Solve (21/2+32/3)(43/4+4)

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

Evaluate

$$\frac{1295}{24}\approx 53.958333333$$

Solution Steps

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

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

Multiply 3 and 3 to get 9.

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

Add 9 and 2 to get 11.

$$\left(\frac{5}{2}+\frac{11}{3}\right)\left(\frac{4\times 4+3}{4}+4\right)$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{11}{3} to fractions with denominator 6.

$$\left(\frac{15}{6}+\frac{22}{6}\right)\left(\frac{4\times 4+3}{4}+4\right)$$

Since \frac{15}{6} and \frac{22}{6} have the same denominator, add them by adding their numerators.

$$\frac{15+22}{6}\left(\frac{4\times 4+3}{4}+4\right)$$

Add 15 and 22 to get 37.

$$\frac{37}{6}\left(\frac{4\times 4+3}{4}+4\right)$$

Multiply 4 and 4 to get 16.

$$\frac{37}{6}\left(\frac{16+3}{4}+4\right)$$

Add 16 and 3 to get 19.

$$\frac{37}{6}\left(\frac{19}{4}+4\right)$$

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

$$\frac{37}{6}\left(\frac{19}{4}+\frac{16}{4}\right)$$

Since \frac{19}{4} and \frac{16}{4} have the same denominator, add them by adding their numerators.

$$\frac{37}{6}\times \frac{19+16}{4}$$

Add 19 and 16 to get 35.

$$\frac{37}{6}\times \frac{35}{4}$$

Multiply \frac{37}{6} times \frac{35}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{37\times 35}{6\times 4}$$

Do the multiplications in the fraction \frac{37\times 35}{6\times 4}.

$$\frac{1295}{24}$$

Factor

$$\frac{5 \cdot 7 \cdot 37}{2 ^ {3} \cdot 3} = 53\frac{23}{24} = 53.958333333333336$$