Basic Math Examples

$\frac{7}{3} d + \frac{1}{3} d = 2 d + \frac{18}{2} + \frac{8}{3} d$

Step 1

Simplify $\frac{7}{3} d + \frac{1}{3} d$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{7}{3}$ and $d$ .

$\frac{7 d}{3} + \frac{1}{3} d = 2 d + \frac{18}{2} + \frac{8}{3} d$

Step 1.1.2

Combine $\frac{1}{3}$ and $d$ .

$\frac{7 d}{3} + \frac{d}{3} = 2 d + \frac{18}{2} + \frac{8}{3} d$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$\frac{7 d + d}{3} = 2 d + \frac{18}{2} + \frac{8}{3} d$

Step 1.2.2

Add $7 d$ and $d$ .

$\frac{8 d}{3} = 2 d + \frac{18}{2} + \frac{8}{3} d$

Step 2

Simplify $2 d + \frac{18}{2} + \frac{8}{3} d$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Divide $18$ by $2$ .

$\frac{8 d}{3} = 2 d + 9 + \frac{8}{3} d$

Step 2.1.2

Combine $\frac{8}{3}$ and $d$ .

$\frac{8 d}{3} = 2 d + 9 + \frac{8 d}{3}$

Step 2.2

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

$\frac{8 d}{3} = 2 d \cdot \frac{3}{3} + \frac{8 d}{3} + 9$

Step 2.3

Simplify terms.

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Step 2.3.1

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

$\frac{8 d}{3} = \frac{2 d \cdot 3}{3} + \frac{8 d}{3} + 9$

Step 2.3.2

Combine the numerators over the common denominator.

$\frac{8 d}{3} = \frac{2 d \cdot 3 + 8 d}{3} + 9$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Factor $2 d$ out of $2 d \cdot 3 + 8 d$ .

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Step 2.4.1.1

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

$\frac{8 d}{3} = \frac{2 d (3) + 8 d}{3} + 9$

Step 2.4.1.2

Factor $2 d$ out of $8 d$ .

$\frac{8 d}{3} = \frac{2 d (3) + 2 d (4)}{3} + 9$

Step 2.4.1.3

Factor $2 d$ out of $2 d (3) + 2 d (4)$ .

$\frac{8 d}{3} = \frac{2 d (3 + 4)}{3} + 9$

Step 2.4.2

Add $3$ and $4$ .

$\frac{8 d}{3} = \frac{2 d \cdot 7}{3} + 9$

Step 2.4.3

Multiply $7$ by $2$ .

$\frac{8 d}{3} = \frac{14 d}{3} + 9$

Step 3

Move all terms containing $d$ to the left side of the equation.

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Step 3.1

Subtract $\frac{14 d}{3}$ from both sides of the equation.

$\frac{8 d}{3} - \frac{14 d}{3} = 9$

Step 3.2

Combine the numerators over the common denominator.

$\frac{8 d - 14 d}{3} = 9$

Step 3.3

Subtract $14 d$ from $8 d$ .

$\frac{- 6 d}{3} = 9$

Step 3.4

Cancel the common factor of $- 6$ and $3$ .

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Step 3.4.1

Factor $3$ out of $- 6 d$ .

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

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $3$ out of $3$ .

$\frac{3 (- 2 d)}{3 (1)} = 9$

Step 3.4.2.2

Cancel the common factor.

$\frac{3 (- 2 d)}{3 \cdot 1} = 9$

Step 3.4.2.3

Rewrite the expression.

$\frac{- 2 d}{1} = 9$

Step 3.4.2.4

Divide $- 2 d$ by $1$ .

$- 2 d = 9$

Step 4

Divide each term in $- 2 d = 9$ by $- 2$ and simplify.

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Step 4.1

Divide each term in $- 2 d = 9$ by $- 2$ .

$\frac{- 2 d}{- 2} = \frac{9}{- 2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 2 d}{- 2} = \frac{9}{- 2}$

Step 4.2.1.2

Divide $d$ by $1$ .

$d = \frac{9}{- 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$d = - \frac{9}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$d = - \frac{9}{2}$

Decimal Form:

$d = - 4.5$

Mixed Number Form:

$d = - 4 \frac{1}{2}$