Solve 7/25div[7/10*(2/7+3/5)]

$$\frac { 7 } { 25 } \div [ \frac { 7 } { 10 } \times ( \frac { 2 } { 7 } + \frac { 3 } { 5 } ) ]$$

Evaluate

$$\frac{14}{31}\approx 0.451612903$$

Solution Steps

Least common multiple of 7 and 5 is 35. Convert \frac{2}{7} and \frac{3}{5} to fractions with denominator 35.

$$\frac{\frac{7}{25}}{\frac{7}{10}\left(\frac{10}{35}+\frac{21}{35}\right)}$$

Since \frac{10}{35} and \frac{21}{35} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{25}}{\frac{7}{10}\times \frac{10+21}{35}}$$

Add 10 and 21 to get 31.

$$\frac{\frac{7}{25}}{\frac{7}{10}\times \frac{31}{35}}$$

Multiply \frac{7}{10} times \frac{31}{35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7}{25}}{\frac{7\times 31}{10\times 35}}$$

Do the multiplications in the fraction \frac{7\times 31}{10\times 35}.

$$\frac{\frac{7}{25}}{\frac{217}{350}}$$

Reduce the fraction \frac{217}{350} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{7}{25}}{\frac{31}{50}}$$

Divide \frac{7}{25} by \frac{31}{50} by multiplying \frac{7}{25} by the reciprocal of \frac{31}{50}.

$$\frac{7}{25}\times \frac{50}{31}$$

Multiply \frac{7}{25} times \frac{50}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 50}{25\times 31}$$

Do the multiplications in the fraction \frac{7\times 50}{25\times 31}.

$$\frac{350}{775}$$

Reduce the fraction \frac{350}{775} to lowest terms by extracting and canceling out 25.

$$\frac{14}{31}$$

Factor

$$\frac{2 \cdot 7}{31} = 0.45161290322580644$$