Basic Math Examples

$\frac{1}{9} a - \frac{1}{18} + \frac{1}{3} a = \frac{1}{3} + a$

Step 1

Simplify $\frac{1}{9} a - \frac{1}{18} + \frac{1}{3} a$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Combine $\frac{1}{9}$ and $a$ .

$\frac{a}{9} - \frac{1}{18} + \frac{1}{3} a = \frac{1}{3} + a$

Step 1.1.2

Combine $\frac{1}{3}$ and $a$ .

$\frac{a}{9} - \frac{1}{18} + \frac{a}{3} = \frac{1}{3} + a$

Step 1.2

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

$\frac{a}{9} + \frac{a}{3} \cdot \frac{3}{3} - \frac{1}{18} = \frac{1}{3} + a$

Step 1.3

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

Tap for more steps...

Step 1.3.1

Multiply $\frac{a}{3}$ by $\frac{3}{3}$ .

$\frac{a}{9} + \frac{a \cdot 3}{3 \cdot 3} - \frac{1}{18} = \frac{1}{3} + a$

Step 1.3.2

Multiply $3$ by $3$ .

$\frac{a}{9} + \frac{a \cdot 3}{9} - \frac{1}{18} = \frac{1}{3} + a$

Step 1.4

Combine the numerators over the common denominator.

$\frac{a + a \cdot 3}{9} - \frac{1}{18} = \frac{1}{3} + a$

Step 1.5

Add $a$ and $a \cdot 3$ .

Tap for more steps...

Step 1.5.1

Reorder $a$ and $3$ .

$\frac{a + 3 \cdot a}{9} - \frac{1}{18} = \frac{1}{3} + a$

Step 1.5.2

Add $a$ and $3 \cdot a$ .

$\frac{4 a}{9} - \frac{1}{18} = \frac{1}{3} + a$

Step 2

Move all terms containing $a$ to the left side of the equation.

Tap for more steps...

Step 2.1

Subtract $a$ from both sides of the equation.

$\frac{4 a}{9} - \frac{1}{18} - a = \frac{1}{3}$

Step 2.2

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

$\frac{4 a}{9} - a \cdot \frac{9}{9} - \frac{1}{18} = \frac{1}{3}$

Step 2.3

Combine $- a$ and $\frac{9}{9}$ .

$\frac{4 a}{9} + \frac{- a \cdot 9}{9} - \frac{1}{18} = \frac{1}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{4 a - a \cdot 9}{9} - \frac{1}{18} = \frac{1}{3}$

Step 2.5

Simplify each term.

Tap for more steps...

Step 2.5.1

Simplify the numerator.

Tap for more steps...

Step 2.5.1.1

Factor $a$ out of $4 a - a \cdot 9$ .

Tap for more steps...

Step 2.5.1.1.1

Factor $a$ out of $4 a$ .

$\frac{a \cdot 4 - a \cdot 9}{9} - \frac{1}{18} = \frac{1}{3}$

Step 2.5.1.1.2

Factor $a$ out of $- a \cdot 9$ .

$\frac{a \cdot 4 + a (- 1 \cdot 9)}{9} - \frac{1}{18} = \frac{1}{3}$

Step 2.5.1.1.3

Factor $a$ out of $a \cdot 4 + a (- 1 \cdot 9)$ .

$\frac{a (4 - 1 \cdot 9)}{9} - \frac{1}{18} = \frac{1}{3}$

Step 2.5.1.2

Multiply $- 1$ by $9$ .

$\frac{a (4 - 9)}{9} - \frac{1}{18} = \frac{1}{3}$

Step 2.5.1.3

Subtract $9$ from $4$ .

$\frac{a \cdot - 5}{9} - \frac{1}{18} = \frac{1}{3}$

Step 2.5.2

Move $- 5$ to the left of $a$ .

$\frac{- 5 \cdot a}{9} - \frac{1}{18} = \frac{1}{3}$

Step 2.5.3

Move the negative in front of the fraction.

$- \frac{5 a}{9} - \frac{1}{18} = \frac{1}{3}$

Step 3

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

Tap for more steps...

Step 3.1

Add $\frac{1}{18}$ to both sides of the equation.

