Algebra Examples

Solve the following equation: $\frac{1}{4} d = 2 \frac{1}{8}$

Step 1

Simplify the left side.

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Step 1.1

Combine $\frac{1}{4}$ and $d$ .

$\frac{d}{4} = 2 \frac{1}{8}$

Step 2

Simplify the right side.

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Step 2.1

Convert $2 \frac{1}{8}$ to an improper fraction.

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Step 2.1.1

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

$\frac{d}{4} = 2 + \frac{1}{8}$

Step 2.1.2

Add $2$ and $\frac{1}{8}$ .

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Step 2.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{d}{4} = 2 \cdot \frac{8}{8} + \frac{1}{8}$

Step 2.1.2.2

Combine $2$ and $\frac{8}{8}$ .

$\frac{d}{4} = \frac{2 \cdot 8}{8} + \frac{1}{8}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{d}{4} = \frac{2 \cdot 8 + 1}{8}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $2$ by $8$ .

$\frac{d}{4} = \frac{16 + 1}{8}$

Step 2.1.2.4.2

Add $16$ and $1$ .

$\frac{d}{4} = \frac{17}{8}$

Step 3

Multiply both sides of the equation by $4$ .

$4 \frac{d}{4} = 4 (\frac{17}{8})$

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 $4$ .

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Step 4.1.1.1

Cancel the common factor.

$4 \frac{d}{4} = 4 (\frac{17}{8})$

Step 4.1.1.2

Rewrite the expression.

$d = 4 (\frac{17}{8})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Factor $4$ out of $8$ .

$d = 4 \frac{17}{4 (2)}$

Step 4.2.1.2

Cancel the common factor.

$d = 4 \frac{17}{4 \cdot 2}$

Step 4.2.1.3

Rewrite the expression.

$d = \frac{17}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$d = \frac{17}{2}$

Decimal Form:

$d = 8.5$

Mixed Number Form:

$d = 8 \frac{1}{2}$