Basic Math Examples

$\frac{45}{12} y = 5 z + 98$

Step 1

Multiply both sides of the equation by $\frac{12}{45}$ .

$\frac{12}{45} (\frac{45}{12} y) = \frac{12}{45} (5 z + 98)$

Step 2

Simplify both sides of the equation.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $\frac{12}{45} (\frac{45}{12} y)$ .

Tap for more steps...

Step 2.1.1.1

Cancel the common factor of $12$ and $45$ .

Tap for more steps...

Step 2.1.1.1.1

Factor $3$ out of $12$ .

$\frac{3 (4)}{45} (\frac{45}{12} y) = \frac{12}{45} (5 z + 98)$

Step 2.1.1.1.2

Cancel the common factors.

Tap for more steps...

Step 2.1.1.1.2.1

Factor $3$ out of $45$ .

$\frac{3 \cdot 4}{3 \cdot 15} (\frac{45}{12} y) = \frac{12}{45} (5 z + 98)$

Step 2.1.1.1.2.2

Cancel the common factor.

$\frac{3 \cdot 4}{3 \cdot 15} (\frac{45}{12} y) = \frac{12}{45} (5 z + 98)$

Step 2.1.1.1.2.3

Rewrite the expression.

$\frac{4}{15} (\frac{45}{12} y) = \frac{12}{45} (5 z + 98)$

Step 2.1.1.2

Cancel the common factor of $45$ and $12$ .

Tap for more steps...

Step 2.1.1.2.1

Factor $3$ out of $45$ .

$\frac{4}{15} (\frac{3 (15)}{12} y) = \frac{12}{45} (5 z + 98)$

Step 2.1.1.2.2

Cancel the common factors.

Tap for more steps...

Step 2.1.1.2.2.1

Factor $3$ out of $12$ .

$\frac{4}{15} (\frac{3 \cdot 15}{3 \cdot 4} y) = \frac{12}{45} (5 z + 98)$

Step 2.1.1.2.2.2

Cancel the common factor.

$\frac{4}{15} (\frac{3 \cdot 15}{3 \cdot 4} y) = \frac{12}{45} (5 z + 98)$

Step 2.1.1.2.2.3

Rewrite the expression.

$\frac{4}{15} (\frac{15}{4} y) = \frac{12}{45} (5 z + 98)$

Step 2.1.1.3

Combine $\frac{15}{4}$ and $y$ .

$\frac{4}{15} \cdot \frac{15 y}{4} = \frac{12}{45} (5 z + 98)$

Step 2.1.1.4

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.1.1.4.1

Cancel the common factor.

$\frac{4}{15} \cdot \frac{15 y}{4} = \frac{12}{45} (5 z + 98)$

Step 2.1.1.4.2

Rewrite the expression.

$\frac{1}{15} (15 y) = \frac{12}{45} (5 z + 98)$

Step 2.1.1.5

Cancel the common factor of $15$ .

Tap for more steps...

Step 2.1.1.5.1

Factor $15$ out of $15 y$ .

$\frac{1}{15} (15 (y)) = \frac{12}{45} (5 z + 98)$

Step 2.1.1.5.2

Cancel the common factor.

$\frac{1}{15} (15 y) = \frac{12}{45} (5 z + 98)$

Step 2.1.1.5.3

Rewrite the expression.

$y = \frac{12}{45} (5 z + 98)$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Simplify $\frac{12}{45} (5 z + 98)$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor of $12$ and $45$ .

Tap for more steps...

Step 2.2.1.1.1

Factor $3$ out of $12$ .

$y = \frac{3 (4)}{45} (5 z + 98)$

Step 2.2.1.1.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1.1.2.1

Factor $3$ out of $45$ .

$y = \frac{3 \cdot 4}{3 \cdot 15} (5 z + 98)$

Step 2.2.1.1.2.2

Cancel the common factor.

$y = \frac{3 \cdot 4}{3 \cdot 15} (5 z + 98)$

Step 2.2.1.1.2.3

Rewrite the expression.

$y = \frac{4}{15} (5 z + 98)$

Step 2.2.1.2

Apply the distributive property.

$y = \frac{4}{15} (5 z) + \frac{4}{15} \cdot 98$

Step 2.2.1.3

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.2.1.3.1

Factor $5$ out of $15$ .

$y = \frac{4}{5 (3)} (5 z) + \frac{4}{15} \cdot 98$

Step 2.2.1.3.2

Factor $5$ out of $5 z$ .

$y = \frac{4}{5 (3)} (5 (z)) + \frac{4}{15} \cdot 98$

Step 2.2.1.3.3

Cancel the common factor.

$y = \frac{4}{5 \cdot 3} (5 z) + \frac{4}{15} \cdot 98$

Step 2.2.1.3.4

Rewrite the expression.

$y = \frac{4}{3} z + \frac{4}{15} \cdot 98$

Step 2.2.1.4

Combine $\frac{4}{3}$ and $z$ .

$y = \frac{4 z}{3} + \frac{4}{15} \cdot 98$

Step 2.2.1.5

Multiply $\frac{4}{15} \cdot 98$ .

Tap for more steps...

Step 2.2.1.5.1

Combine $\frac{4}{15}$ and $98$ .

$y = \frac{4 z}{3} + \frac{4 \cdot 98}{15}$

Step 2.2.1.5.2

Multiply $4$ by $98$ .

$y = \frac{4 z}{3} + \frac{392}{15}$