Solve 22/3*(21/3+25/12)-44/5

$$2 \frac { 2 } { 3 } \cdot ( 2 \frac { 1 } { 3 } + 2 \frac { 5 } { 12 } ) - 4 \frac { 4 } { 5 }$$

Evaluate

$$\frac{118}{15}\approx 7.866666667$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{6+2}{3}\left(\frac{2\times 3+1}{3}+\frac{2\times 12+5}{12}\right)-\frac{4\times 5+4}{5}$$

Add 6 and 2 to get 8.

$$\frac{8}{3}\left(\frac{2\times 3+1}{3}+\frac{2\times 12+5}{12}\right)-\frac{4\times 5+4}{5}$$

Multiply 2 and 3 to get 6.

$$\frac{8}{3}\left(\frac{6+1}{3}+\frac{2\times 12+5}{12}\right)-\frac{4\times 5+4}{5}$$

Add 6 and 1 to get 7.

$$\frac{8}{3}\left(\frac{7}{3}+\frac{2\times 12+5}{12}\right)-\frac{4\times 5+4}{5}$$

Multiply 2 and 12 to get 24.

$$\frac{8}{3}\left(\frac{7}{3}+\frac{24+5}{12}\right)-\frac{4\times 5+4}{5}$$

Add 24 and 5 to get 29.

$$\frac{8}{3}\left(\frac{7}{3}+\frac{29}{12}\right)-\frac{4\times 5+4}{5}$$

Least common multiple of 3 and 12 is 12. Convert \frac{7}{3} and \frac{29}{12} to fractions with denominator 12.

$$\frac{8}{3}\left(\frac{28}{12}+\frac{29}{12}\right)-\frac{4\times 5+4}{5}$$

Since \frac{28}{12} and \frac{29}{12} have the same denominator, add them by adding their numerators.

$$\frac{8}{3}\times \frac{28+29}{12}-\frac{4\times 5+4}{5}$$

Add 28 and 29 to get 57.

$$\frac{8}{3}\times \frac{57}{12}-\frac{4\times 5+4}{5}$$

Reduce the fraction \frac{57}{12} to lowest terms by extracting and canceling out 3.

$$\frac{8}{3}\times \frac{19}{4}-\frac{4\times 5+4}{5}$$

Multiply \frac{8}{3} times \frac{19}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 19}{3\times 4}-\frac{4\times 5+4}{5}$$

Do the multiplications in the fraction \frac{8\times 19}{3\times 4}.

$$\frac{152}{12}-\frac{4\times 5+4}{5}$$

Reduce the fraction \frac{152}{12} to lowest terms by extracting and canceling out 4.

$$\frac{38}{3}-\frac{4\times 5+4}{5}$$

Multiply 4 and 5 to get 20.

$$\frac{38}{3}-\frac{20+4}{5}$$

Add 20 and 4 to get 24.

$$\frac{38}{3}-\frac{24}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{38}{3} and \frac{24}{5} to fractions with denominator 15.

$$\frac{190}{15}-\frac{72}{15}$$

Since \frac{190}{15} and \frac{72}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{190-72}{15}$$

Subtract 72 from 190 to get 118.

$$\frac{118}{15}$$

Factor

$$\frac{2 \cdot 59}{3 \cdot 5} = 7\frac{13}{15} = 7.866666666666666$$