Solve (3/4div3/100-231/2)div11/2*frac{2}{3}+1frac{1}{6}

$$( \frac { 3 } { 4 } \div \frac { 3 } { 100 } - 23 \frac { 1 } { 2 } ) \div 1 \frac { 1 } { 2 } \cdot \frac { 2 } { 3 } + 1 \frac { 1 } { 6 }$$

Evaluate

$$\frac{11}{6}\approx 1.833333333$$

Solution Steps

Divide \frac{3}{4} by \frac{3}{100} by multiplying \frac{3}{4} by the reciprocal of \frac{3}{100}.

$$\frac{\frac{3}{4}\times \frac{100}{3}-\frac{23\times 2+1}{2}}{\frac{1\times 2+1}{2}}\times \frac{2}{3}+\frac{1\times 6+1}{6}$$

Multiply \frac{3}{4} times \frac{100}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 100}{4\times 3}-\frac{23\times 2+1}{2}}{\frac{1\times 2+1}{2}}\times \frac{2}{3}+\frac{1\times 6+1}{6}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{100}{4}-\frac{23\times 2+1}{2}}{\frac{1\times 2+1}{2}}\times \frac{2}{3}+\frac{1\times 6+1}{6}$$

Divide 100 by 4 to get 25.

$$\frac{25-\frac{23\times 2+1}{2}}{\frac{1\times 2+1}{2}}\times \frac{2}{3}+\frac{1\times 6+1}{6}$$

Multiply 23 and 2 to get 46.

$$\frac{25-\frac{46+1}{2}}{\frac{1\times 2+1}{2}}\times \frac{2}{3}+\frac{1\times 6+1}{6}$$

Add 46 and 1 to get 47.

$$\frac{25-\frac{47}{2}}{\frac{1\times 2+1}{2}}\times \frac{2}{3}+\frac{1\times 6+1}{6}$$

Convert 25 to fraction \frac{50}{2}.

$$\frac{\frac{50}{2}-\frac{47}{2}}{\frac{1\times 2+1}{2}}\times \frac{2}{3}+\frac{1\times 6+1}{6}$$

Since \frac{50}{2} and \frac{47}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{50-47}{2}}{\frac{1\times 2+1}{2}}\times \frac{2}{3}+\frac{1\times 6+1}{6}$$

Subtract 47 from 50 to get 3.

$$\frac{\frac{3}{2}}{\frac{1\times 2+1}{2}}\times \frac{2}{3}+\frac{1\times 6+1}{6}$$

Multiply 1 and 2 to get 2.

$$\frac{\frac{3}{2}}{\frac{2+1}{2}}\times \frac{2}{3}+\frac{1\times 6+1}{6}$$

Add 2 and 1 to get 3.

$$\frac{\frac{3}{2}}{\frac{3}{2}}\times \frac{2}{3}+\frac{1\times 6+1}{6}$$

Divide \frac{3}{2} by \frac{3}{2} to get 1.

$$1\times \frac{2}{3}+\frac{1\times 6+1}{6}$$

Multiply 1 and \frac{2}{3} to get \frac{2}{3}.

$$\frac{2}{3}+\frac{1\times 6+1}{6}$$

Multiply 1 and 6 to get 6.

$$\frac{2}{3}+\frac{6+1}{6}$$

Add 6 and 1 to get 7.

$$\frac{2}{3}+\frac{7}{6}$$

Least common multiple of 3 and 6 is 6. Convert \frac{2}{3} and \frac{7}{6} to fractions with denominator 6.

$$\frac{4}{6}+\frac{7}{6}$$

Since \frac{4}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$\frac{4+7}{6}$$

Add 4 and 7 to get 11.

$$\frac{11}{6}$$

Factor

$$\frac{11}{2 \cdot 3} = 1\frac{5}{6} = 1.8333333333333333$$