Pre-Algebra Examples

$12 y = 2 \frac{1}{4}$

Step 1

Simplify the right side.

Tap for more steps...

Step 1.1

Convert $2 \frac{1}{4}$ to an improper fraction.

Tap for more steps...

Step 1.1.1

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

$12 y = 2 + \frac{1}{4}$

Step 1.1.2

Add $2$ and $\frac{1}{4}$ .

Tap for more steps...

Step 1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$12 y = 2 \cdot \frac{4}{4} + \frac{1}{4}$

Step 1.1.2.2

Combine $2$ and $\frac{4}{4}$ .

$12 y = \frac{2 \cdot 4}{4} + \frac{1}{4}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$12 y = \frac{2 \cdot 4 + 1}{4}$

Step 1.1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.1.2.4.1

Multiply $2$ by $4$ .

$12 y = \frac{8 + 1}{4}$

Step 1.1.2.4.2

Add $8$ and $1$ .

$12 y = \frac{9}{4}$

Step 2

Divide each term in $12 y = \frac{9}{4}$ by $12$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $12 y = \frac{9}{4}$ by $12$ .

$\frac{12 y}{12} = \frac{\frac{9}{4}}{12}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $12$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{12 y}{12} = \frac{\frac{9}{4}}{12}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{9}{4}}{12}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{9}{4} \cdot \frac{1}{12}$

Step 2.3.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.3.2.1

Factor $3$ out of $9$ .

$y = \frac{3 (3)}{4} \cdot \frac{1}{12}$

Step 2.3.2.2

Factor $3$ out of $12$ .

$y = \frac{3 \cdot 3}{4} \cdot \frac{1}{3 \cdot 4}$

Step 2.3.2.3

Cancel the common factor.

$y = \frac{3 \cdot 3}{4} \cdot \frac{1}{3 \cdot 4}$

Step 2.3.2.4

Rewrite the expression.

$y = \frac{3}{4} \cdot \frac{1}{4}$

Step 2.3.3

Multiply $\frac{3}{4}$ by $\frac{1}{4}$ .

$y = \frac{3}{4 \cdot 4}$

Step 2.3.4

Multiply $4$ by $4$ .

$y = \frac{3}{16}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{3}{16}$

Decimal Form:

$y = 0.1875$