Solve 3/frac{1{40}+1/48+1/32}

$$\frac{ 3 }{ \frac{ 1 }{ 40 } + \frac{ 1 }{ 48 } + \frac{ 1 }{ 32 } }$$

Evaluate

$$\frac{1440}{37}\approx 38.918918919$$

Solution Steps

Least common multiple of 40 and 48 is 240. Convert \frac{1}{40} and \frac{1}{48} to fractions with denominator 240.

$$\frac{3}{\frac{6}{240}+\frac{5}{240}+\frac{1}{32}}$$

Since \frac{6}{240} and \frac{5}{240} have the same denominator, add them by adding their numerators.

$$\frac{3}{\frac{6+5}{240}+\frac{1}{32}}$$

Add 6 and 5 to get 11.

$$\frac{3}{\frac{11}{240}+\frac{1}{32}}$$

Least common multiple of 240 and 32 is 480. Convert \frac{11}{240} and \frac{1}{32} to fractions with denominator 480.

$$\frac{3}{\frac{22}{480}+\frac{15}{480}}$$

Since \frac{22}{480} and \frac{15}{480} have the same denominator, add them by adding their numerators.

$$\frac{3}{\frac{22+15}{480}}$$

Add 22 and 15 to get 37.

$$\frac{3}{\frac{37}{480}}$$

Divide 3 by \frac{37}{480} by multiplying 3 by the reciprocal of \frac{37}{480}.

$$3\times \frac{480}{37}$$

Express 3\times \frac{480}{37} as a single fraction.

$$\frac{3\times 480}{37}$$

Multiply 3 and 480 to get 1440.

$$\frac{1440}{37}$$

Factor

$$\frac{2 ^ {5} \cdot 3 ^ {2} \cdot 5}{37} = 38\frac{34}{37} = 38.91891891891892$$