Basic Math Examples

$13 \frac{5}{8} + 9 \frac{3}{4} + 9 \frac{3}{4} + 11 \frac{1}{2}$

Step 1

Convert $13 \frac{5}{8}$ to an improper fraction.

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Step 1.1

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

$13 + \frac{5}{8} + 9 \frac{3}{4} + 9 \frac{3}{4} + 11 \frac{1}{2}$

Step 1.2

Add $13$ and $\frac{5}{8}$ .

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Step 1.2.1

To write $13$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$13 \cdot \frac{8}{8} + \frac{5}{8} + 9 \frac{3}{4} + 9 \frac{3}{4} + 11 \frac{1}{2}$

Step 1.2.2

Combine $13$ and $\frac{8}{8}$ .

$\frac{13 \cdot 8}{8} + \frac{5}{8} + 9 \frac{3}{4} + 9 \frac{3}{4} + 11 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{13 \cdot 8 + 5}{8} + 9 \frac{3}{4} + 9 \frac{3}{4} + 11 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $13$ by $8$ .

$\frac{104 + 5}{8} + 9 \frac{3}{4} + 9 \frac{3}{4} + 11 \frac{1}{2}$

Step 1.2.4.2

Add $104$ and $5$ .

$\frac{109}{8} + 9 \frac{3}{4} + 9 \frac{3}{4} + 11 \frac{1}{2}$

Step 2

Convert $9 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{109}{8} + 9 + \frac{3}{4} + 9 \frac{3}{4} + 11 \frac{1}{2}$

Step 2.2

Add $9$ and $\frac{3}{4}$ .

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Step 2.2.1

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

$\frac{109}{8} + 9 \cdot \frac{4}{4} + \frac{3}{4} + 9 \frac{3}{4} + 11 \frac{1}{2}$

Step 2.2.2

Combine $9$ and $\frac{4}{4}$ .

$\frac{109}{8} + \frac{9 \cdot 4}{4} + \frac{3}{4} + 9 \frac{3}{4} + 11 \frac{1}{2}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{109}{8} + \frac{9 \cdot 4 + 3}{4} + 9 \frac{3}{4} + 11 \frac{1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $9$ by $4$ .

$\frac{109}{8} + \frac{36 + 3}{4} + 9 \frac{3}{4} + 11 \frac{1}{2}$

Step 2.2.4.2

Add $36$ and $3$ .

$\frac{109}{8} + \frac{39}{4} + 9 \frac{3}{4} + 11 \frac{1}{2}$

Step 3

Convert $9 \frac{3}{4}$ to an improper fraction.

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Step 3.1

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

$\frac{109}{8} + \frac{39}{4} + 9 + \frac{3}{4} + 11 \frac{1}{2}$

Step 3.2

Add $9$ and $\frac{3}{4}$ .

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Step 3.2.1

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

$\frac{109}{8} + \frac{39}{4} + 9 \cdot \frac{4}{4} + \frac{3}{4} + 11 \frac{1}{2}$

Step 3.2.2

Combine $9$ and $\frac{4}{4}$ .

$\frac{109}{8} + \frac{39}{4} + \frac{9 \cdot 4}{4} + \frac{3}{4} + 11 \frac{1}{2}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{109}{8} + \frac{39}{4} + \frac{9 \cdot 4 + 3}{4} + 11 \frac{1}{2}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $9$ by $4$ .

$\frac{109}{8} + \frac{39}{4} + \frac{36 + 3}{4} + 11 \frac{1}{2}$

Step 3.2.4.2

Add $36$ and $3$ .

$\frac{109}{8} + \frac{39}{4} + \frac{39}{4} + 11 \frac{1}{2}$

Step 4

Convert $11 \frac{1}{2}$ to an improper fraction.

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Step 4.1

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

$\frac{109}{8} + \frac{39}{4} + \frac{39}{4} + 11 + \frac{1}{2}$

Step 4.2

Add $11$ and $\frac{1}{2}$ .

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Step 4.2.1

To write $11$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{109}{8} + \frac{39}{4} + \frac{39}{4} + 11 \cdot \frac{2}{2} + \frac{1}{2}$

Step 4.2.2

Combine $11$ and $\frac{2}{2}$ .

$\frac{109}{8} + \frac{39}{4} + \frac{39}{4} + \frac{11 \cdot 2}{2} + \frac{1}{2}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{109}{8} + \frac{39}{4} + \frac{39}{4} + \frac{11 \cdot 2 + 1}{2}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $11$ by $2$ .

$\frac{109}{8} + \frac{39}{4} + \frac{39}{4} + \frac{22 + 1}{2}$

Step 4.2.4.2

Add $22$ and $1$ .

$\frac{109}{8} + \frac{39}{4} + \frac{39}{4} + \frac{23}{2}$

Step 5

Combine the numerators over the common denominator.

$\frac{109}{8} + \frac{39 + 39}{4} + \frac{23}{2}$

Step 6

Add $39$ and $39$ .

$\frac{109}{8} + \frac{78}{4} + \frac{23}{2}$

Step 7

Find the common denominator.

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Step 7.1

Multiply $\frac{78}{4}$ by $\frac{2}{2}$ .

$\frac{109}{8} + \frac{78}{4} \cdot \frac{2}{2} + \frac{23}{2}$

Step 7.2

Multiply $\frac{78}{4}$ by $\frac{2}{2}$ .

$\frac{109}{8} + \frac{78 \cdot 2}{4 \cdot 2} + \frac{23}{2}$

Step 7.3

Multiply $\frac{23}{2}$ by $\frac{4}{4}$ .

$\frac{109}{8} + \frac{78 \cdot 2}{4 \cdot 2} + \frac{23}{2} \cdot \frac{4}{4}$

Step 7.4

Multiply $\frac{23}{2}$ by $\frac{4}{4}$ .

$\frac{109}{8} + \frac{78 \cdot 2}{4 \cdot 2} + \frac{23 \cdot 4}{2 \cdot 4}$

Step 7.5

Reorder the factors of $4 \cdot 2$ .

$\frac{109}{8} + \frac{78 \cdot 2}{2 \cdot 4} + \frac{23 \cdot 4}{2 \cdot 4}$

Step 7.6

Multiply $2$ by $4$ .

$\frac{109}{8} + \frac{78 \cdot 2}{8} + \frac{23 \cdot 4}{2 \cdot 4}$

Step 7.7

Multiply $2$ by $4$ .

$\frac{109}{8} + \frac{78 \cdot 2}{8} + \frac{23 \cdot 4}{8}$

Step 8

Combine the numerators over the common denominator.

$\frac{109 + 78 \cdot 2 + 23 \cdot 4}{8}$

Step 9

Simplify each term.

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Step 9.1

Multiply $78$ by $2$ .

$\frac{109 + 156 + 23 \cdot 4}{8}$

Step 9.2

Multiply $23$ by $4$ .

$\frac{109 + 156 + 92}{8}$

Step 10

Simplify by adding numbers.

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Step 10.1

Add $109$ and $156$ .

$\frac{265 + 92}{8}$

Step 10.2

Add $265$ and $92$ .

$\frac{357}{8}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{357}{8}$

Decimal Form:

$44.625$

Mixed Number Form:

$44 \frac{5}{8}$