Solve (30/5+36/7)div(2/5+2/7)

$$( \frac { 30 } { 5 } + \frac { 36 } { 7 } ) \div ( \frac { 2 } { 5 } + \frac { 2 } { 7 } )$$

Evaluate

$$\frac{65}{4}=16.25$$

Solution Steps

Divide 30 by 5 to get 6.

$$\frac{6+\frac{36}{7}}{\frac{2}{5}+\frac{2}{7}}$$

Convert 6 to fraction \frac{42}{7}.

$$\frac{\frac{42}{7}+\frac{36}{7}}{\frac{2}{5}+\frac{2}{7}}$$

Since \frac{42}{7} and \frac{36}{7} have the same denominator, add them by adding their numerators.

$$\frac{\frac{42+36}{7}}{\frac{2}{5}+\frac{2}{7}}$$

Add 42 and 36 to get 78.

$$\frac{\frac{78}{7}}{\frac{2}{5}+\frac{2}{7}}$$

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

$$\frac{\frac{78}{7}}{\frac{14}{35}+\frac{10}{35}}$$

Since \frac{14}{35} and \frac{10}{35} have the same denominator, add them by adding their numerators.

$$\frac{\frac{78}{7}}{\frac{14+10}{35}}$$

Add 14 and 10 to get 24.

$$\frac{\frac{78}{7}}{\frac{24}{35}}$$

Divide \frac{78}{7} by \frac{24}{35} by multiplying \frac{78}{7} by the reciprocal of \frac{24}{35}.

$$\frac{78}{7}\times \frac{35}{24}$$

Multiply \frac{78}{7} times \frac{35}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{78\times 35}{7\times 24}$$

Do the multiplications in the fraction \frac{78\times 35}{7\times 24}.

$$\frac{2730}{168}$$

Reduce the fraction \frac{2730}{168} to lowest terms by extracting and canceling out 42.

$$\frac{65}{4}$$

Factor

$$\frac{5 \cdot 13}{2 ^ {2}} = 16\frac{1}{4} = 16.25$$