Solve 33/10div(11/3+1/12)-11/2

$$3 \frac { 3 } { 10 } \div ( 1 \frac { 1 } { 3 } + \frac { 1 } { 12 } ) - 1 \frac { 1 } { 2 }$$

Evaluate

$$\frac{141}{170}\approx 0.829411765$$

Solution Steps

Multiply 3 and 10 to get 30.

$$\frac{\frac{30+3}{10}}{\frac{1\times 3+1}{3}+\frac{1}{12}}-\frac{1\times 2+1}{2}$$

Add 30 and 3 to get 33.

$$\frac{\frac{33}{10}}{\frac{1\times 3+1}{3}+\frac{1}{12}}-\frac{1\times 2+1}{2}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{33}{10}}{\frac{3+1}{3}+\frac{1}{12}}-\frac{1\times 2+1}{2}$$

Add 3 and 1 to get 4.

$$\frac{\frac{33}{10}}{\frac{4}{3}+\frac{1}{12}}-\frac{1\times 2+1}{2}$$

Least common multiple of 3 and 12 is 12. Convert \frac{4}{3} and \frac{1}{12} to fractions with denominator 12.

$$\frac{\frac{33}{10}}{\frac{16}{12}+\frac{1}{12}}-\frac{1\times 2+1}{2}$$

Since \frac{16}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{33}{10}}{\frac{16+1}{12}}-\frac{1\times 2+1}{2}$$

Add 16 and 1 to get 17.

$$\frac{\frac{33}{10}}{\frac{17}{12}}-\frac{1\times 2+1}{2}$$

Divide \frac{33}{10} by \frac{17}{12} by multiplying \frac{33}{10} by the reciprocal of \frac{17}{12}.

$$\frac{33}{10}\times \frac{12}{17}-\frac{1\times 2+1}{2}$$

Multiply \frac{33}{10} times \frac{12}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{33\times 12}{10\times 17}-\frac{1\times 2+1}{2}$$

Do the multiplications in the fraction \frac{33\times 12}{10\times 17}.

$$\frac{396}{170}-\frac{1\times 2+1}{2}$$

Reduce the fraction \frac{396}{170} to lowest terms by extracting and canceling out 2.

$$\frac{198}{85}-\frac{1\times 2+1}{2}$$

Multiply 1 and 2 to get 2.

$$\frac{198}{85}-\frac{2+1}{2}$$

Add 2 and 1 to get 3.

$$\frac{198}{85}-\frac{3}{2}$$

Least common multiple of 85 and 2 is 170. Convert \frac{198}{85} and \frac{3}{2} to fractions with denominator 170.

$$\frac{396}{170}-\frac{255}{170}$$

Since \frac{396}{170} and \frac{255}{170} have the same denominator, subtract them by subtracting their numerators.

$$\frac{396-255}{170}$$

Subtract 255 from 396 to get 141.

$$\frac{141}{170}$$

Factor

$$\frac{3 \cdot 47}{2 \cdot 5 \cdot 17} = 0.8294117647058824$$