Pre-Algebra Examples

$8 n = 5 \frac{7}{2}$

Step 1

Simplify the right side.

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Step 1.1

Convert $5 \frac{7}{2}$ to an improper fraction.

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Step 1.1.1

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

$8 n = 5 + \frac{7}{2}$

Step 1.1.2

Add $5$ and $\frac{7}{2}$ .

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Step 1.1.2.1

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

$8 n = 5 \cdot \frac{2}{2} + \frac{7}{2}$

Step 1.1.2.2

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

$8 n = \frac{5 \cdot 2}{2} + \frac{7}{2}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$8 n = \frac{5 \cdot 2 + 7}{2}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $5$ by $2$ .

$8 n = \frac{10 + 7}{2}$

Step 1.1.2.4.2

Add $10$ and $7$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $8$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $n$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.3.2

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

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Step 2.3.2.1

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

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

Step 2.3.2.2

Multiply $2$ by $8$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$n = 1.0625$

Mixed Number Form:

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