Basic Math Examples

$10 - \frac{5}{2} = r - 6 \cdot 3$

Step 1

Rewrite the equation as $r - 6 \cdot 3 = 10 - \frac{5}{2}$ .

$r - 6 \cdot 3 = 10 - \frac{5}{2}$

Step 2

Multiply $- 6$ by $3$ .

$r - 18 = 10 - \frac{5}{2}$

Step 3

Simplify $10 - \frac{5}{2}$ .

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Step 3.1

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

$r - 18 = 10 \cdot \frac{2}{2} - \frac{5}{2}$

Step 3.2

Combine $10$ and $\frac{2}{2}$ .

$r - 18 = \frac{10 \cdot 2}{2} - \frac{5}{2}$

Step 3.3

Combine the numerators over the common denominator.

$r - 18 = \frac{10 \cdot 2 - 5}{2}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $10$ by $2$ .

$r - 18 = \frac{20 - 5}{2}$

Step 3.4.2

Subtract $5$ from $20$ .

$r - 18 = \frac{15}{2}$

Step 4

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

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Step 4.1

Add $18$ to both sides of the equation.

$r = \frac{15}{2} + 18$

Step 4.2

To write $18$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$r = \frac{15}{2} + 18 \cdot \frac{2}{2}$

Step 4.3

Combine $18$ and $\frac{2}{2}$ .

$r = \frac{15}{2} + \frac{18 \cdot 2}{2}$

Step 4.4

Combine the numerators over the common denominator.

$r = \frac{15 + 18 \cdot 2}{2}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $18$ by $2$ .

$r = \frac{15 + 36}{2}$

Step 4.5.2

Add $15$ and $36$ .

$r = \frac{51}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$r = \frac{51}{2}$

Decimal Form:

$r = 25.5$

Mixed Number Form:

$r = 25 \frac{1}{2}$