Solve 1/2+5/4/frac{4{3}+frac{3/2+frac{2}{3}}{frac{5}{4}}}

$$\frac{ \frac{ 1 }{ 2 } + \frac{ 5 }{ 4 } }{ \frac{ 4 }{ 3 } + \frac{ \frac{ 3 }{ 2 } + \frac{ 2 }{ 3 } }{ \frac{ 5 }{ 4 } } }$$

Evaluate

$$\frac{105}{184}\approx 0.570652174$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{5}{4} to fractions with denominator 4.

$$\frac{\frac{2}{4}+\frac{5}{4}}{\frac{4}{3}+\frac{\frac{3}{2}+\frac{2}{3}}{\frac{5}{4}}}$$

Since \frac{2}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2+5}{4}}{\frac{4}{3}+\frac{\frac{3}{2}+\frac{2}{3}}{\frac{5}{4}}}$$

Add 2 and 5 to get 7.

$$\frac{\frac{7}{4}}{\frac{4}{3}+\frac{\frac{3}{2}+\frac{2}{3}}{\frac{5}{4}}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{\frac{7}{4}}{\frac{4}{3}+\frac{\frac{9}{6}+\frac{4}{6}}{\frac{5}{4}}}$$

Since \frac{9}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{4}}{\frac{4}{3}+\frac{\frac{9+4}{6}}{\frac{5}{4}}}$$

Add 9 and 4 to get 13.

$$\frac{\frac{7}{4}}{\frac{4}{3}+\frac{\frac{13}{6}}{\frac{5}{4}}}$$

Divide \frac{13}{6} by \frac{5}{4} by multiplying \frac{13}{6} by the reciprocal of \frac{5}{4}.

$$\frac{\frac{7}{4}}{\frac{4}{3}+\frac{13}{6}\times \frac{4}{5}}$$

Multiply \frac{13}{6} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7}{4}}{\frac{4}{3}+\frac{13\times 4}{6\times 5}}$$

Do the multiplications in the fraction \frac{13\times 4}{6\times 5}.

$$\frac{\frac{7}{4}}{\frac{4}{3}+\frac{52}{30}}$$

Reduce the fraction \frac{52}{30} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{7}{4}}{\frac{4}{3}+\frac{26}{15}}$$

Least common multiple of 3 and 15 is 15. Convert \frac{4}{3} and \frac{26}{15} to fractions with denominator 15.

$$\frac{\frac{7}{4}}{\frac{20}{15}+\frac{26}{15}}$$

Since \frac{20}{15} and \frac{26}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{4}}{\frac{20+26}{15}}$$

Add 20 and 26 to get 46.

$$\frac{\frac{7}{4}}{\frac{46}{15}}$$

Divide \frac{7}{4} by \frac{46}{15} by multiplying \frac{7}{4} by the reciprocal of \frac{46}{15}.

$$\frac{7}{4}\times \frac{15}{46}$$

Multiply \frac{7}{4} times \frac{15}{46} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 15}{4\times 46}$$

Do the multiplications in the fraction \frac{7\times 15}{4\times 46}.

$$\frac{105}{184}$$

Factor

$$\frac{3 \cdot 5 \cdot 7}{2 ^ {3} \cdot 23} = 0.5706521739130435$$