Solve 2.8*left(21/3div2.8-1right)+24/5

$$2.8 \times \left( 2 \frac{ 1 }{ 3 } \div 2.8-1 \right) +2 \frac{ 4 }{ 5 }$$

Evaluate

$$\frac{7}{3}\approx 2.333333333$$

Solution Steps

Express \frac{\frac{2\times 3+1}{3}}{2.8} as a single fraction.

$$2.8\left(\frac{2\times 3+1}{3\times 2.8}-1\right)+\frac{2\times 5+4}{5}$$

Multiply 2 and 3 to get 6.

$$2.8\left(\frac{6+1}{3\times 2.8}-1\right)+\frac{2\times 5+4}{5}$$

Add 6 and 1 to get 7.

$$2.8\left(\frac{7}{3\times 2.8}-1\right)+\frac{2\times 5+4}{5}$$

Multiply 3 and 2.8 to get 8.4.

$$2.8\left(\frac{7}{8.4}-1\right)+\frac{2\times 5+4}{5}$$

Expand \frac{7}{8.4} by multiplying both numerator and the denominator by 10.

$$2.8\left(\frac{70}{84}-1\right)+\frac{2\times 5+4}{5}$$

Reduce the fraction \frac{70}{84} to lowest terms by extracting and canceling out 14.

$$2.8\left(\frac{5}{6}-1\right)+\frac{2\times 5+4}{5}$$

Convert 1 to fraction \frac{6}{6}.

$$2.8\left(\frac{5}{6}-\frac{6}{6}\right)+\frac{2\times 5+4}{5}$$

Since \frac{5}{6} and \frac{6}{6} have the same denominator, subtract them by subtracting their numerators.

$$2.8\times \frac{5-6}{6}+\frac{2\times 5+4}{5}$$

Subtract 6 from 5 to get -1.

$$2.8\left(-\frac{1}{6}\right)+\frac{2\times 5+4}{5}$$

Convert decimal number 2.8 to fraction \frac{28}{10}. Reduce the fraction \frac{28}{10} to lowest terms by extracting and canceling out 2.

$$\frac{14}{5}\left(-\frac{1}{6}\right)+\frac{2\times 5+4}{5}$$

Multiply \frac{14}{5} times -\frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14\left(-1\right)}{5\times 6}+\frac{2\times 5+4}{5}$$

Do the multiplications in the fraction \frac{14\left(-1\right)}{5\times 6}.

$$\frac{-14}{30}+\frac{2\times 5+4}{5}$$

Reduce the fraction \frac{-14}{30} to lowest terms by extracting and canceling out 2.

$$-\frac{7}{15}+\frac{2\times 5+4}{5}$$

Multiply 2 and 5 to get 10.

$$-\frac{7}{15}+\frac{10+4}{5}$$

Add 10 and 4 to get 14.

$$-\frac{7}{15}+\frac{14}{5}$$

Least common multiple of 15 and 5 is 15. Convert -\frac{7}{15} and \frac{14}{5} to fractions with denominator 15.

$$-\frac{7}{15}+\frac{42}{15}$$

Since -\frac{7}{15} and \frac{42}{15} have the same denominator, add them by adding their numerators.

$$\frac{-7+42}{15}$$

Add -7 and 42 to get 35.

$$\frac{35}{15}$$

Reduce the fraction \frac{35}{15} to lowest terms by extracting and canceling out 5.

$$\frac{7}{3}$$

Factor

$$\frac{7}{3} = 2\frac{1}{3} = 2.3333333333333335$$