Solve 31/4+1/2/3frac{1{3}*(15/6-1frac{1}{12})}=

$$\frac { 3 \frac { 1 } { 4 } + \frac { 1 } { 2 } } { 3 \frac { 1 } { 3 } \cdot ( 1 \frac { 5 } { 6 } - 1 \frac { 1 } { 12 } ) } =$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\frac{\frac{12+1}{4}+\frac{1}{2}}{\frac{3\times 3+1}{3}\left(\frac{1\times 6+5}{6}-\frac{1\times 12+1}{12}\right)}$$

Add 12 and 1 to get 13.

$$\frac{\frac{13}{4}+\frac{1}{2}}{\frac{3\times 3+1}{3}\left(\frac{1\times 6+5}{6}-\frac{1\times 12+1}{12}\right)}$$

Least common multiple of 4 and 2 is 4. Convert \frac{13}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{\frac{13}{4}+\frac{2}{4}}{\frac{3\times 3+1}{3}\left(\frac{1\times 6+5}{6}-\frac{1\times 12+1}{12}\right)}$$

Since \frac{13}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13+2}{4}}{\frac{3\times 3+1}{3}\left(\frac{1\times 6+5}{6}-\frac{1\times 12+1}{12}\right)}$$

Add 13 and 2 to get 15.

$$\frac{\frac{15}{4}}{\frac{3\times 3+1}{3}\left(\frac{1\times 6+5}{6}-\frac{1\times 12+1}{12}\right)}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{15}{4}}{\frac{9+1}{3}\left(\frac{1\times 6+5}{6}-\frac{1\times 12+1}{12}\right)}$$

Add 9 and 1 to get 10.

$$\frac{\frac{15}{4}}{\frac{10}{3}\left(\frac{1\times 6+5}{6}-\frac{1\times 12+1}{12}\right)}$$

Multiply 1 and 6 to get 6.

$$\frac{\frac{15}{4}}{\frac{10}{3}\left(\frac{6+5}{6}-\frac{1\times 12+1}{12}\right)}$$

Add 6 and 5 to get 11.

$$\frac{\frac{15}{4}}{\frac{10}{3}\left(\frac{11}{6}-\frac{1\times 12+1}{12}\right)}$$

Multiply 1 and 12 to get 12.

$$\frac{\frac{15}{4}}{\frac{10}{3}\left(\frac{11}{6}-\frac{12+1}{12}\right)}$$

Add 12 and 1 to get 13.

$$\frac{\frac{15}{4}}{\frac{10}{3}\left(\frac{11}{6}-\frac{13}{12}\right)}$$

Least common multiple of 6 and 12 is 12. Convert \frac{11}{6} and \frac{13}{12} to fractions with denominator 12.

$$\frac{\frac{15}{4}}{\frac{10}{3}\left(\frac{22}{12}-\frac{13}{12}\right)}$$

Since \frac{22}{12} and \frac{13}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15}{4}}{\frac{10}{3}\times \frac{22-13}{12}}$$

Subtract 13 from 22 to get 9.

$$\frac{\frac{15}{4}}{\frac{10}{3}\times \frac{9}{12}}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{15}{4}}{\frac{10}{3}\times \frac{3}{4}}$$

Multiply \frac{10}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{15}{4}}{\frac{10\times 3}{3\times 4}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{15}{4}}{\frac{10}{4}}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{15}{4}}{\frac{5}{2}}$$

Divide \frac{15}{4} by \frac{5}{2} by multiplying \frac{15}{4} by the reciprocal of \frac{5}{2}.

$$\frac{15}{4}\times \frac{2}{5}$$

Multiply \frac{15}{4} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\times 2}{4\times 5}$$

Do the multiplications in the fraction \frac{15\times 2}{4\times 5}.

$$\frac{30}{20}$$

Reduce the fraction \frac{30}{20} to lowest terms by extracting and canceling out 10.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$