Basic Math Examples

$8 \frac{3}{4} + n + 2 \frac{3}{8} + 4 \frac{1}{2} = 23 \frac{1}{8}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $8 \frac{3}{4} + n + 2 \frac{3}{8} + 4 \frac{1}{2}$ .

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Step 1.1.1

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

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Step 1.1.1.1

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

$8 + \frac{3}{4} + n + 2 \frac{3}{8} + 4 \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.1.2

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

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Step 1.1.1.2.1

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

$8 \cdot \frac{4}{4} + \frac{3}{4} + n + 2 \frac{3}{8} + 4 \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.1.2.2

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

$\frac{8 \cdot 4}{4} + \frac{3}{4} + n + 2 \frac{3}{8} + 4 \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 4 + 3}{4} + n + 2 \frac{3}{8} + 4 \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $8$ by $4$ .

$\frac{32 + 3}{4} + n + 2 \frac{3}{8} + 4 \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.1.2.4.2

Add $32$ and $3$ .

$\frac{35}{4} + n + 2 \frac{3}{8} + 4 \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.2

Convert $2 \frac{3}{8}$ to an improper fraction.

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Step 1.1.2.1

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

$\frac{35}{4} + n + 2 + \frac{3}{8} + 4 \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.2.2

Add $2$ and $\frac{3}{8}$ .

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Step 1.1.2.2.1

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

$\frac{35}{4} + n + 2 \cdot \frac{8}{8} + \frac{3}{8} + 4 \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.2.2.2

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

$\frac{35}{4} + n + \frac{2 \cdot 8}{8} + \frac{3}{8} + 4 \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

$\frac{35}{4} + n + \frac{2 \cdot 8 + 3}{8} + 4 \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply $2$ by $8$ .

$\frac{35}{4} + n + \frac{16 + 3}{8} + 4 \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.2.2.4.2

Add $16$ and $3$ .

$\frac{35}{4} + n + \frac{19}{8} + 4 \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.3

Convert $4 \frac{1}{2}$ to an improper fraction.

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Step 1.1.3.1

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

$\frac{35}{4} + n + \frac{19}{8} + 4 + \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.3.2

Add $4$ and $\frac{1}{2}$ .

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Step 1.1.3.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{35}{4} + n + \frac{19}{8} + 4 \cdot \frac{2}{2} + \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.3.2.2

Combine $4$ and $\frac{2}{2}$ .

$\frac{35}{4} + n + \frac{19}{8} + \frac{4 \cdot 2}{2} + \frac{1}{2} = 23 \frac{1}{8}$

Step 1.1.3.2.3

Combine the numerators over the common denominator.

$\frac{35}{4} + n + \frac{19}{8} + \frac{4 \cdot 2 + 1}{2} = 23 \frac{1}{8}$

Step 1.1.3.2.4

Simplify the numerator.

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Step 1.1.3.2.4.1

Multiply $4$ by $2$ .

$\frac{35}{4} + n + \frac{19}{8} + \frac{8 + 1}{2} = 23 \frac{1}{8}$

Step 1.1.3.2.4.2

Add $8$ and $1$ .

$\frac{35}{4} + n + \frac{19}{8} + \frac{9}{2} = 23 \frac{1}{8}$

Step 1.1.4

To write $\frac{35}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$n + \frac{35}{4} \cdot \frac{2}{2} + \frac{19}{8} + \frac{9}{2} = 23 \frac{1}{8}$

Step 1.1.5

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.1.5.1

Multiply $\frac{35}{4}$ by $\frac{2}{2}$ .

$n + \frac{35 \cdot 2}{4 \cdot 2} + \frac{19}{8} + \frac{9}{2} = 23 \frac{1}{8}$

Step 1.1.5.2

Multiply $4$ by $2$ .

$n + \frac{35 \cdot 2}{8} + \frac{19}{8} + \frac{9}{2} = 23 \frac{1}{8}$

Step 1.1.6

Combine the numerators over the common denominator.

$n + \frac{35 \cdot 2 + 19}{8} + \frac{9}{2} = 23 \frac{1}{8}$

Step 1.1.7

Simplify the numerator.

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Step 1.1.7.1

Multiply $35$ by $2$ .

$n + \frac{70 + 19}{8} + \frac{9}{2} = 23 \frac{1}{8}$

Step 1.1.7.2

Add $70$ and $19$ .

$n + \frac{89}{8} + \frac{9}{2} = 23 \frac{1}{8}$

Step 1.1.8

To write $\frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$n + \frac{89}{8} + \frac{9}{2} \cdot \frac{4}{4} = 23 \frac{1}{8}$

Step 1.1.9

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.1.9.1

Multiply $\frac{9}{2}$ by $\frac{4}{4}$ .

$n + \frac{89}{8} + \frac{9 \cdot 4}{2 \cdot 4} = 23 \frac{1}{8}$

Step 1.1.9.2

Multiply $2$ by $4$ .

$n + \frac{89}{8} + \frac{9 \cdot 4}{8} = 23 \frac{1}{8}$

Step 1.1.10

Combine the numerators over the common denominator.

$n + \frac{89 + 9 \cdot 4}{8} = 23 \frac{1}{8}$

Step 1.1.11

Simplify the numerator.

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Step 1.1.11.1

Multiply $9$ by $4$ .

$n + \frac{89 + 36}{8} = 23 \frac{1}{8}$

Step 1.1.11.2

Add $89$ and $36$ .

$n + \frac{125}{8} = 23 \frac{1}{8}$

Step 2

Simplify the right side.

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Step 2.1

Convert $23 \frac{1}{8}$ to an improper fraction.

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Step 2.1.1

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

$n + \frac{125}{8} = 23 + \frac{1}{8}$

Step 2.1.2

Add $23$ and $\frac{1}{8}$ .

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Step 2.1.2.1

To write $23$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$n + \frac{125}{8} = 23 \cdot \frac{8}{8} + \frac{1}{8}$

Step 2.1.2.2

Combine $23$ and $\frac{8}{8}$ .

$n + \frac{125}{8} = \frac{23 \cdot 8}{8} + \frac{1}{8}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$n + \frac{125}{8} = \frac{23 \cdot 8 + 1}{8}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $23$ by $8$ .

$n + \frac{125}{8} = \frac{184 + 1}{8}$

Step 2.1.2.4.2

Add $184$ and $1$ .

$n + \frac{125}{8} = \frac{185}{8}$

Step 3

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

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Step 3.1

Subtract $\frac{125}{8}$ from both sides of the equation.

$n = \frac{185}{8} - \frac{125}{8}$

Step 3.2

Combine the numerators over the common denominator.

$n = \frac{185 - 125}{8}$

Step 3.3

Subtract $125$ from $185$ .

$n = \frac{60}{8}$

Step 3.4

Cancel the common factor of $60$ and $8$ .

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Step 3.4.1

Factor $4$ out of $60$ .

$n = \frac{4 (15)}{8}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $4$ out of $8$ .

$n = \frac{4 \cdot 15}{4 \cdot 2}$

Step 3.4.2.2

Cancel the common factor.

$n = \frac{4 \cdot 15}{4 \cdot 2}$

Step 3.4.2.3

Rewrite the expression.

$n = \frac{15}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$n = \frac{15}{2}$

Decimal Form:

$n = 7.5$

Mixed Number Form:

$n = 7 \frac{1}{2}$