Solve 74/5[51/4-(14/5+11/2)]

$$7 \frac { 4 } { 5 } [ 5 \frac { 1 } { 4 } - ( 1 \frac { 4 } { 5 } + 1 \frac { 1 } { 2 } ) ]$$

Evaluate

$$\frac{1521}{100}=15.21$$

Solution Steps

Multiply 7 and 5 to get 35.

$$\frac{35+4}{5}\left(\frac{5\times 4+1}{4}-\left(\frac{1\times 5+4}{5}+\frac{1\times 2+1}{2}\right)\right)$$

Add 35 and 4 to get 39.

$$\frac{39}{5}\left(\frac{5\times 4+1}{4}-\left(\frac{1\times 5+4}{5}+\frac{1\times 2+1}{2}\right)\right)$$

Multiply 5 and 4 to get 20.

$$\frac{39}{5}\left(\frac{20+1}{4}-\left(\frac{1\times 5+4}{5}+\frac{1\times 2+1}{2}\right)\right)$$

Add 20 and 1 to get 21.

$$\frac{39}{5}\left(\frac{21}{4}-\left(\frac{1\times 5+4}{5}+\frac{1\times 2+1}{2}\right)\right)$$

Multiply 1 and 5 to get 5.

$$\frac{39}{5}\left(\frac{21}{4}-\left(\frac{5+4}{5}+\frac{1\times 2+1}{2}\right)\right)$$

Add 5 and 4 to get 9.

$$\frac{39}{5}\left(\frac{21}{4}-\left(\frac{9}{5}+\frac{1\times 2+1}{2}\right)\right)$$

Multiply 1 and 2 to get 2.

$$\frac{39}{5}\left(\frac{21}{4}-\left(\frac{9}{5}+\frac{2+1}{2}\right)\right)$$

Add 2 and 1 to get 3.

$$\frac{39}{5}\left(\frac{21}{4}-\left(\frac{9}{5}+\frac{3}{2}\right)\right)$$

Least common multiple of 5 and 2 is 10. Convert \frac{9}{5} and \frac{3}{2} to fractions with denominator 10.

$$\frac{39}{5}\left(\frac{21}{4}-\left(\frac{18}{10}+\frac{15}{10}\right)\right)$$

Since \frac{18}{10} and \frac{15}{10} have the same denominator, add them by adding their numerators.

$$\frac{39}{5}\left(\frac{21}{4}-\frac{18+15}{10}\right)$$

Add 18 and 15 to get 33.

$$\frac{39}{5}\left(\frac{21}{4}-\frac{33}{10}\right)$$

Least common multiple of 4 and 10 is 20. Convert \frac{21}{4} and \frac{33}{10} to fractions with denominator 20.

$$\frac{39}{5}\left(\frac{105}{20}-\frac{66}{20}\right)$$

Since \frac{105}{20} and \frac{66}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{39}{5}\times \frac{105-66}{20}$$

Subtract 66 from 105 to get 39.

$$\frac{39}{5}\times \frac{39}{20}$$

Multiply \frac{39}{5} times \frac{39}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{39\times 39}{5\times 20}$$

Do the multiplications in the fraction \frac{39\times 39}{5\times 20}.

$$\frac{1521}{100}$$

Factor

$$\frac{3 ^ {2} \cdot 13 ^ {2}}{2 ^ {2} \cdot 5 ^ {2}} = 15\frac{21}{100} = 15.21$$