Solve 411/13+3/5-15/6

$$4 \frac { 11 } { 13 } + \frac { 3 } { 5 } - 1 \frac { 5 } { 6 }$$

Evaluate

$$\frac{1409}{390}\approx 3.612820513$$

Solution Steps

Multiply 4 and 13 to get 52.

$$\frac{52+11}{13}+\frac{3}{5}-\frac{1\times 6+5}{6}$$

Add 52 and 11 to get 63.

$$\frac{63}{13}+\frac{3}{5}-\frac{1\times 6+5}{6}$$

Least common multiple of 13 and 5 is 65. Convert \frac{63}{13} and \frac{3}{5} to fractions with denominator 65.

$$\frac{315}{65}+\frac{39}{65}-\frac{1\times 6+5}{6}$$

Since \frac{315}{65} and \frac{39}{65} have the same denominator, add them by adding their numerators.

$$\frac{315+39}{65}-\frac{1\times 6+5}{6}$$

Add 315 and 39 to get 354.

$$\frac{354}{65}-\frac{1\times 6+5}{6}$$

Multiply 1 and 6 to get 6.

$$\frac{354}{65}-\frac{6+5}{6}$$

Add 6 and 5 to get 11.

$$\frac{354}{65}-\frac{11}{6}$$

Least common multiple of 65 and 6 is 390. Convert \frac{354}{65} and \frac{11}{6} to fractions with denominator 390.

$$\frac{2124}{390}-\frac{715}{390}$$

Since \frac{2124}{390} and \frac{715}{390} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2124-715}{390}$$

Subtract 715 from 2124 to get 1409.

$$\frac{1409}{390}$$

Factor

$$\frac{1409}{2 \cdot 3 \cdot 5 \cdot 13} = 3\frac{239}{390} = 3.612820512820513$$