Solve for y 8 3/4+3 2/3+6 5/6=simplify

$8 \frac{3}{4} + 3 \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Step 1

Simplify the left side.

Simplify

$8 \frac{3}{4} + 3 \frac{2}{3} + 6 \frac{5}{6}$ .

Convert

$8 \frac{3}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$8 + \frac{3}{4} + 3 \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Add

$8$ and

$\frac{3}{4}$ .

To write

$8$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$8 \cdot \frac{4}{4} + \frac{3}{4} + 3 \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Combine

$8$ and

$\frac{4}{4}$ .

$\frac{8 \cdot 4}{4} + \frac{3}{4} + 3 \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Combine the numerators over the common denominator.

$\frac{8 \cdot 4 + 3}{4} + 3 \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Simplify the numerator.

Multiply

$8$ by

$4$ .

$\frac{32 + 3}{4} + 3 \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Add

$32$ and

$3$ .

$\frac{35}{4} + 3 \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Convert

$3 \frac{2}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{35}{4} + 3 + \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Add

$3$ and

$\frac{2}{3}$ .

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{35}{4} + 3 \cdot \frac{3}{3} + \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Combine

$3$ and

$\frac{3}{3}$ .

$\frac{35}{4} + \frac{3 \cdot 3}{3} + \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Combine the numerators over the common denominator.

$\frac{35}{4} + \frac{3 \cdot 3 + 2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Simplify the numerator.

Multiply

$3$ by

$3$ .

$\frac{35}{4} + \frac{9 + 2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Add

$9$ and

$2$ .

$\frac{35}{4} + \frac{11}{3} + 6 \frac{5}{6} = s i m p l i f y$

Convert

$6 \frac{5}{6}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{35}{4} + \frac{11}{3} + 6 + \frac{5}{6} = s i m p l i f y$

Add

$6$ and

$\frac{5}{6}$ .

To write

$6$ as a fraction with a common denominator, multiply by

$\frac{6}{6}$ .

$\frac{35}{4} + \frac{11}{3} + 6 \cdot \frac{6}{6} + \frac{5}{6} = s i m p l i f y$

Combine

$6$ and

$\frac{6}{6}$ .

$\frac{35}{4} + \frac{11}{3} + \frac{6 \cdot 6}{6} + \frac{5}{6} = s i m p l i f y$

Combine the numerators over the common denominator.

$\frac{35}{4} + \frac{11}{3} + \frac{6 \cdot 6 + 5}{6} = s i m p l i f y$

Simplify the numerator.

Multiply

$6$ by

$6$ .

$\frac{35}{4} + \frac{11}{3} + \frac{36 + 5}{6} = s i m p l i f y$

Add

$36$ and

$5$ .

$\frac{35}{4} + \frac{11}{3} + \frac{41}{6} = s i m p l i f y$

Find the common denominator.

Multiply

$\frac{35}{4}$ by

$\frac{3}{3}$ .

$\frac{35}{4} \cdot \frac{3}{3} + \frac{11}{3} + \frac{41}{6} = s i m p l i f y$

Multiply

$\frac{35}{4}$ by

$\frac{3}{3}$ .

$\frac{35 \cdot 3}{4 \cdot 3} + \frac{11}{3} + \frac{41}{6} = s i m p l i f y$

Multiply

$\frac{11}{3}$ by

$\frac{4}{4}$ .

$\frac{35 \cdot 3}{4 \cdot 3} + \frac{11}{3} \cdot \frac{4}{4} + \frac{41}{6} = s i m p l i f y$

Multiply

$\frac{11}{3}$ by

$\frac{4}{4}$ .

$\frac{35 \cdot 3}{4 \cdot 3} + \frac{11 \cdot 4}{3 \cdot 4} + \frac{41}{6} = s i m p l i f y$

Multiply

$\frac{41}{6}$ by

$\frac{2}{2}$ .

$\frac{35 \cdot 3}{4 \cdot 3} + \frac{11 \cdot 4}{3 \cdot 4} + \frac{41}{6} \cdot \frac{2}{2} = s i m p l i f y$

Multiply

$\frac{41}{6}$ by

$\frac{2}{2}$ .

$\frac{35 \cdot 3}{4 \cdot 3} + \frac{11 \cdot 4}{3 \cdot 4} + \frac{41 \cdot 2}{6 \cdot 2} = s i m p l i f y$

Reorder the factors of

$4 \cdot 3$ .

$\frac{35 \cdot 3}{3 \cdot 4} + \frac{11 \cdot 4}{3 \cdot 4} + \frac{41 \cdot 2}{6 \cdot 2} = s i m p l i f y$

Multiply

$3$ by

$4$ .

$\frac{35 \cdot 3}{12} + \frac{11 \cdot 4}{3 \cdot 4} + \frac{41 \cdot 2}{6 \cdot 2} = s i m p l i f y$

Multiply

$3$ by

$4$ .

$\frac{35 \cdot 3}{12} + \frac{11 \cdot 4}{12} + \frac{41 \cdot 2}{6 \cdot 2} = s i m p l i f y$

Reorder the factors of

$6 \cdot 2$ .

$\frac{35 \cdot 3}{12} + \frac{11 \cdot 4}{12} + \frac{41 \cdot 2}{2 \cdot 6} = s i m p l i f y$

Multiply

$2$ by

$6$ .

