Solve (33/4+4/15)(3/4+11/4)

$$( 3 \frac { 3 } { 4 } + \frac { 4 } { 15 } ) ( \frac { 3 } { 4 } + 1 \frac { 1 } { 4 } )$$

Evaluate

$$\frac{241}{30}\approx 8.033333333$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\left(\frac{12+3}{4}+\frac{4}{15}\right)\left(\frac{3}{4}+\frac{1\times 4+1}{4}\right)$$

Add 12 and 3 to get 15.

$$\left(\frac{15}{4}+\frac{4}{15}\right)\left(\frac{3}{4}+\frac{1\times 4+1}{4}\right)$$

Least common multiple of 4 and 15 is 60. Convert \frac{15}{4} and \frac{4}{15} to fractions with denominator 60.

$$\left(\frac{225}{60}+\frac{16}{60}\right)\left(\frac{3}{4}+\frac{1\times 4+1}{4}\right)$$

Since \frac{225}{60} and \frac{16}{60} have the same denominator, add them by adding their numerators.

$$\frac{225+16}{60}\left(\frac{3}{4}+\frac{1\times 4+1}{4}\right)$$

Add 225 and 16 to get 241.

$$\frac{241}{60}\left(\frac{3}{4}+\frac{1\times 4+1}{4}\right)$$

Multiply 1 and 4 to get 4.

$$\frac{241}{60}\left(\frac{3}{4}+\frac{4+1}{4}\right)$$

Add 4 and 1 to get 5.

$$\frac{241}{60}\left(\frac{3}{4}+\frac{5}{4}\right)$$

Since \frac{3}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{241}{60}\times \frac{3+5}{4}$$

Add 3 and 5 to get 8.

$$\frac{241}{60}\times \frac{8}{4}$$

Divide 8 by 4 to get 2.

$$\frac{241}{60}\times 2$$

Express \frac{241}{60}\times 2 as a single fraction.

$$\frac{241\times 2}{60}$$

Multiply 241 and 2 to get 482.

$$\frac{482}{60}$$

Reduce the fraction \frac{482}{60} to lowest terms by extracting and canceling out 2.

$$\frac{241}{30}$$

Factor

$$\frac{241}{2 \cdot 3 \cdot 5} = 8\frac{1}{30} = 8.033333333333333$$