Algebra Examples

$14.5 d + 8.5 - \frac{1}{2} d + \frac{1}{2} + 2.5 d$

Step 1

Combine $d$ and $\frac{1}{2}$ .

$14.5 d + 8.5 - \frac{d}{2} + \frac{1}{2} + 2.5 d$

Step 2

To write $14.5 d$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$14.5 d \cdot \frac{2}{2} - \frac{d}{2} + 8.5 + \frac{1}{2} + 2.5 d$

Step 3

Combine $14.5 d$ and $\frac{2}{2}$ .

$\frac{14.5 d \cdot 2}{2} - \frac{d}{2} + 8.5 + \frac{1}{2} + 2.5 d$

Step 4

Combine the numerators over the common denominator.

$\frac{14.5 d \cdot 2 - d}{2} + 8.5 + \frac{1}{2} + 2.5 d$

Step 5

Combine the numerators over the common denominator.

$8.5 + 2.5 d + \frac{14.5 d \cdot 2 - d + 1}{2}$

Step 6

Multiply $2$ by $14.5$ .

$8.5 + 2.5 d + \frac{29 d - d + 1}{2}$

Step 7

Subtract $d$ from $29 d$ .

$8.5 + 2.5 d + \frac{28 d + 1}{2}$

Step 8

To write $8.5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2.5 d + 8.5 \cdot \frac{2}{2} + \frac{28 d + 1}{2}$

Step 9

Combine $8.5$ and $\frac{2}{2}$ .

$2.5 d + \frac{8.5 \cdot 2}{2} + \frac{28 d + 1}{2}$

Step 10

Combine the numerators over the common denominator.

$2.5 d + \frac{8.5 \cdot 2 + 28 d + 1}{2}$

Step 11

Simplify the expression.

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Step 11.1

Multiply $8.5$ by $2$ .

$2.5 d + \frac{17 + 28 d + 1}{2}$

Step 11.2

Add $17$ and $1$ .

$2.5 d + \frac{28 d + 18}{2}$

Step 12

Cancel the common factor of $28 d + 18$ and $2$ .

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Step 12.1

Factor $2$ out of $28 d$ .

$2.5 d + \frac{2 (14 d) + 18}{2}$

Step 12.2

Factor $2$ out of $18$ .

$2.5 d + \frac{2 (14 d) + 2 \cdot 9}{2}$

Step 12.3

Factor $2$ out of $2 (14 d) + 2 (9)$ .

$2.5 d + \frac{2 (14 d + 9)}{2}$

Step 12.4

Cancel the common factors.

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Step 12.4.1

Factor $2$ out of $2$ .

$2.5 d + \frac{2 (14 d + 9)}{2 (1)}$

Step 12.4.2

Cancel the common factor.

$2.5 d + \frac{2 (14 d + 9)}{2 \cdot 1}$

Step 12.4.3

Rewrite the expression.

$2.5 d + \frac{14 d + 9}{1}$

Step 12.4.4

Divide $14 d + 9$ by $1$ .

$2.5 d + 14 d + 9$

Step 13

Add $2.5 d$ and $14 d$ .

$16.5 d + 9$