Basic Math Examples

$n - 6 \frac{1}{8} = 4 \frac{3}{8}$

Step 1

Simplify the left side.

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Step 1.1

Convert $6 \frac{1}{8}$ to an improper fraction.

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Step 1.1.1

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

$n - (6 + \frac{1}{8}) = 4 \frac{3}{8}$

Step 1.1.2

Add $6$ and $\frac{1}{8}$ .

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Step 1.1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$n - (6 \cdot \frac{8}{8} + \frac{1}{8}) = 4 \frac{3}{8}$

Step 1.1.2.2

Combine $6$ and $\frac{8}{8}$ .

$n - (\frac{6 \cdot 8}{8} + \frac{1}{8}) = 4 \frac{3}{8}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$n - \frac{6 \cdot 8 + 1}{8} = 4 \frac{3}{8}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $6$ by $8$ .

$n - \frac{48 + 1}{8} = 4 \frac{3}{8}$

Step 1.1.2.4.2

Add $48$ and $1$ .

$n - \frac{49}{8} = 4 \frac{3}{8}$

Step 2

Simplify the right side.

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Step 2.1

Convert $4 \frac{3}{8}$ to an improper fraction.

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Step 2.1.1

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

$n - \frac{49}{8} = 4 + \frac{3}{8}$

Step 2.1.2

Add $4$ and $\frac{3}{8}$ .

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Step 2.1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$n - \frac{49}{8} = 4 \cdot \frac{8}{8} + \frac{3}{8}$

Step 2.1.2.2

Combine $4$ and $\frac{8}{8}$ .

$n - \frac{49}{8} = \frac{4 \cdot 8}{8} + \frac{3}{8}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$n - \frac{49}{8} = \frac{4 \cdot 8 + 3}{8}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $4$ by $8$ .

$n - \frac{49}{8} = \frac{32 + 3}{8}$

Step 2.1.2.4.2

Add $32$ and $3$ .

$n - \frac{49}{8} = \frac{35}{8}$

Step 3

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

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Step 3.1

Add $\frac{49}{8}$ to both sides of the equation.

$n = \frac{35}{8} + \frac{49}{8}$

Step 3.2

Combine the numerators over the common denominator.

$n = \frac{35 + 49}{8}$

Step 3.3

Add $35$ and $49$ .

$n = \frac{84}{8}$

Step 3.4

Cancel the common factor of $84$ and $8$ .

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Step 3.4.1

Factor $4$ out of $84$ .

$n = \frac{4 (21)}{8}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $4$ out of $8$ .

$n = \frac{4 \cdot 21}{4 \cdot 2}$

Step 3.4.2.2

Cancel the common factor.

$n = \frac{4 \cdot 21}{4 \cdot 2}$

Step 3.4.2.3

Rewrite the expression.

$n = \frac{21}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$n = \frac{21}{2}$

Decimal Form:

$n = 10.5$

Mixed Number Form:

$n = 10 \frac{1}{2}$