$\frac{35 \cdot 3}{12} + \frac{11 \cdot 4}{12} + \frac{41 \cdot 2}{12} = s i m p l i f y$

Combine the numerators over the common denominator.

$\frac{35 \cdot 3 + 11 \cdot 4 + 41 \cdot 2}{12} = s i m p l i f y$

Simplify each term.

Multiply

$35$ by

$3$ .

$\frac{105 + 11 \cdot 4 + 41 \cdot 2}{12} = s i m p l i f y$

Multiply

$11$ by

$4$ .

$\frac{105 + 44 + 41 \cdot 2}{12} = s i m p l i f y$

Multiply

$41$ by

$2$ .

$\frac{105 + 44 + 82}{12} = s i m p l i f y$

Reduce the expression by cancelling the common factors.

Add

$105$ and

$44$ .

$\frac{149 + 82}{12} = s i m p l i f y$

Add

$149$ and

$82$ .

$\frac{231}{12} = s i m p l i f y$

Cancel the common factor of

$231$ and

$12$ .

Factor

$3$ out of

$231$ .

$\frac{3 (77)}{12} = s i m p l i f y$

Cancel the common factors.

Factor

$3$ out of

$12$ .

$\frac{3 \cdot 77}{3 \cdot 4} = s i m p l i f y$

Cancel the common factor.

$\frac{3 \cdot 77}{3 \cdot 4} = s i m p l i f y$

Rewrite the expression.

$\frac{77}{4} = s i m p l i f y$

Step 2

Simplify the right side.

Simplify

$s i m p l i f y$ .

Multiply

$s i m p l i$ .

Raise

$i$ to the power of

$1$ .

$\frac{77}{4} = s m p l (i^{1} i) f y$

Raise

$i$ to the power of

$1$ .

$\frac{77}{4} = s m p l (i^{1} i^{1}) f y$

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{77}{4} = s m p l i^{1 + 1} f y$

Add

$1$ and

$1$ .

$\frac{77}{4} = s m p l i^{2} f y$

Rewrite

$i^{2}$ as

$- 1$ .

$\frac{77}{4} = s m p l \cdot - 1 f y$

Move

$- 1$ to the left of

$s m p l$ .

$\frac{77}{4} = - 1 \cdot (s m p l) f y$

Rewrite

$- 1 (s m p l)$ as

$- (s m p l)$ .

$\frac{77}{4} = - s m p l f y$

Step 3

Rewrite the equation as

$- s m p l f y = \frac{77}{4}$ .

$- s m p l f y = \frac{77}{4}$

Step 4

Divide each term in

$- s m p l f y = \frac{77}{4}$ by

$- 1 s m p l f$ and simplify.

Divide each term in

$- s m p l f y = \frac{77}{4}$ by

$- 1 s m p l f$ .

$\frac{- s m p l f y}{- 1 s m p l f} = \frac{\frac{77}{4}}{- 1 s m p l f}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{s m p l f y}{s m p l f} = \frac{\frac{77}{4}}{- 1 s m p l f}$

Cancel the common factor of

$s$ .

Cancel the common factor.

$\frac{s m p l f y}{s m p l f} = \frac{\frac{77}{4}}{- 1 s m p l f}$

Rewrite the expression.

$\frac{m p l f y}{m p l f} = \frac{\frac{77}{4}}{- 1 s m p l f}$

Cancel the common factor of

$m$ .

Cancel the common factor.

$\frac{m p l f y}{m p l f} = \frac{\frac{77}{4}}{- 1 s m p l f}$

Rewrite the expression.

$\frac{p l f y}{p l f} = \frac{\frac{77}{4}}{- 1 s m p l f}$

Cancel the common factor of

$p$ .

Cancel the common factor.

$\frac{p l f y}{p l f} = \frac{\frac{77}{4}}{- 1 s m p l f}$

Rewrite the expression.

$\frac{l f y}{l f} = \frac{\frac{77}{4}}{- 1 s m p l f}$

Cancel the common factor of

$l$ .

Cancel the common factor.

$\frac{l f y}{l f} = \frac{\frac{77}{4}}{- 1 s m p l f}$

Rewrite the expression.

$\frac{f y}{f} = \frac{\frac{77}{4}}{- 1 s m p l f}$

Cancel the common factor of

$f$ .

Cancel the common factor.

$\frac{f y}{f} = \frac{\frac{77}{4}}{- 1 s m p l f}$

Divide

$y$ by

$1$ .

$y = \frac{\frac{77}{4}}{- 1 s m p l f}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{77}{4} \cdot \frac{1}{- 1 s m p l f}$

Cancel the common factor of

$1$ and

$- 1$ .

Rewrite

$1$ as

$- 1 (- 1)$ .

$y = \frac{77}{4} \cdot \frac{- 1 (- 1)}{- 1 s m p l f}$

Move the negative in front of the fraction.

$y = \frac{77}{4} (- \frac{1}{s m p l f})$

Multiply

$\frac{77}{4}$ by

$\frac{1}{s m p l f}$ .

$y = - \frac{77}{4 s m p l f}$

Solve for y 8 3/4+3 2/3+6 5/6=simplify

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