Solve for y y+3 7/9=2/3

$y + 3 \frac{7}{9} = \frac{2}{3}$

Convert $3 \frac{7}{9}$ to an improper fraction.

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

$y + 3 + \frac{7}{9} = \frac{2}{3}$

Add $3$ and $\frac{7}{9}$ .

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To write $3$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$y + 3 \cdot \frac{9}{9} + \frac{7}{9} = \frac{2}{3}$

Combine $3$ and $\frac{9}{9}$ .

$y + \frac{3 \cdot 9}{9} + \frac{7}{9} = \frac{2}{3}$

Combine the numerators over the common denominator.

$y + \frac{3 \cdot 9 + 7}{9} = \frac{2}{3}$

Simplify the numerator.

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Multiply $3$ by $9$ .

$y + \frac{27 + 7}{9} = \frac{2}{3}$

Add $27$ and $7$ .

$y + \frac{34}{9} = \frac{2}{3}$

Move all terms not containing $y$ to the right side of the equation.

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Subtract $\frac{34}{9}$ from both sides of the equation.

$y = \frac{2}{3} - \frac{34}{9}$

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{2}{3} \cdot \frac{3}{3} - \frac{34}{9}$

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{2}{3}$ and $\frac{3}{3}$ .

$y = \frac{2 \cdot 3}{3 \cdot 3} - \frac{34}{9}$

Multiply $3$ by $3$ .

$y = \frac{2 \cdot 3}{9} - \frac{34}{9}$

Combine the numerators over the common denominator.

$y = \frac{2 \cdot 3 - 34}{9}$

Simplify the numerator.

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Multiply $2$ by $3$ .

$y = \frac{6 - 34}{9}$

Subtract $34$ from $6$ .

$y = \frac{- 28}{9}$

Move the negative in front of the fraction.

$y = - \frac{28}{9}$

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{28}{9}$

Decimal Form:

$y = - 3.\overline{1}$

Mixed Number Form:

$y = - 3 \frac{1}{9}$

Solve for y y+3 7/9=2/3

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