Solve 2(11/2*4+11/2*21/2+21/2*4)=

$$2( \frac{ 11 }{ 2 } \times 4+ \frac{ 11 }{ 2 } \times \frac{ 21 }{ 2 } + \frac{ 21 }{ 2 } \times 4)=$$

Evaluate

$$\frac{487}{2}=243.5$$

Solution Steps

Express \frac{11}{2}\times 4 as a single fraction.

$$2\left(\frac{11\times 4}{2}+\frac{11}{2}\times \frac{21}{2}+\frac{21}{2}\times 4\right)$$

Multiply 11 and 4 to get 44.

$$2\left(\frac{44}{2}+\frac{11}{2}\times \frac{21}{2}+\frac{21}{2}\times 4\right)$$

Divide 44 by 2 to get 22.

$$2\left(22+\frac{11}{2}\times \frac{21}{2}+\frac{21}{2}\times 4\right)$$

Multiply \frac{11}{2} times \frac{21}{2} by multiplying numerator times numerator and denominator times denominator.

$$2\left(22+\frac{11\times 21}{2\times 2}+\frac{21}{2}\times 4\right)$$

Do the multiplications in the fraction \frac{11\times 21}{2\times 2}.

$$2\left(22+\frac{231}{4}+\frac{21}{2}\times 4\right)$$

Convert 22 to fraction \frac{88}{4}.

$$2\left(\frac{88}{4}+\frac{231}{4}+\frac{21}{2}\times 4\right)$$

Since \frac{88}{4} and \frac{231}{4} have the same denominator, add them by adding their numerators.

$$2\left(\frac{88+231}{4}+\frac{21}{2}\times 4\right)$$

Add 88 and 231 to get 319.

$$2\left(\frac{319}{4}+\frac{21}{2}\times 4\right)$$

Express \frac{21}{2}\times 4 as a single fraction.

$$2\left(\frac{319}{4}+\frac{21\times 4}{2}\right)$$

Multiply 21 and 4 to get 84.

$$2\left(\frac{319}{4}+\frac{84}{2}\right)$$

Divide 84 by 2 to get 42.

$$2\left(\frac{319}{4}+42\right)$$

Convert 42 to fraction \frac{168}{4}.

$$2\left(\frac{319}{4}+\frac{168}{4}\right)$$

Since \frac{319}{4} and \frac{168}{4} have the same denominator, add them by adding their numerators.

$$2\times \frac{319+168}{4}$$

Add 319 and 168 to get 487.

$$2\times \frac{487}{4}$$

Express 2\times \frac{487}{4} as a single fraction.

$$\frac{2\times 487}{4}$$

Multiply 2 and 487 to get 974.

$$\frac{974}{4}$$

Reduce the fraction \frac{974}{4} to lowest terms by extracting and canceling out 2.

$$\frac{487}{2}$$

Factor

$$\frac{487}{2} = 243\frac{1}{2} = 243.5$$