Solve (1/3+3/4)*11/frac{1{3}*23/4*13}=

$$\frac { ( \frac { 1 } { 3 } + \frac { 3 } { 4 } ) \cdot 11 } { \frac { 1 } { 3 } \cdot 2 \frac { 3 } { 4 } \cdot 13 } =$$

Evaluate

$$1$$

Solution Steps

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

$$\frac{\left(\frac{4}{12}+\frac{9}{12}\right)\times 11}{\frac{1}{3}\times \frac{2\times 4+3}{4}\times 13}$$

Since \frac{4}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+9}{12}\times 11}{\frac{1}{3}\times \frac{2\times 4+3}{4}\times 13}$$

Add 4 and 9 to get 13.

$$\frac{\frac{13}{12}\times 11}{\frac{1}{3}\times \frac{2\times 4+3}{4}\times 13}$$

Express \frac{13}{12}\times 11 as a single fraction.

$$\frac{\frac{13\times 11}{12}}{\frac{1}{3}\times \frac{2\times 4+3}{4}\times 13}$$

Multiply 13 and 11 to get 143.

$$\frac{\frac{143}{12}}{\frac{1}{3}\times \frac{2\times 4+3}{4}\times 13}$$

Multiply 2 and 4 to get 8.

$$\frac{\frac{143}{12}}{\frac{1}{3}\times \frac{8+3}{4}\times 13}$$

Add 8 and 3 to get 11.

$$\frac{\frac{143}{12}}{\frac{1}{3}\times \frac{11}{4}\times 13}$$

Multiply \frac{1}{3} times \frac{11}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{143}{12}}{\frac{1\times 11}{3\times 4}\times 13}$$

Do the multiplications in the fraction \frac{1\times 11}{3\times 4}.

$$\frac{\frac{143}{12}}{\frac{11}{12}\times 13}$$

Express \frac{11}{12}\times 13 as a single fraction.

$$\frac{\frac{143}{12}}{\frac{11\times 13}{12}}$$

Multiply 11 and 13 to get 143.

$$\frac{\frac{143}{12}}{\frac{143}{12}}$$

Divide \frac{143}{12} by \frac{143}{12} to get 1.

$$1$$

Factor

$$1$$