Solve 12/9div{3-(5/36+11/9*0.6)div1.45}

$$1 \frac { 2 } { 9 } \div \{ 3 - ( \frac { 5 } { 36 } + 1 \frac { 1 } { 9 } \times 0.6 ) \div 1.45 \}$$

Evaluate

$$0.5$$

Solution Steps

Multiply 1 and 9 to get 9.

$$\frac{\frac{9+2}{9}}{3-\frac{\frac{5}{36}+\frac{1\times 9+1}{9}\times 0.6}{1.45}}$$

Add 9 and 2 to get 11.

$$\frac{\frac{11}{9}}{3-\frac{\frac{5}{36}+\frac{1\times 9+1}{9}\times 0.6}{1.45}}$$

Multiply 1 and 9 to get 9.

$$\frac{\frac{11}{9}}{3-\frac{\frac{5}{36}+\frac{9+1}{9}\times 0.6}{1.45}}$$

Add 9 and 1 to get 10.

$$\frac{\frac{11}{9}}{3-\frac{\frac{5}{36}+\frac{10}{9}\times 0.6}{1.45}}$$

Convert decimal number 0.6 to fraction \frac{6}{10}. Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{11}{9}}{3-\frac{\frac{5}{36}+\frac{10}{9}\times \frac{3}{5}}{1.45}}$$

Multiply \frac{10}{9} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{11}{9}}{3-\frac{\frac{5}{36}+\frac{10\times 3}{9\times 5}}{1.45}}$$

Do the multiplications in the fraction \frac{10\times 3}{9\times 5}.

$$\frac{\frac{11}{9}}{3-\frac{\frac{5}{36}+\frac{30}{45}}{1.45}}$$

Reduce the fraction \frac{30}{45} to lowest terms by extracting and canceling out 15.

$$\frac{\frac{11}{9}}{3-\frac{\frac{5}{36}+\frac{2}{3}}{1.45}}$$

Least common multiple of 36 and 3 is 36. Convert \frac{5}{36} and \frac{2}{3} to fractions with denominator 36.

$$\frac{\frac{11}{9}}{3-\frac{\frac{5}{36}+\frac{24}{36}}{1.45}}$$

Since \frac{5}{36} and \frac{24}{36} have the same denominator, add them by adding their numerators.

$$\frac{\frac{11}{9}}{3-\frac{\frac{5+24}{36}}{1.45}}$$

Add 5 and 24 to get 29.

$$\frac{\frac{11}{9}}{3-\frac{\frac{29}{36}}{1.45}}$$

Express \frac{\frac{29}{36}}{1.45} as a single fraction.

$$\frac{\frac{11}{9}}{3-\frac{29}{36\times 1.45}}$$

Multiply 36 and 1.45 to get 52.2.

$$\frac{\frac{11}{9}}{3-\frac{29}{52.2}}$$

Expand \frac{29}{52.2} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{11}{9}}{3-\frac{290}{522}}$$

Reduce the fraction \frac{290}{522} to lowest terms by extracting and canceling out 58.

$$\frac{\frac{11}{9}}{3-\frac{5}{9}}$$

Convert 3 to fraction \frac{27}{9}.

$$\frac{\frac{11}{9}}{\frac{27}{9}-\frac{5}{9}}$$

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

$$\frac{\frac{11}{9}}{\frac{27-5}{9}}$$

Subtract 5 from 27 to get 22.

$$\frac{\frac{11}{9}}{\frac{22}{9}}$$

Divide \frac{11}{9} by \frac{22}{9} by multiplying \frac{11}{9} by the reciprocal of \frac{22}{9}.

$$\frac{11}{9}\times \frac{9}{22}$$

Multiply \frac{11}{9} times \frac{9}{22} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 9}{9\times 22}$$

Cancel out 9 in both numerator and denominator.

$$\frac{11}{22}$$

Reduce the fraction \frac{11}{22} to lowest terms by extracting and canceling out 11.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$