Pre-Algebra Examples

$q + \frac{7}{9} = 2 \frac{4}{6}$

Step 1

Simplify the right side.

Tap for more steps...

Step 1.1

Simplify $2 \frac{4}{6}$ .

Tap for more steps...

Step 1.1.1

Convert $2 \frac{4}{6}$ to an improper fraction.

Tap for more steps...

Step 1.1.1.1

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

$q + \frac{7}{9} = 2 + \frac{4}{6}$

Step 1.1.1.2

Add $2$ and $\frac{4}{6}$ .

Tap for more steps...

Step 1.1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$q + \frac{7}{9} = 2 \cdot \frac{6}{6} + \frac{4}{6}$

Step 1.1.1.2.2

Combine $2$ and $\frac{6}{6}$ .

$q + \frac{7}{9} = \frac{2 \cdot 6}{6} + \frac{4}{6}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$q + \frac{7}{9} = \frac{2 \cdot 6 + 4}{6}$

Step 1.1.1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.1.1.2.4.1

Multiply $2$ by $6$ .

$q + \frac{7}{9} = \frac{12 + 4}{6}$

Step 1.1.1.2.4.2

Add $12$ and $4$ .

$q + \frac{7}{9} = \frac{16}{6}$

Step 1.1.2

Cancel the common factor of $16$ and $6$ .

Tap for more steps...

Step 1.1.2.1

Factor $2$ out of $16$ .

$q + \frac{7}{9} = \frac{2 (8)}{6}$

Step 1.1.2.2

Cancel the common factors.

Tap for more steps...

Step 1.1.2.2.1

Factor $2$ out of $6$ .

$q + \frac{7}{9} = \frac{2 \cdot 8}{2 \cdot 3}$

Step 1.1.2.2.2

Cancel the common factor.

$q + \frac{7}{9} = \frac{2 \cdot 8}{2 \cdot 3}$

Step 1.1.2.2.3

Rewrite the expression.

$q + \frac{7}{9} = \frac{8}{3}$

Step 2

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

Tap for more steps...

Step 2.1

Subtract $\frac{7}{9}$ from both sides of the equation.

$q = \frac{8}{3} - \frac{7}{9}$

Step 2.2

To write $\frac{8}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$q = \frac{8}{3} \cdot \frac{3}{3} - \frac{7}{9}$

Step 2.3

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

Tap for more steps...

Step 2.3.1

Multiply $\frac{8}{3}$ by $\frac{3}{3}$ .

$q = \frac{8 \cdot 3}{3 \cdot 3} - \frac{7}{9}$

Step 2.3.2

Multiply $3$ by $3$ .

$q = \frac{8 \cdot 3}{9} - \frac{7}{9}$

Step 2.4

Combine the numerators over the common denominator.

$q = \frac{8 \cdot 3 - 7}{9}$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $8$ by $3$ .

$q = \frac{24 - 7}{9}$

Step 2.5.2

Subtract $7$ from $24$ .

$q = \frac{17}{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$q = \frac{17}{9}$

Decimal Form:

$q = 1.\overline{8}$

Mixed Number Form:

$q = 1 \frac{8}{9}$