Solve 7/9div21/5+5/11*2/9

$$\frac{ 7 }{ 9 } \div 2 \frac{ 1 }{ 5 } + \frac{ 5 }{ 11 } \times \frac{ 2 }{ 9 }$$

Evaluate

$$\frac{5}{11}\approx 0.454545455$$

Solution Steps

Divide \frac{7}{9} by \frac{2\times 5+1}{5} by multiplying \frac{7}{9} by the reciprocal of \frac{2\times 5+1}{5}.

$$\frac{7\times 5}{9\left(2\times 5+1\right)}+\frac{5}{11}\times \frac{2}{9}$$

Multiply 7 and 5 to get 35.

$$\frac{35}{9\left(2\times 5+1\right)}+\frac{5}{11}\times \frac{2}{9}$$

Multiply 2 and 5 to get 10.

$$\frac{35}{9\left(10+1\right)}+\frac{5}{11}\times \frac{2}{9}$$

Add 10 and 1 to get 11.

$$\frac{35}{9\times 11}+\frac{5}{11}\times \frac{2}{9}$$

Multiply 9 and 11 to get 99.

$$\frac{35}{99}+\frac{5}{11}\times \frac{2}{9}$$

Multiply \frac{5}{11} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35}{99}+\frac{5\times 2}{11\times 9}$$

Do the multiplications in the fraction \frac{5\times 2}{11\times 9}.

$$\frac{35}{99}+\frac{10}{99}$$

Since \frac{35}{99} and \frac{10}{99} have the same denominator, add them by adding their numerators.

$$\frac{35+10}{99}$$

Add 35 and 10 to get 45.

$$\frac{45}{99}$$

Reduce the fraction \frac{45}{99} to lowest terms by extracting and canceling out 9.

$$\frac{5}{11}$$

Factor

$$\frac{5}{11} = 0.45454545454545453$$