Solve 1/1{40/93+frac{8/3}+1/frac{25{93}+frac{5}{3}}}

$$\frac { 1 } { \frac { 1 } { \frac { 40 } { 93 } + \frac { 8 } { 3 } } + \frac { 1 } { \frac { 25 } { 93 } + \frac { 5 } { 3 } } }$$

Evaluate

$$\frac{480}{403}\approx 1.191066998$$

Solution Steps

Least common multiple of 93 and 3 is 93. Convert \frac{40}{93} and \frac{8}{3} to fractions with denominator 93.

$$\frac{1}{\frac{1}{\frac{40}{93}+\frac{248}{93}}+\frac{1}{\frac{25}{93}+\frac{5}{3}}}$$

Since \frac{40}{93} and \frac{248}{93} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{1}{\frac{40+248}{93}}+\frac{1}{\frac{25}{93}+\frac{5}{3}}}$$

Add 40 and 248 to get 288.

$$\frac{1}{\frac{1}{\frac{288}{93}}+\frac{1}{\frac{25}{93}+\frac{5}{3}}}$$

Reduce the fraction \frac{288}{93} to lowest terms by extracting and canceling out 3.

$$\frac{1}{\frac{1}{\frac{96}{31}}+\frac{1}{\frac{25}{93}+\frac{5}{3}}}$$

Divide 1 by \frac{96}{31} by multiplying 1 by the reciprocal of \frac{96}{31}.

$$\frac{1}{1\times \frac{31}{96}+\frac{1}{\frac{25}{93}+\frac{5}{3}}}$$

Multiply 1 and \frac{31}{96} to get \frac{31}{96}.

$$\frac{1}{\frac{31}{96}+\frac{1}{\frac{25}{93}+\frac{5}{3}}}$$

Least common multiple of 93 and 3 is 93. Convert \frac{25}{93} and \frac{5}{3} to fractions with denominator 93.

$$\frac{1}{\frac{31}{96}+\frac{1}{\frac{25}{93}+\frac{155}{93}}}$$

Since \frac{25}{93} and \frac{155}{93} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{31}{96}+\frac{1}{\frac{25+155}{93}}}$$

Add 25 and 155 to get 180.

$$\frac{1}{\frac{31}{96}+\frac{1}{\frac{180}{93}}}$$

Reduce the fraction \frac{180}{93} to lowest terms by extracting and canceling out 3.

$$\frac{1}{\frac{31}{96}+\frac{1}{\frac{60}{31}}}$$

Divide 1 by \frac{60}{31} by multiplying 1 by the reciprocal of \frac{60}{31}.

$$\frac{1}{\frac{31}{96}+1\times \frac{31}{60}}$$

Multiply 1 and \frac{31}{60} to get \frac{31}{60}.

$$\frac{1}{\frac{31}{96}+\frac{31}{60}}$$

Least common multiple of 96 and 60 is 480. Convert \frac{31}{96} and \frac{31}{60} to fractions with denominator 480.

$$\frac{1}{\frac{155}{480}+\frac{248}{480}}$$

Since \frac{155}{480} and \frac{248}{480} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{155+248}{480}}$$

Add 155 and 248 to get 403.

$$\frac{1}{\frac{403}{480}}$$

Divide 1 by \frac{403}{480} by multiplying 1 by the reciprocal of \frac{403}{480}.

$$1\times \frac{480}{403}$$

Multiply 1 and \frac{480}{403} to get \frac{480}{403}.

$$\frac{480}{403}$$

Factor

$$\frac{2 ^ {5} \cdot 3 \cdot 5}{13 \cdot 31} = 1\frac{77}{403} = 1.1910669975186103$$