Solve (1/2+3/4*5/7)div(4/7*frac{2}{3}*frac{5}{2})

$$( \frac { 1 } { 2 } + \frac { 3 } { 4 } \times \frac { 5 } { 7 } ) \div ( \frac { 4 } { 7 } \times \frac { 2 } { 3 } \times \frac { 5 } { 2 } )$$

Evaluate

$$\frac{87}{80}=1.0875$$

Solution Steps

Multiply \frac{3}{4} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{2}+\frac{3\times 5}{4\times 7}}{\frac{4}{7}\times \frac{2}{3}\times \frac{5}{2}}$$

Do the multiplications in the fraction \frac{3\times 5}{4\times 7}.

$$\frac{\frac{1}{2}+\frac{15}{28}}{\frac{4}{7}\times \frac{2}{3}\times \frac{5}{2}}$$

Least common multiple of 2 and 28 is 28. Convert \frac{1}{2} and \frac{15}{28} to fractions with denominator 28.

$$\frac{\frac{14}{28}+\frac{15}{28}}{\frac{4}{7}\times \frac{2}{3}\times \frac{5}{2}}$$

Since \frac{14}{28} and \frac{15}{28} have the same denominator, add them by adding their numerators.

$$\frac{\frac{14+15}{28}}{\frac{4}{7}\times \frac{2}{3}\times \frac{5}{2}}$$

Add 14 and 15 to get 29.

$$\frac{\frac{29}{28}}{\frac{4}{7}\times \frac{2}{3}\times \frac{5}{2}}$$

Multiply \frac{4}{7} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{29}{28}}{\frac{4\times 2}{7\times 3}\times \frac{5}{2}}$$

Do the multiplications in the fraction \frac{4\times 2}{7\times 3}.

$$\frac{\frac{29}{28}}{\frac{8}{21}\times \frac{5}{2}}$$

Multiply \frac{8}{21} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{29}{28}}{\frac{8\times 5}{21\times 2}}$$

Do the multiplications in the fraction \frac{8\times 5}{21\times 2}.

$$\frac{\frac{29}{28}}{\frac{40}{42}}$$

Reduce the fraction \frac{40}{42} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{29}{28}}{\frac{20}{21}}$$

Divide \frac{29}{28} by \frac{20}{21} by multiplying \frac{29}{28} by the reciprocal of \frac{20}{21}.

$$\frac{29}{28}\times \frac{21}{20}$$

Multiply \frac{29}{28} times \frac{21}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{29\times 21}{28\times 20}$$

Do the multiplications in the fraction \frac{29\times 21}{28\times 20}.

$$\frac{609}{560}$$

Reduce the fraction \frac{609}{560} to lowest terms by extracting and canceling out 7.

$$\frac{87}{80}$$

Factor

$$\frac{3 \cdot 29}{2 ^ {4} \cdot 5} = 1\frac{7}{80} = 1.0875$$