Solve 46/11*(11/5+41/2)

$$4 \frac{ 6 }{ 11 } \times (1 \frac{ 1 }{ 5 } +4 \frac{ 1 }{ 2 } )$$

Evaluate

$$\frac{285}{11}\approx 25.909090909$$

Solution Steps

Multiply 4 and 11 to get 44.

$$\frac{44+6}{11}\left(\frac{1\times 5+1}{5}+\frac{4\times 2+1}{2}\right)$$

Add 44 and 6 to get 50.

$$\frac{50}{11}\left(\frac{1\times 5+1}{5}+\frac{4\times 2+1}{2}\right)$$

Multiply 1 and 5 to get 5.

$$\frac{50}{11}\left(\frac{5+1}{5}+\frac{4\times 2+1}{2}\right)$$

Add 5 and 1 to get 6.

$$\frac{50}{11}\left(\frac{6}{5}+\frac{4\times 2+1}{2}\right)$$

Multiply 4 and 2 to get 8.

$$\frac{50}{11}\left(\frac{6}{5}+\frac{8+1}{2}\right)$$

Add 8 and 1 to get 9.

$$\frac{50}{11}\left(\frac{6}{5}+\frac{9}{2}\right)$$

Least common multiple of 5 and 2 is 10. Convert \frac{6}{5} and \frac{9}{2} to fractions with denominator 10.

$$\frac{50}{11}\left(\frac{12}{10}+\frac{45}{10}\right)$$

Since \frac{12}{10} and \frac{45}{10} have the same denominator, add them by adding their numerators.

$$\frac{50}{11}\times \frac{12+45}{10}$$

Add 12 and 45 to get 57.

$$\frac{50}{11}\times \frac{57}{10}$$

Multiply \frac{50}{11} times \frac{57}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{50\times 57}{11\times 10}$$

Do the multiplications in the fraction \frac{50\times 57}{11\times 10}.

$$\frac{2850}{110}$$

Reduce the fraction \frac{2850}{110} to lowest terms by extracting and canceling out 10.

$$\frac{285}{11}$$

Factor

$$\frac{3 \cdot 5 \cdot 19}{11} = 25\frac{10}{11} = 25.90909090909091$$