Solve 1+1/1+3{1+frac{4/5}}=1+1/1+3{frac{9/3}}

$$1 + \frac { 1 } { 1 + \frac { 3 } { 1 + \frac { 4 } { 5 } } } = 1 + \frac { 1 } { 1 + \frac { 3 } { \frac { 9 } { 3 } } }$$

Verify

Solution Steps

Convert 1 to fraction \frac{5}{5}.

$$1+\frac{1}{1+\frac{3}{\frac{5}{5}+\frac{4}{5}}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Since \frac{5}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$1+\frac{1}{1+\frac{3}{\frac{5+4}{5}}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Add 5 and 4 to get 9.

$$1+\frac{1}{1+\frac{3}{\frac{9}{5}}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Divide 3 by \frac{9}{5} by multiplying 3 by the reciprocal of \frac{9}{5}.

$$1+\frac{1}{1+3\times \frac{5}{9}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Express 3\times \frac{5}{9} as a single fraction.

$$1+\frac{1}{1+\frac{3\times 5}{9}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Multiply 3 and 5 to get 15.

$$1+\frac{1}{1+\frac{15}{9}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Reduce the fraction \frac{15}{9} to lowest terms by extracting and canceling out 3.

$$1+\frac{1}{1+\frac{5}{3}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Convert 1 to fraction \frac{3}{3}.

$$1+\frac{1}{\frac{3}{3}+\frac{5}{3}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Since \frac{3}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

$$1+\frac{1}{\frac{3+5}{3}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Add 3 and 5 to get 8.

$$1+\frac{1}{\frac{8}{3}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Divide 1 by \frac{8}{3} by multiplying 1 by the reciprocal of \frac{8}{3}.

$$1+1\times \frac{3}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Multiply 1 and \frac{3}{8} to get \frac{3}{8}.

$$1+\frac{3}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{8}{8}+\frac{3}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Since \frac{8}{8} and \frac{3}{8} have the same denominator, add them by adding their numerators.

$$\frac{8+3}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Add 8 and 3 to get 11.

$$\frac{11}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Divide 3 by \frac{9}{3} by multiplying 3 by the reciprocal of \frac{9}{3}.

$$\frac{11}{8}=1+\frac{1}{1+\frac{3\times 3}{9}}$$

Multiply 3 and 3 to get 9.

$$\frac{11}{8}=1+\frac{1}{1+\frac{9}{9}}$$

Divide 9 by 9 to get 1.

$$\frac{11}{8}=1+\frac{1}{1+1}$$

Add 1 and 1 to get 2.

$$\frac{11}{8}=1+\frac{1}{2}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{11}{8}=\frac{2}{2}+\frac{1}{2}$$

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

$$\frac{11}{8}=\frac{2+1}{2}$$

Add 2 and 1 to get 3.

$$\frac{11}{8}=\frac{3}{2}$$

Least common multiple of 8 and 2 is 8. Convert \frac{11}{8} and \frac{3}{2} to fractions with denominator 8.

$$\frac{11}{8}=\frac{12}{8}$$

Compare \frac{11}{8} and \frac{12}{8}.

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