Solve (21/2+35/3)(41/4+2^2)

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

Evaluate

$$\frac{473}{8}=59.125$$

Solution Steps

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

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

Multiply 3 and 3 to get 9.

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

Add 9 and 5 to get 14.

$$\left(\frac{5}{2}+\frac{14}{3}\right)\left(\frac{4\times 4+1}{4}+2^{2}\right)$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{14}{3} to fractions with denominator 6.

$$\left(\frac{15}{6}+\frac{28}{6}\right)\left(\frac{4\times 4+1}{4}+2^{2}\right)$$

Since \frac{15}{6} and \frac{28}{6} have the same denominator, add them by adding their numerators.

$$\frac{15+28}{6}\left(\frac{4\times 4+1}{4}+2^{2}\right)$$

Add 15 and 28 to get 43.

$$\frac{43}{6}\left(\frac{4\times 4+1}{4}+2^{2}\right)$$

Multiply 4 and 4 to get 16.

$$\frac{43}{6}\left(\frac{16+1}{4}+2^{2}\right)$$

Add 16 and 1 to get 17.

$$\frac{43}{6}\left(\frac{17}{4}+2^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$\frac{43}{6}\left(\frac{17}{4}+4\right)$$

Convert 4 to fraction \frac{16}{4}.

$$\frac{43}{6}\left(\frac{17}{4}+\frac{16}{4}\right)$$

Since \frac{17}{4} and \frac{16}{4} have the same denominator, add them by adding their numerators.

$$\frac{43}{6}\times \frac{17+16}{4}$$

Add 17 and 16 to get 33.

$$\frac{43}{6}\times \frac{33}{4}$$

Multiply \frac{43}{6} times \frac{33}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{43\times 33}{6\times 4}$$

Do the multiplications in the fraction \frac{43\times 33}{6\times 4}.

$$\frac{1419}{24}$$

Reduce the fraction \frac{1419}{24} to lowest terms by extracting and canceling out 3.

$$\frac{473}{8}$$

Factor

$$\frac{11 \cdot 43}{2 ^ {3}} = 59\frac{1}{8} = 59.125$$