Solve 39*(2/13+1/11)*33

$$39 \times ( \frac{ 2 }{ 13 } + \frac{ 1 }{ 11 } ) \times 33$$

Evaluate

$$315$$

Solution Steps

Least common multiple of 13 and 11 is 143. Convert \frac{2}{13} and \frac{1}{11} to fractions with denominator 143.

$$39\left(\frac{22}{143}+\frac{13}{143}\right)\times 33$$

Since \frac{22}{143} and \frac{13}{143} have the same denominator, add them by adding their numerators.

$$39\times \frac{22+13}{143}\times 33$$

Add 22 and 13 to get 35.

$$39\times \frac{35}{143}\times 33$$

Express 39\times \frac{35}{143} as a single fraction.

$$\frac{39\times 35}{143}\times 33$$

Multiply 39 and 35 to get 1365.

$$\frac{1365}{143}\times 33$$

Reduce the fraction \frac{1365}{143} to lowest terms by extracting and canceling out 13.

$$\frac{105}{11}\times 33$$

Express \frac{105}{11}\times 33 as a single fraction.

$$\frac{105\times 33}{11}$$

Multiply 105 and 33 to get 3465.

$$\frac{3465}{11}$$

Divide 3465 by 11 to get 315.

$$315$$

Factor

$$3^{2}\times 5\times 7$$