Basic Math Examples

$\frac{6}{2} d + \frac{9}{2} d + \frac{6}{4} d - \frac{9}{6} d$

Step 1

Simplify each term.

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Step 1.1

Divide $6$ by $2$ .

$3 d + \frac{9}{2} d + \frac{6}{4} d - \frac{9}{6} d$

Step 1.2

Combine $\frac{9}{2}$ and $d$ .

$3 d + \frac{9 d}{2} + \frac{6}{4} d - \frac{9}{6} d$

Step 1.3

Cancel the common factor of $6$ and $4$ .

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Step 1.3.1

Factor $2$ out of $6$ .

$3 d + \frac{9 d}{2} + \frac{2 (3)}{4} d - \frac{9}{6} d$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $4$ .

$3 d + \frac{9 d}{2} + \frac{2 \cdot 3}{2 \cdot 2} d - \frac{9}{6} d$

Step 1.3.2.2

Cancel the common factor.

$3 d + \frac{9 d}{2} + \frac{2 \cdot 3}{2 \cdot 2} d - \frac{9}{6} d$

Step 1.3.2.3

Rewrite the expression.

$3 d + \frac{9 d}{2} + \frac{3}{2} d - \frac{9}{6} d$

Step 1.4

Combine $\frac{3}{2}$ and $d$ .

$3 d + \frac{9 d}{2} + \frac{3 d}{2} - \frac{9}{6} d$

Step 1.5

Cancel the common factor of $9$ and $6$ .

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Step 1.5.1

Factor $3$ out of $9$ .

$3 d + \frac{9 d}{2} + \frac{3 d}{2} - \frac{3 (3)}{6} d$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $3$ out of $6$ .

$3 d + \frac{9 d}{2} + \frac{3 d}{2} - \frac{3 \cdot 3}{3 \cdot 2} d$

Step 1.5.2.2

Cancel the common factor.

$3 d + \frac{9 d}{2} + \frac{3 d}{2} - \frac{3 \cdot 3}{3 \cdot 2} d$

Step 1.5.2.3

Rewrite the expression.

$3 d + \frac{9 d}{2} + \frac{3 d}{2} - \frac{3}{2} d$

Step 1.6

Combine $d$ and $\frac{3}{2}$ .

$3 d + \frac{9 d}{2} + \frac{3 d}{2} - \frac{d \cdot 3}{2}$

Step 1.7

Move $3$ to the left of $d$ .

$3 d + \frac{9 d}{2} + \frac{3 d}{2} - \frac{3 d}{2}$

Step 2

Combine the opposite terms in $3 d + \frac{9 d}{2} + \frac{3 d}{2} - \frac{3 d}{2}$ .

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Step 2.1

Subtract $\frac{3 d}{2}$ from $\frac{3 d}{2}$ .

$3 d + \frac{9 d}{2} + 0$

Step 2.2

Add $3 d + \frac{9 d}{2}$ and $0$ .

$3 d + \frac{9 d}{2}$

Step 3

To write $3 d$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 d \cdot \frac{2}{2} + \frac{9 d}{2}$

Step 4

Simplify terms.

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Step 4.1

Combine $3 d$ and $\frac{2}{2}$ .

$\frac{3 d \cdot 2}{2} + \frac{9 d}{2}$

Step 4.2

Combine the numerators over the common denominator.

$\frac{3 d \cdot 2 + 9 d}{2}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $3 d$ out of $3 d \cdot 2 + 9 d$ .

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Step 5.1.1

Factor $3 d$ out of $3 d \cdot 2$ .

$\frac{3 d (2) + 9 d}{2}$

Step 5.1.2

Factor $3 d$ out of $9 d$ .

$\frac{3 d (2) + 3 d (3)}{2}$

Step 5.1.3

Factor $3 d$ out of $3 d (2) + 3 d (3)$ .

$\frac{3 d (2 + 3)}{2}$

Step 5.2

Add $2$ and $3$ .

$\frac{3 d \cdot 5}{2}$

Step 5.3

Multiply $5$ by $3$ .

$\frac{15 d}{2}$