Solve for a a+3 1/2=-1 1/9

$a + 3 \frac{1}{2} = - 1 \frac{1}{9}$

Simplify the left side.

Convert $3 \frac{1}{2}$ to an improper fraction.

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

$a + 3 + \frac{1}{2} = - 1 \frac{1}{9}$

Add $3$ and $\frac{1}{2}$ .

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

$a + 3 \cdot \frac{2}{2} + \frac{1}{2} = - 1 \frac{1}{9}$

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

$a + \frac{3 \cdot 2}{2} + \frac{1}{2} = - 1 \frac{1}{9}$

Combine the numerators over the common denominator.

$a + \frac{3 \cdot 2 + 1}{2} = - 1 \frac{1}{9}$

Simplify the numerator.

Multiply $3$ by $2$ .

$a + \frac{6 + 1}{2} = - 1 \frac{1}{9}$

Add $6$ and $1$ .

$a + \frac{7}{2} = - 1 \frac{1}{9}$

Simplify the right side.

Convert $1 \frac{1}{9}$ to an improper fraction.

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

$a + \frac{7}{2} = - (1 + \frac{1}{9})$

Add $1$ and $\frac{1}{9}$ .

Write $1$ as a fraction with a common denominator.

$a + \frac{7}{2} = - (\frac{9}{9} + \frac{1}{9})$

Combine the numerators over the common denominator.

$a + \frac{7}{2} = - \frac{9 + 1}{9}$

Add $9$ and $1$ .

$a + \frac{7}{2} = - \frac{10}{9}$

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

Subtract $\frac{7}{2}$ from both sides of the equation.

$a = - \frac{10}{9} - \frac{7}{2}$

To write $- \frac{10}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$a = - \frac{10}{9} \cdot \frac{2}{2} - \frac{7}{2}$

To write $- \frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$a = - \frac{10}{9} \cdot \frac{2}{2} - \frac{7}{2} \cdot \frac{9}{9}$

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{10}{9}$ by $\frac{2}{2}$ .

$a = - \frac{10 \cdot 2}{9 \cdot 2} - \frac{7}{2} \cdot \frac{9}{9}$

Multiply $9$ by $2$ .

$a = - \frac{10 \cdot 2}{18} - \frac{7}{2} \cdot \frac{9}{9}$

Multiply $\frac{7}{2}$ by $\frac{9}{9}$ .

$a = - \frac{10 \cdot 2}{18} - \frac{7 \cdot 9}{2 \cdot 9}$

Multiply $2$ by $9$ .

$a = - \frac{10 \cdot 2}{18} - \frac{7 \cdot 9}{18}$

Combine the numerators over the common denominator.

$a = \frac{- 10 \cdot 2 - 7 \cdot 9}{18}$

Simplify the numerator.

Multiply $- 10$ by $2$ .

$a = \frac{- 20 - 7 \cdot 9}{18}$

Multiply $- 7$ by $9$ .

$a = \frac{- 20 - 63}{18}$

Subtract $63$ from $- 20$ .

$a = \frac{- 83}{18}$

Move the negative in front of the fraction.

$a = - \frac{83}{18}$

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{83}{18}$

Decimal Form:

$a = - 4.6\overline{1}$

Mixed Number Form:

$a = - 4 \frac{11}{18}$

Solve for a a+3 1/2=-1 1/9

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