Solve [21/2+(5.4-14/5)*12/3]div37/9=

$$[ 2 \frac { 1 } { 2 } + ( 5.4 - 1 \frac { 4 } { 5 } ) \times 1 \frac { 2 } { 3 } ] \div 3 \frac { 7 } { 9 } =$$

Evaluate

$$2.25$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{\frac{4+1}{2}+\left(5.4-\frac{1\times 5+4}{5}\right)\times \frac{1\times 3+2}{3}}{\frac{3\times 9+7}{9}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{5}{2}+\left(5.4-\frac{1\times 5+4}{5}\right)\times \frac{1\times 3+2}{3}}{\frac{3\times 9+7}{9}}$$

Multiply 1 and 5 to get 5.

$$\frac{\frac{5}{2}+\left(5.4-\frac{5+4}{5}\right)\times \frac{1\times 3+2}{3}}{\frac{3\times 9+7}{9}}$$

Add 5 and 4 to get 9.

$$\frac{\frac{5}{2}+\left(5.4-\frac{9}{5}\right)\times \frac{1\times 3+2}{3}}{\frac{3\times 9+7}{9}}$$

Convert decimal number 5.4 to fraction \frac{54}{10}. Reduce the fraction \frac{54}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{5}{2}+\left(\frac{27}{5}-\frac{9}{5}\right)\times \frac{1\times 3+2}{3}}{\frac{3\times 9+7}{9}}$$

Since \frac{27}{5} and \frac{9}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{2}+\frac{27-9}{5}\times \frac{1\times 3+2}{3}}{\frac{3\times 9+7}{9}}$$

Subtract 9 from 27 to get 18.

$$\frac{\frac{5}{2}+\frac{18}{5}\times \frac{1\times 3+2}{3}}{\frac{3\times 9+7}{9}}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{5}{2}+\frac{18}{5}\times \frac{3+2}{3}}{\frac{3\times 9+7}{9}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{5}{2}+\frac{18}{5}\times \frac{5}{3}}{\frac{3\times 9+7}{9}}$$

Multiply \frac{18}{5} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{2}+\frac{18\times 5}{5\times 3}}{\frac{3\times 9+7}{9}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{5}{2}+\frac{18}{3}}{\frac{3\times 9+7}{9}}$$

Divide 18 by 3 to get 6.

$$\frac{\frac{5}{2}+6}{\frac{3\times 9+7}{9}}$$

Convert 6 to fraction \frac{12}{2}.

$$\frac{\frac{5}{2}+\frac{12}{2}}{\frac{3\times 9+7}{9}}$$

Since \frac{5}{2} and \frac{12}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+12}{2}}{\frac{3\times 9+7}{9}}$$

Add 5 and 12 to get 17.

$$\frac{\frac{17}{2}}{\frac{3\times 9+7}{9}}$$

Multiply 3 and 9 to get 27.

$$\frac{\frac{17}{2}}{\frac{27+7}{9}}$$

Add 27 and 7 to get 34.

$$\frac{\frac{17}{2}}{\frac{34}{9}}$$

Divide \frac{17}{2} by \frac{34}{9} by multiplying \frac{17}{2} by the reciprocal of \frac{34}{9}.

$$\frac{17}{2}\times \frac{9}{34}$$

Multiply \frac{17}{2} times \frac{9}{34} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 9}{2\times 34}$$

Do the multiplications in the fraction \frac{17\times 9}{2\times 34}.

$$\frac{153}{68}$$

Reduce the fraction \frac{153}{68} to lowest terms by extracting and canceling out 17.

$$\frac{9}{4}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25$$