Solve 24/9div[(75/12-5.25)div1.5+10*5/18]

$$2 \frac { 4 } { 9 } \div [ ( 7 \frac { 5 } { 12 } - 5.25 ) \div 1.5 + 10 \times \frac { 5 } { 18 } ]$$

Evaluate

$$\frac{11}{19}\approx 0.578947368$$

Solution Steps

Multiply 2 and 9 to get 18.

$$\frac{\frac{18+4}{9}}{\frac{\frac{7\times 12+5}{12}-5.25}{1.5}+10\times \frac{5}{18}}$$

Add 18 and 4 to get 22.

$$\frac{\frac{22}{9}}{\frac{\frac{7\times 12+5}{12}-5.25}{1.5}+10\times \frac{5}{18}}$$

Multiply 7 and 12 to get 84.

$$\frac{\frac{22}{9}}{\frac{\frac{84+5}{12}-5.25}{1.5}+10\times \frac{5}{18}}$$

Add 84 and 5 to get 89.

$$\frac{\frac{22}{9}}{\frac{\frac{89}{12}-5.25}{1.5}+10\times \frac{5}{18}}$$

Convert decimal number 5.25 to fraction \frac{525}{100}. Reduce the fraction \frac{525}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{22}{9}}{\frac{\frac{89}{12}-\frac{21}{4}}{1.5}+10\times \frac{5}{18}}$$

Least common multiple of 12 and 4 is 12. Convert \frac{89}{12} and \frac{21}{4} to fractions with denominator 12.

$$\frac{\frac{22}{9}}{\frac{\frac{89}{12}-\frac{63}{12}}{1.5}+10\times \frac{5}{18}}$$

Since \frac{89}{12} and \frac{63}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{22}{9}}{\frac{\frac{89-63}{12}}{1.5}+10\times \frac{5}{18}}$$

Subtract 63 from 89 to get 26.

$$\frac{\frac{22}{9}}{\frac{\frac{26}{12}}{1.5}+10\times \frac{5}{18}}$$

Reduce the fraction \frac{26}{12} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{22}{9}}{\frac{\frac{13}{6}}{1.5}+10\times \frac{5}{18}}$$

Express \frac{\frac{13}{6}}{1.5} as a single fraction.

$$\frac{\frac{22}{9}}{\frac{13}{6\times 1.5}+10\times \frac{5}{18}}$$

Multiply 6 and 1.5 to get 9.

$$\frac{\frac{22}{9}}{\frac{13}{9}+10\times \frac{5}{18}}$$

Express 10\times \frac{5}{18} as a single fraction.

$$\frac{\frac{22}{9}}{\frac{13}{9}+\frac{10\times 5}{18}}$$

Multiply 10 and 5 to get 50.

$$\frac{\frac{22}{9}}{\frac{13}{9}+\frac{50}{18}}$$

Reduce the fraction \frac{50}{18} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{22}{9}}{\frac{13}{9}+\frac{25}{9}}$$

Since \frac{13}{9} and \frac{25}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{22}{9}}{\frac{13+25}{9}}$$

Add 13 and 25 to get 38.

$$\frac{\frac{22}{9}}{\frac{38}{9}}$$

Divide \frac{22}{9} by \frac{38}{9} by multiplying \frac{22}{9} by the reciprocal of \frac{38}{9}.

$$\frac{22}{9}\times \frac{9}{38}$$

Multiply \frac{22}{9} times \frac{9}{38} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22\times 9}{9\times 38}$$

Cancel out 9 in both numerator and denominator.

$$\frac{22}{38}$$

Reduce the fraction \frac{22}{38} to lowest terms by extracting and canceling out 2.

$$\frac{11}{19}$$

Factor

$$\frac{11}{19} = 0.5789473684210527$$