Basic Math Examples

$(4 \frac{5}{2} + 5 \frac{4}{2} + 6 \frac{3}{2}) - 9 \frac{1}{2}$

Step 1

Convert $4 \frac{5}{2}$ to an improper fraction.

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Step 1.1

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

$4 + \frac{5}{2} + 5 \frac{4}{2} + 6 \frac{3}{2} - 9 \frac{1}{2}$

Step 1.2

Add $4$ and $\frac{5}{2}$ .

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Step 1.2.1

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

$4 \cdot \frac{2}{2} + \frac{5}{2} + 5 \frac{4}{2} + 6 \frac{3}{2} - 9 \frac{1}{2}$

Step 1.2.2

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

$\frac{4 \cdot 2}{2} + \frac{5}{2} + 5 \frac{4}{2} + 6 \frac{3}{2} - 9 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 2 + 5}{2} + 5 \frac{4}{2} + 6 \frac{3}{2} - 9 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $2$ .

$\frac{8 + 5}{2} + 5 \frac{4}{2} + 6 \frac{3}{2} - 9 \frac{1}{2}$

Step 1.2.4.2

Add $8$ and $5$ .

$\frac{13}{2} + 5 \frac{4}{2} + 6 \frac{3}{2} - 9 \frac{1}{2}$

Step 2

Convert $5 \frac{4}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{13}{2} + 5 + \frac{4}{2} + 6 \frac{3}{2} - 9 \frac{1}{2}$

Step 2.2

Add $5$ and $\frac{4}{2}$ .

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Step 2.2.1

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

$\frac{13}{2} + 5 \cdot \frac{2}{2} + \frac{4}{2} + 6 \frac{3}{2} - 9 \frac{1}{2}$

Step 2.2.2

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

$\frac{13}{2} + \frac{5 \cdot 2}{2} + \frac{4}{2} + 6 \frac{3}{2} - 9 \frac{1}{2}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{13}{2} + \frac{5 \cdot 2 + 4}{2} + 6 \frac{3}{2} - 9 \frac{1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $2$ .

$\frac{13}{2} + \frac{10 + 4}{2} + 6 \frac{3}{2} - 9 \frac{1}{2}$

Step 2.2.4.2

Add $10$ and $4$ .

$\frac{13}{2} + \frac{14}{2} + 6 \frac{3}{2} - 9 \frac{1}{2}$

Step 3

Convert $6 \frac{3}{2}$ to an improper fraction.

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Step 3.1

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

$\frac{13}{2} + \frac{14}{2} + 6 + \frac{3}{2} - 9 \frac{1}{2}$

Step 3.2

Add $6$ and $\frac{3}{2}$ .

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Step 3.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{13}{2} + \frac{14}{2} + 6 \cdot \frac{2}{2} + \frac{3}{2} - 9 \frac{1}{2}$

Step 3.2.2

Combine $6$ and $\frac{2}{2}$ .

$\frac{13}{2} + \frac{14}{2} + \frac{6 \cdot 2}{2} + \frac{3}{2} - 9 \frac{1}{2}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{13}{2} + \frac{14}{2} + \frac{6 \cdot 2 + 3}{2} - 9 \frac{1}{2}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $6$ by $2$ .

$\frac{13}{2} + \frac{14}{2} + \frac{12 + 3}{2} - 9 \frac{1}{2}$

Step 3.2.4.2

Add $12$ and $3$ .

$\frac{13}{2} + \frac{14}{2} + \frac{15}{2} - 9 \frac{1}{2}$

Step 4

Convert $9 \frac{1}{2}$ to an improper fraction.

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Step 4.1

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

$\frac{13}{2} + \frac{14}{2} + \frac{15}{2} - (9 + \frac{1}{2})$

Step 4.2

Add $9$ and $\frac{1}{2}$ .

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Step 4.2.1

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

$\frac{13}{2} + \frac{14}{2} + \frac{15}{2} - (9 \cdot \frac{2}{2} + \frac{1}{2})$

Step 4.2.2

Combine $9$ and $\frac{2}{2}$ .

$\frac{13}{2} + \frac{14}{2} + \frac{15}{2} - (\frac{9 \cdot 2}{2} + \frac{1}{2})$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{13}{2} + \frac{14}{2} + \frac{15}{2} - \frac{9 \cdot 2 + 1}{2}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $9$ by $2$ .

$\frac{13}{2} + \frac{14}{2} + \frac{15}{2} - \frac{18 + 1}{2}$

Step 4.2.4.2

Add $18$ and $1$ .

$\frac{13}{2} + \frac{14}{2} + \frac{15}{2} - \frac{19}{2}$

Step 5

Combine the numerators over the common denominator.

$\frac{13 + 14 + 15 - 19}{2}$

Step 6

Simplify by adding and subtracting.

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Step 6.1

Add $13$ and $14$ .

$\frac{27 + 15 - 19}{2}$

Step 6.2

Add $27$ and $15$ .

$\frac{42 - 19}{2}$

Step 6.3

Subtract $19$ from $42$ .

$\frac{23}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{23}{2}$

Decimal Form:

$11.5$

Mixed Number Form:

$11 \frac{1}{2}$