Solve 1/2(36div53/2)+1/3S_{3}=2

$$\frac { 1 } { 2 } ( \frac { 36 \div 53 } { 2 } ) + \frac { 1 } { 3 } S _ { 3 } = 2$$

Solve for S_3

$$S_{3} = \frac{291}{53} = 5\frac{26}{53} \approx 5.490566038$$

Steps for Solving Linear Equation

Express \frac{\frac{36}{53}}{2} as a single fraction.

$$\frac{1}{2}\times \frac{36}{53\times 2}+\frac{1}{3}S_{3}=2$$

Multiply 53 and 2 to get 106.

$$\frac{1}{2}\times \frac{36}{106}+\frac{1}{3}S_{3}=2$$

Reduce the fraction \frac{36}{106} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}\times \frac{18}{53}+\frac{1}{3}S_{3}=2$$

Multiply \frac{1}{2} times \frac{18}{53} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 18}{2\times 53}+\frac{1}{3}S_{3}=2$$

Do the multiplications in the fraction \frac{1\times 18}{2\times 53}.

$$\frac{18}{106}+\frac{1}{3}S_{3}=2$$

Reduce the fraction \frac{18}{106} to lowest terms by extracting and canceling out 2.

$$\frac{9}{53}+\frac{1}{3}S_{3}=2$$

Subtract \frac{9}{53} from both sides.

$$\frac{1}{3}S_{3}=2-\frac{9}{53}$$

Convert 2 to fraction \frac{106}{53}.

$$\frac{1}{3}S_{3}=\frac{106}{53}-\frac{9}{53}$$

Since \frac{106}{53} and \frac{9}{53} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}S_{3}=\frac{106-9}{53}$$

Subtract 9 from 106 to get 97.

$$\frac{1}{3}S_{3}=\frac{97}{53}$$

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

$$S_{3}=\frac{97}{53}\times 3$$

Express \frac{97}{53}\times 3 as a single fraction.

$$S_{3}=\frac{97\times 3}{53}$$

Multiply 97 and 3 to get 291.

$$S_{3}=\frac{291}{53}$$