$- \frac{5 a}{9} = \frac{1}{3} + \frac{1}{18}$

Step 3.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- \frac{5 a}{9} = \frac{1}{3} \cdot \frac{6}{6} + \frac{1}{18}$

Step 3.3

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

Tap for more steps...

Step 3.3.1

Multiply $\frac{1}{3}$ by $\frac{6}{6}$ .

$- \frac{5 a}{9} = \frac{6}{3 \cdot 6} + \frac{1}{18}$

Step 3.3.2

Multiply $3$ by $6$ .

$- \frac{5 a}{9} = \frac{6}{18} + \frac{1}{18}$

Step 3.4

Combine the numerators over the common denominator.

$- \frac{5 a}{9} = \frac{6 + 1}{18}$

Step 3.5

Add $6$ and $1$ .

$- \frac{5 a}{9} = \frac{7}{18}$

Step 4

Multiply both sides of the equation by $- \frac{9}{5}$ .

$- \frac{9}{5} (- \frac{5 a}{9}) = - \frac{9}{5} \cdot \frac{7}{18}$

Step 5

Simplify both sides of the equation.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

Simplify $- \frac{9}{5} (- \frac{5 a}{9})$ .

Tap for more steps...

Step 5.1.1.1

Cancel the common factor of $9$ .

Tap for more steps...

Step 5.1.1.1.1

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$\frac{- 9}{5} (- \frac{5 a}{9}) = - \frac{9}{5} \cdot \frac{7}{18}$

Step 5.1.1.1.2

Move the leading negative in $- \frac{5 a}{9}$ into the numerator.

$\frac{- 9}{5} \cdot \frac{- 5 a}{9} = - \frac{9}{5} \cdot \frac{7}{18}$

Step 5.1.1.1.3

Factor $9$ out of $- 9$ .

$\frac{9 (- 1)}{5} \cdot \frac{- 5 a}{9} = - \frac{9}{5} \cdot \frac{7}{18}$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{9 \cdot - 1}{5} \cdot \frac{- 5 a}{9} = - \frac{9}{5} \cdot \frac{7}{18}$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 a) = - \frac{9}{5} \cdot \frac{7}{18}$

Step 5.1.1.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 5.1.1.2.1

Factor $5$ out of $- 5 a$ .

$\frac{- 1}{5} (5 (- a)) = - \frac{9}{5} \cdot \frac{7}{18}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- a)) = - \frac{9}{5} \cdot \frac{7}{18}$

Step 5.1.1.2.3

Rewrite the expression.

$- - a = - \frac{9}{5} \cdot \frac{7}{18}$

Step 5.1.1.3

Multiply.

Tap for more steps...

Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 a = - \frac{9}{5} \cdot \frac{7}{18}$

Step 5.1.1.3.2

Multiply $a$ by $1$ .

$a = - \frac{9}{5} \cdot \frac{7}{18}$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Simplify $- \frac{9}{5} \cdot \frac{7}{18}$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor of $9$ .

Tap for more steps...

Step 5.2.1.1.1

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$a = \frac{- 9}{5} \cdot \frac{7}{18}$

Step 5.2.1.1.2

Factor $9$ out of $- 9$ .

$a = \frac{9 (- 1)}{5} \cdot \frac{7}{18}$

Step 5.2.1.1.3

Factor $9$ out of $18$ .

$a = \frac{9 \cdot - 1}{5} \cdot \frac{7}{9 \cdot 2}$

Step 5.2.1.1.4

Cancel the common factor.

$a = \frac{9 \cdot - 1}{5} \cdot \frac{7}{9 \cdot 2}$

Step 5.2.1.1.5

Rewrite the expression.

$a = \frac{- 1}{5} \cdot \frac{7}{2}$

Step 5.2.1.2

Multiply $\frac{- 1}{5}$ by $\frac{7}{2}$ .

$a = \frac{- 1 \cdot 7}{5 \cdot 2}$

Step 5.2.1.3

Simplify the expression.

Tap for more steps...

Step 5.2.1.3.1

Multiply $- 1$ by $7$ .

$a = \frac{- 7}{5 \cdot 2}$

Step 5.2.1.3.2

Multiply $5$ by $2$ .

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

Step 5.2.1.3.3

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = - 0.7$