Solve (51/9-0.8+24/9)*(7.6div4/5+22/5*1.25)

$$( 5 \frac { 1 } { 9 } - 0.8 + 2 \frac { 4 } { 9 } ) \times ( 7.6 \div \frac { 4 } { 5 } + 2 \frac { 2 } { 5 } \times 1.25 )$$

Evaluate

$$\frac{760}{9}\approx 84.444444444$$

Solution Steps

Multiply 5 and 9 to get 45.

$$\left(\frac{45+1}{9}-0.8+\frac{2\times 9+4}{9}\right)\left(\frac{7.6}{\frac{4}{5}}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Add 45 and 1 to get 46.

$$\left(\frac{46}{9}-0.8+\frac{2\times 9+4}{9}\right)\left(\frac{7.6}{\frac{4}{5}}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Convert decimal number 0.8 to fraction \frac{8}{10}. Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\left(\frac{46}{9}-\frac{4}{5}+\frac{2\times 9+4}{9}\right)\left(\frac{7.6}{\frac{4}{5}}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Least common multiple of 9 and 5 is 45. Convert \frac{46}{9} and \frac{4}{5} to fractions with denominator 45.

$$\left(\frac{230}{45}-\frac{36}{45}+\frac{2\times 9+4}{9}\right)\left(\frac{7.6}{\frac{4}{5}}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Since \frac{230}{45} and \frac{36}{45} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{230-36}{45}+\frac{2\times 9+4}{9}\right)\left(\frac{7.6}{\frac{4}{5}}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Subtract 36 from 230 to get 194.

$$\left(\frac{194}{45}+\frac{2\times 9+4}{9}\right)\left(\frac{7.6}{\frac{4}{5}}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Multiply 2 and 9 to get 18.

$$\left(\frac{194}{45}+\frac{18+4}{9}\right)\left(\frac{7.6}{\frac{4}{5}}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Add 18 and 4 to get 22.

$$\left(\frac{194}{45}+\frac{22}{9}\right)\left(\frac{7.6}{\frac{4}{5}}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Least common multiple of 45 and 9 is 45. Convert \frac{194}{45} and \frac{22}{9} to fractions with denominator 45.

$$\left(\frac{194}{45}+\frac{110}{45}\right)\left(\frac{7.6}{\frac{4}{5}}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Since \frac{194}{45} and \frac{110}{45} have the same denominator, add them by adding their numerators.

$$\frac{194+110}{45}\left(\frac{7.6}{\frac{4}{5}}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Add 194 and 110 to get 304.

$$\frac{304}{45}\left(\frac{7.6}{\frac{4}{5}}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Divide 7.6 by \frac{4}{5} by multiplying 7.6 by the reciprocal of \frac{4}{5}.

$$\frac{304}{45}\left(7.6\times \frac{5}{4}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Convert decimal number 7.6 to fraction \frac{76}{10}. Reduce the fraction \frac{76}{10} to lowest terms by extracting and canceling out 2.

$$\frac{304}{45}\left(\frac{38}{5}\times \frac{5}{4}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Multiply \frac{38}{5} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{304}{45}\left(\frac{38\times 5}{5\times 4}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Cancel out 5 in both numerator and denominator.

$$\frac{304}{45}\left(\frac{38}{4}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Reduce the fraction \frac{38}{4} to lowest terms by extracting and canceling out 2.

$$\frac{304}{45}\left(\frac{19}{2}+\frac{2\times 5+2}{5}\times 1.25\right)$$

Multiply 2 and 5 to get 10.

$$\frac{304}{45}\left(\frac{19}{2}+\frac{10+2}{5}\times 1.25\right)$$

Add 10 and 2 to get 12.

$$\frac{304}{45}\left(\frac{19}{2}+\frac{12}{5}\times 1.25\right)$$

Convert decimal number 1.25 to fraction \frac{125}{100}. Reduce the fraction \frac{125}{100} to lowest terms by extracting and canceling out 25.

$$\frac{304}{45}\left(\frac{19}{2}+\frac{12}{5}\times \frac{5}{4}\right)$$

Multiply \frac{12}{5} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{304}{45}\left(\frac{19}{2}+\frac{12\times 5}{5\times 4}\right)$$

Cancel out 5 in both numerator and denominator.

$$\frac{304}{45}\left(\frac{19}{2}+\frac{12}{4}\right)$$

Divide 12 by 4 to get 3.

$$\frac{304}{45}\left(\frac{19}{2}+3\right)$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{304}{45}\left(\frac{19}{2}+\frac{6}{2}\right)$$

Since \frac{19}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{304}{45}\times \frac{19+6}{2}$$

Add 19 and 6 to get 25.

$$\frac{304}{45}\times \frac{25}{2}$$

Multiply \frac{304}{45} times \frac{25}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{304\times 25}{45\times 2}$$

Do the multiplications in the fraction \frac{304\times 25}{45\times 2}.

$$\frac{7600}{90}$$

Reduce the fraction \frac{7600}{90} to lowest terms by extracting and canceling out 10.

$$\frac{760}{9}$$

Factor

$$\frac{5 \cdot 19 \cdot 2 ^ {3}}{3 ^ {2}} = 84\frac{4}{9} = 84.44444444444444$$