Solve 1/4+4/5/frac{1{8}+1/2}

$$\frac { \frac { 1 } { 4 } + \frac { 4 } { 5 } } { \frac { 1 } { 8 } + \frac { 1 } { 2 } }$$

Evaluate

$$\frac{42}{25}=1.68$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{4}{5} to fractions with denominator 20.

$$\frac{\frac{5}{20}+\frac{16}{20}}{\frac{1}{8}+\frac{1}{2}}$$

Since \frac{5}{20} and \frac{16}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+16}{20}}{\frac{1}{8}+\frac{1}{2}}$$

Add 5 and 16 to get 21.

$$\frac{\frac{21}{20}}{\frac{1}{8}+\frac{1}{2}}$$

Least common multiple of 8 and 2 is 8. Convert \frac{1}{8} and \frac{1}{2} to fractions with denominator 8.

$$\frac{\frac{21}{20}}{\frac{1}{8}+\frac{4}{8}}$$

Since \frac{1}{8} and \frac{4}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{21}{20}}{\frac{1+4}{8}}$$

Add 1 and 4 to get 5.

$$\frac{\frac{21}{20}}{\frac{5}{8}}$$

Divide \frac{21}{20} by \frac{5}{8} by multiplying \frac{21}{20} by the reciprocal of \frac{5}{8}.

$$\frac{21}{20}\times \frac{8}{5}$$

Multiply \frac{21}{20} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\times 8}{20\times 5}$$

Do the multiplications in the fraction \frac{21\times 8}{20\times 5}.

$$\frac{168}{100}$$

Reduce the fraction \frac{168}{100} to lowest terms by extracting and canceling out 4.

$$\frac{42}{25}$$

Factor

$$\frac{2 \cdot 3 \cdot 7}{5 ^ {2}} = 1\frac{17}{25} = 1.68$$