Solve 11/2+(61/3-4.75)*22/5

$$1 \frac { 1 } { 2 } + ( 6 \frac { 1 } { 3 } - 4.75 ) \times 2 \frac { 2 } { 5 }$$

Evaluate

$$5.3$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{2+1}{2}+\left(\frac{6\times 3+1}{3}-4.75\right)\times \frac{2\times 5+2}{5}$$

Add 2 and 1 to get 3.

$$\frac{3}{2}+\left(\frac{6\times 3+1}{3}-4.75\right)\times \frac{2\times 5+2}{5}$$

Multiply 6 and 3 to get 18.

$$\frac{3}{2}+\left(\frac{18+1}{3}-4.75\right)\times \frac{2\times 5+2}{5}$$

Add 18 and 1 to get 19.

$$\frac{3}{2}+\left(\frac{19}{3}-4.75\right)\times \frac{2\times 5+2}{5}$$

Convert decimal number 4.75 to fraction \frac{475}{100}. Reduce the fraction \frac{475}{100} to lowest terms by extracting and canceling out 25.

$$\frac{3}{2}+\left(\frac{19}{3}-\frac{19}{4}\right)\times \frac{2\times 5+2}{5}$$

Least common multiple of 3 and 4 is 12. Convert \frac{19}{3} and \frac{19}{4} to fractions with denominator 12.

$$\frac{3}{2}+\left(\frac{76}{12}-\frac{57}{12}\right)\times \frac{2\times 5+2}{5}$$

Since \frac{76}{12} and \frac{57}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}+\frac{76-57}{12}\times \frac{2\times 5+2}{5}$$

Subtract 57 from 76 to get 19.

$$\frac{3}{2}+\frac{19}{12}\times \frac{2\times 5+2}{5}$$

Multiply 2 and 5 to get 10.

$$\frac{3}{2}+\frac{19}{12}\times \frac{10+2}{5}$$

Add 10 and 2 to get 12.

$$\frac{3}{2}+\frac{19}{12}\times \frac{12}{5}$$

Multiply \frac{19}{12} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}+\frac{19\times 12}{12\times 5}$$

Cancel out 12 in both numerator and denominator.

$$\frac{3}{2}+\frac{19}{5}$$

Least common multiple of 2 and 5 is 10. Convert \frac{3}{2} and \frac{19}{5} to fractions with denominator 10.

$$\frac{15}{10}+\frac{38}{10}$$

Since \frac{15}{10} and \frac{38}{10} have the same denominator, add them by adding their numerators.

$$\frac{15+38}{10}$$

Add 15 and 38 to get 53.

$$\frac{53}{10}$$

Factor

$$\frac{53}{2 \cdot 5} = 5\frac{3}{10} = 5.3$$