Basic Math Examples

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

Step 1

Simplify the left side.

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Step 1.1

Convert $2 \frac{2}{3}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

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

Step 1.1.2

Add $2$ and $\frac{2}{3}$ .

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Step 1.1.2.1

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

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

Step 1.1.2.2

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

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

Step 1.1.2.3

Combine the numerators over the common denominator.

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

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $3$ .

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

Step 1.1.2.4.2

Add $6$ and $2$ .

$- \frac{8}{3} + \frac{d}{6} = \frac{2}{3}$

Step 2

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

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Step 2.1

Add $\frac{8}{3}$ to both sides of the equation.

$\frac{d}{6} = \frac{2}{3} + \frac{8}{3}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{d}{6} = \frac{2 + 8}{3}$

Step 2.3

Add $2$ and $8$ .

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

Step 3

Multiply both sides of the equation by $6$ .

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $6$ .

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Step 4.1.1.1

Cancel the common factor.

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

Step 4.1.1.2

Rewrite the expression.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $6 (\frac{10}{3})$ .

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Step 4.2.1.1

Cancel the common factor of $3$ .

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Step 4.2.1.1.1

Factor $3$ out of $6$ .

$d = 3 (2) \frac{10}{3}$

Step 4.2.1.1.2

Cancel the common factor.

$d = 3 \cdot 2 \frac{10}{3}$

Step 4.2.1.1.3

Rewrite the expression.

$d = 2 \cdot 10$

Step 4.2.1.2

Multiply $2$ by $10$ .

$d = 20$