Solve 2+1/2+1{1+frac{1/1}}=61/24

$$2 + \frac { 1 } { 2 + \frac { 1 } { 1 + \frac { 1 } { 1 } } } = \frac { 61 } { 24 }$$

Verify

Solution Steps

Divide 1 by 1 to get 1.

$$2+\frac{1}{2+\frac{1}{1+1}}=\frac{61}{24}$$

Add 1 and 1 to get 2.

$$2+\frac{1}{2+\frac{1}{2}}=\frac{61}{24}$$

Convert 2 to fraction \frac{4}{2}.

$$2+\frac{1}{\frac{4}{2}+\frac{1}{2}}=\frac{61}{24}$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$2+\frac{1}{\frac{4+1}{2}}=\frac{61}{24}$$

Add 4 and 1 to get 5.

$$2+\frac{1}{\frac{5}{2}}=\frac{61}{24}$$

Divide 1 by \frac{5}{2} by multiplying 1 by the reciprocal of \frac{5}{2}.

$$2+1\times \frac{2}{5}=\frac{61}{24}$$

Multiply 1 and \frac{2}{5} to get \frac{2}{5}.

$$2+\frac{2}{5}=\frac{61}{24}$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{10}{5}+\frac{2}{5}=\frac{61}{24}$$

Since \frac{10}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$\frac{10+2}{5}=\frac{61}{24}$$

Add 10 and 2 to get 12.

$$\frac{12}{5}=\frac{61}{24}$$

Least common multiple of 5 and 24 is 120. Convert \frac{12}{5} and \frac{61}{24} to fractions with denominator 120.

$$\frac{288}{120}=\frac{305}{120}$$

Compare \frac{288}{120} and \frac{305}{120}.

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