Solve {l}{81/125*1/2+81/125*1/2}{+frac{125-81}{125}*frac{1}{2}}

$$\left. \begin{array} { l } { \frac { 81 } { 125 } \cdot \frac { 1 } { 2 } + \frac { 81 } { 125 } \cdot \frac { 1 } { 2 } } \\ { + \frac { 125 - 81 } { 125 } \cdot \frac { 1 } { 2 } } \end{array} \right.$$

Evaluate

$$\frac{103}{125}=0.824$$

Solution Steps

Multiply \frac{81}{125} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81\times 1}{125\times 2}+\frac{81}{125}\times \frac{1}{2}+\frac{125-81}{125}\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{81\times 1}{125\times 2}.

$$\frac{81}{250}+\frac{81}{125}\times \frac{1}{2}+\frac{125-81}{125}\times \frac{1}{2}$$

Multiply \frac{81}{125} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81}{250}+\frac{81\times 1}{125\times 2}+\frac{125-81}{125}\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{81\times 1}{125\times 2}.

$$\frac{81}{250}+\frac{81}{250}+\frac{125-81}{125}\times \frac{1}{2}$$

Since \frac{81}{250} and \frac{81}{250} have the same denominator, add them by adding their numerators.

$$\frac{81+81}{250}+\frac{125-81}{125}\times \frac{1}{2}$$

Add 81 and 81 to get 162.

$$\frac{162}{250}+\frac{125-81}{125}\times \frac{1}{2}$$

Reduce the fraction \frac{162}{250} to lowest terms by extracting and canceling out 2.

$$\frac{81}{125}+\frac{125-81}{125}\times \frac{1}{2}$$

Subtract 81 from 125 to get 44.

$$\frac{81}{125}+\frac{44}{125}\times \frac{1}{2}$$

Multiply \frac{44}{125} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81}{125}+\frac{44\times 1}{125\times 2}$$

Do the multiplications in the fraction \frac{44\times 1}{125\times 2}.

$$\frac{81}{125}+\frac{44}{250}$$

Reduce the fraction \frac{44}{250} to lowest terms by extracting and canceling out 2.

$$\frac{81}{125}+\frac{22}{125}$$

Since \frac{81}{125} and \frac{22}{125} have the same denominator, add them by adding their numerators.

$$\frac{81+22}{125}$$

Add 81 and 22 to get 103.

$$\frac{103}{125}$$

Factor

$$\frac{103}{5 ^ {3}} = 0.824$$