Solve 41/2+{(33/5-13/4)*5}

$$4 \frac { 1 } { 2 } + \{ ( 3 \frac { 3 } { 5 } - 1 \frac { 3 } { 4 } ) \times 5 \}$$

Evaluate

$$\frac{55}{4}=13.75$$

Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{8+1}{2}+\left(\frac{3\times 5+3}{5}-\frac{1\times 4+3}{4}\right)\times 5$$

Add 8 and 1 to get 9.

$$\frac{9}{2}+\left(\frac{3\times 5+3}{5}-\frac{1\times 4+3}{4}\right)\times 5$$

Multiply 3 and 5 to get 15.

$$\frac{9}{2}+\left(\frac{15+3}{5}-\frac{1\times 4+3}{4}\right)\times 5$$

Add 15 and 3 to get 18.

$$\frac{9}{2}+\left(\frac{18}{5}-\frac{1\times 4+3}{4}\right)\times 5$$

Multiply 1 and 4 to get 4.

$$\frac{9}{2}+\left(\frac{18}{5}-\frac{4+3}{4}\right)\times 5$$

Add 4 and 3 to get 7.

$$\frac{9}{2}+\left(\frac{18}{5}-\frac{7}{4}\right)\times 5$$

Least common multiple of 5 and 4 is 20. Convert \frac{18}{5} and \frac{7}{4} to fractions with denominator 20.

$$\frac{9}{2}+\left(\frac{72}{20}-\frac{35}{20}\right)\times 5$$

Since \frac{72}{20} and \frac{35}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{2}+\frac{72-35}{20}\times 5$$

Subtract 35 from 72 to get 37.

$$\frac{9}{2}+\frac{37}{20}\times 5$$

Express \frac{37}{20}\times 5 as a single fraction.

$$\frac{9}{2}+\frac{37\times 5}{20}$$

Multiply 37 and 5 to get 185.

$$\frac{9}{2}+\frac{185}{20}$$

Reduce the fraction \frac{185}{20} to lowest terms by extracting and canceling out 5.

$$\frac{9}{2}+\frac{37}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{9}{2} and \frac{37}{4} to fractions with denominator 4.

$$\frac{18}{4}+\frac{37}{4}$$

Since \frac{18}{4} and \frac{37}{4} have the same denominator, add them by adding their numerators.

$$\frac{18+37}{4}$$

Add 18 and 37 to get 55.

$$\frac{55}{4}$$

Factor

$$\frac{5 \cdot 11}{2 ^ {2}} = 13\frac{3}{4} = 13.75$$