Solve =(21/7+13/5):145/9

$$= ( 2 \frac { 1 } { 7 } + 1 \frac { 3 } { 5 } ) : 14 \frac { 5 } { 9 }$$

Evaluate

$$\frac{9}{35}\approx 0.257142857$$

Solution Steps

Multiply 2 and 7 to get 14.

$$\frac{\frac{14+1}{7}+\frac{1\times 5+3}{5}}{\frac{14\times 9+5}{9}}$$

Add 14 and 1 to get 15.

$$\frac{\frac{15}{7}+\frac{1\times 5+3}{5}}{\frac{14\times 9+5}{9}}$$

Multiply 1 and 5 to get 5.

$$\frac{\frac{15}{7}+\frac{5+3}{5}}{\frac{14\times 9+5}{9}}$$

Add 5 and 3 to get 8.

$$\frac{\frac{15}{7}+\frac{8}{5}}{\frac{14\times 9+5}{9}}$$

Least common multiple of 7 and 5 is 35. Convert \frac{15}{7} and \frac{8}{5} to fractions with denominator 35.

$$\frac{\frac{75}{35}+\frac{56}{35}}{\frac{14\times 9+5}{9}}$$

Since \frac{75}{35} and \frac{56}{35} have the same denominator, add them by adding their numerators.

$$\frac{\frac{75+56}{35}}{\frac{14\times 9+5}{9}}$$

Add 75 and 56 to get 131.

$$\frac{\frac{131}{35}}{\frac{14\times 9+5}{9}}$$

Multiply 14 and 9 to get 126.

$$\frac{\frac{131}{35}}{\frac{126+5}{9}}$$

Add 126 and 5 to get 131.

$$\frac{\frac{131}{35}}{\frac{131}{9}}$$

Divide \frac{131}{35} by \frac{131}{9} by multiplying \frac{131}{35} by the reciprocal of \frac{131}{9}.

$$\frac{131}{35}\times \frac{9}{131}$$

Multiply \frac{131}{35} times \frac{9}{131} by multiplying numerator times numerator and denominator times denominator.

$$\frac{131\times 9}{35\times 131}$$

Cancel out 131 in both numerator and denominator.

$$\frac{9}{35}$$

Factor

$$\frac{3 ^ {2}}{5 \cdot 7} = 0.2571428571428571$$