Solve 1/2(36div353/2)+1/3S_{3}=2

$$\frac { 1 } { 2 } ( \frac { 36 \div 353 } { 2 } ) + \frac { 1 } { 3 } S _ { 3 } = 2$$

Solve for S_3

$$S_{3} = \frac{2091}{353} = 5\frac{326}{353} \approx 5.923512748$$

Steps for Solving Linear Equation

Express \frac{\frac{36}{353}}{2} as a single fraction.

$$\frac{1}{2}\times \frac{36}{353\times 2}+\frac{1}{3}S_{3}=2$$

Multiply 353 and 2 to get 706.

$$\frac{1}{2}\times \frac{36}{706}+\frac{1}{3}S_{3}=2$$

Reduce the fraction \frac{36}{706} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}\times \frac{18}{353}+\frac{1}{3}S_{3}=2$$

Multiply \frac{1}{2} times \frac{18}{353} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 18}{2\times 353}+\frac{1}{3}S_{3}=2$$

Do the multiplications in the fraction \frac{1\times 18}{2\times 353}.

$$\frac{18}{706}+\frac{1}{3}S_{3}=2$$

Reduce the fraction \frac{18}{706} to lowest terms by extracting and canceling out 2.

$$\frac{9}{353}+\frac{1}{3}S_{3}=2$$

Subtract \frac{9}{353} from both sides.

$$\frac{1}{3}S_{3}=2-\frac{9}{353}$$

Convert 2 to fraction \frac{706}{353}.

$$\frac{1}{3}S_{3}=\frac{706}{353}-\frac{9}{353}$$

Since \frac{706}{353} and \frac{9}{353} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}S_{3}=\frac{706-9}{353}$$

Subtract 9 from 706 to get 697.

$$\frac{1}{3}S_{3}=\frac{697}{353}$$

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

$$S_{3}=\frac{697}{353}\times 3$$

Express \frac{697}{353}\times 3 as a single fraction.

$$S_{3}=\frac{697\times 3}{353}$$

Multiply 697 and 3 to get 2091.

$$S_{3}=\frac{2091}{353}$$