and \frac{17}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{41-17}{6}$$

Subtract 17 from 41 to get 24.

$$\frac{24}{6}$$

Divide 24 by 6 to get 4.

$$4$$

Factor

$$2^{2}$$