Pre-Algebra Examples

$y \div \frac{1}{2} = 2 \frac{1}{8}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $y \div \frac{1}{2}$ .

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Step 1.1.1

To divide by a fraction, multiply by its reciprocal.

$y \cdot 2 = 2 \frac{1}{8}$

Step 1.1.2

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

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

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.

$2 y = 2 + \frac{1}{8}$

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 $\frac{8}{8}$ .

$2 y = 2 \cdot \frac{8}{8} + \frac{1}{8}$

Step 2.1.2.2

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

$2 y = \frac{2 \cdot 8}{8} + \frac{1}{8}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$2 y = \frac{2 \cdot 8 + 1}{8}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $2$ by $8$ .

$2 y = \frac{16 + 1}{8}$

Step 2.1.2.4.2

Add $16$ and $1$ .

$2 y = \frac{17}{8}$

Step 3

Divide each term in $2 y = \frac{17}{8}$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 y = \frac{17}{8}$ by $2$ .

$\frac{2 y}{2} = \frac{\frac{17}{8}}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{\frac{17}{8}}{2}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{17}{8}}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{17}{8} \cdot \frac{1}{2}$

Step 3.3.2

Multiply $\frac{17}{8} \cdot \frac{1}{2}$ .

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Step 3.3.2.1

Multiply $\frac{17}{8}$ by $\frac{1}{2}$ .

$y = \frac{17}{8 \cdot 2}$

Step 3.3.2.2

Multiply $8$ by $2$ .

$y = \frac{17}{16}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{17}{16}$

Decimal Form:

$y = 1.0625$

Mixed Number Form:

$y = 1 \frac{1}{16}$