Basic Math Examples

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

Step 1

Simplify $\frac{d - 2}{3} + \frac{d - 2}{2}$ .

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{d - 2}{3}$ by $\frac{2}{2}$ .

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

Step 1.3.2

Multiply $3$ by $2$ .

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

Step 1.3.3

Multiply $\frac{d - 2}{2}$ by $\frac{3}{3}$ .

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

Step 1.3.4

Multiply $2$ by $3$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

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

Step 1.5.2

Move $2$ to the left of $d$ .

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

Step 1.5.3

Multiply $- 2$ by $2$ .

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

Step 1.5.4

Apply the distributive property.

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

Step 1.5.5

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

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

Step 1.5.6

Multiply $- 2$ by $3$ .

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

Step 1.5.7

Add $2 d$ and $3 d$ .

$\frac{5 d - 4 - 6}{6} = 3$

Step 1.5.8

Subtract $6$ from $- 4$ .

$\frac{5 d - 10}{6} = 3$

Step 1.5.9

Factor $5$ out of $5 d - 10$ .

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Step 1.5.9.1

Factor $5$ out of $5 d$ .

$\frac{5 (d) - 10}{6} = 3$

Step 1.5.9.2

Factor $5$ out of $- 10$ .

$\frac{5 d + 5 \cdot - 2}{6} = 3$

Step 1.5.9.3

Factor $5$ out of $5 d + 5 \cdot - 2$ .

$\frac{5 (d - 2)}{6} = 3$

Step 2

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} \cdot \frac{5 (d - 2)}{6} = \frac{6}{5} \cdot 3$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{6}{5} \cdot \frac{5 (d - 2)}{6}$ .

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Step 3.1.1.1

Cancel the common factor of $6$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 (d - 2)}{6} = \frac{6}{5} \cdot 3$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 (d - 2)) = \frac{6}{5} \cdot 3$

Step 3.1.1.2

Cancel the common factor of $5$ .

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Step 3.1.1.2.1

Cancel the common factor.

$\frac{1}{5} (5 (d - 2)) = \frac{6}{5} \cdot 3$

Step 3.1.1.2.2

Rewrite the expression.

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $\frac{6}{5} \cdot 3$ .

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Step 3.2.1.1

Combine $\frac{6}{5}$ and $3$ .

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

Step 3.2.1.2

Multiply $6$ by $3$ .

$d - 2 = \frac{18}{5}$

Step 4

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

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Step 4.1

Add $2$ to both sides of the equation.

$d = \frac{18}{5} + 2$

Step 4.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$d = \frac{18}{5} + 2 \cdot \frac{5}{5}$

Step 4.3

Combine $2$ and $\frac{5}{5}$ .

$d = \frac{18}{5} + \frac{2 \cdot 5}{5}$

Step 4.4

Combine the numerators over the common denominator.

$d = \frac{18 + 2 \cdot 5}{5}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $2$ by $5$ .

$d = \frac{18 + 10}{5}$

Step 4.5.2

Add $18$ and $10$ .

$d = \frac{28}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$d = \frac{28}{5}$

Decimal Form:

$d = 5.6$

Mixed Number Form:

$d = 5 \frac{3}{5}$