Solve 910/11:5/22+2,7

$$9 \frac { 10 } { 11 } : \frac { 5 } { 22 } + 2,7$$

Evaluate

$$46,3$$

Solution Steps

Divide \frac{9\times 11+10}{11} by \frac{5}{22} by multiplying \frac{9\times 11+10}{11} by the reciprocal of \frac{5}{22}.

$$\frac{\left(9\times 11+10\right)\times 22}{11\times 5}+2,7$$

Cancel out 11 in both numerator and denominator.

$$\frac{2\left(10+9\times 11\right)}{5}+2,7$$

Multiply 9 and 11 to get 99.

$$\frac{2\left(10+99\right)}{5}+2,7$$

Add 10 and 99 to get 109.

$$\frac{2\times 109}{5}+2,7$$

Multiply 2 and 109 to get 218.

$$\frac{218}{5}+2,7$$

Convert decimal number 2,7 to fraction \frac{27}{10}.

$$\frac{218}{5}+\frac{27}{10}$$

Least common multiple of 5 and 10 is 10. Convert \frac{218}{5} and \frac{27}{10} to fractions with denominator 10.

$$\frac{436}{10}+\frac{27}{10}$$

Since \frac{436}{10} and \frac{27}{10} have the same denominator, add them by adding their numerators.

$$\frac{436+27}{10}$$

Add 436 and 27 to get 463.

$$\frac{463}{10}$$

Factor

$$\frac{463}{2 \cdot 5} = 46\frac{3}{10} = 46.3$$