Basic Math Examples

$(23 \frac{1}{4}) (12 \frac{2}{9})$

Step 1

Convert $23 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

$(23 + \frac{1}{4}) (12 \frac{2}{9})$

Step 1.2

Add $23$ and $\frac{1}{4}$ .

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Step 1.2.1

To write $23$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(23 \cdot \frac{4}{4} + \frac{1}{4}) (12 \frac{2}{9})$

Step 1.2.2

Combine $23$ and $\frac{4}{4}$ .

$(\frac{23 \cdot 4}{4} + \frac{1}{4}) (12 \frac{2}{9})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{23 \cdot 4 + 1}{4} (12 \frac{2}{9})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $23$ by $4$ .

$\frac{92 + 1}{4} (12 \frac{2}{9})$

Step 1.2.4.2

Add $92$ and $1$ .

$\frac{93}{4} (12 \frac{2}{9})$

Step 2

Convert $12 \frac{2}{9}$ to an improper fraction.

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Step 2.1

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

$\frac{93}{4} (12 + \frac{2}{9})$

Step 2.2

Add $12$ and $\frac{2}{9}$ .

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Step 2.2.1

To write $12$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{93}{4} (12 \cdot \frac{9}{9} + \frac{2}{9})$

Step 2.2.2

Combine $12$ and $\frac{9}{9}$ .

$\frac{93}{4} (\frac{12 \cdot 9}{9} + \frac{2}{9})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{93}{4} \cdot \frac{12 \cdot 9 + 2}{9}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $12$ by $9$ .

$\frac{93}{4} \cdot \frac{108 + 2}{9}$

Step 2.2.4.2

Add $108$ and $2$ .

$\frac{93}{4} \cdot \frac{110}{9}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Factor $3$ out of $93$ .

$\frac{3 (31)}{4} \cdot \frac{110}{9}$

Step 3.2

Factor $3$ out of $9$ .

$\frac{3 \cdot 31}{4} \cdot \frac{110}{3 \cdot 3}$

Step 3.3

Cancel the common factor.

$\frac{3 \cdot 31}{4} \cdot \frac{110}{3 \cdot 3}$

Step 3.4

Rewrite the expression.

$\frac{31}{4} \cdot \frac{110}{3}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $4$ .

$\frac{31}{2 (2)} \cdot \frac{110}{3}$

Step 4.2

Factor $2$ out of $110$ .

$\frac{31}{2 \cdot 2} \cdot \frac{2 \cdot 55}{3}$

Step 4.3

Cancel the common factor.

$\frac{31}{2 \cdot 2} \cdot \frac{2 \cdot 55}{3}$

Step 4.4

Rewrite the expression.

$\frac{31}{2} \cdot \frac{55}{3}$

Step 5

Multiply $\frac{31}{2}$ by $\frac{55}{3}$ .

$\frac{31 \cdot 55}{2 \cdot 3}$

Step 6

Multiply.

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Step 6.1

Multiply $31$ by $55$ .

$\frac{1705}{2 \cdot 3}$

Step 6.2

Multiply $2$ by $3$ .

$\frac{1705}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1705}{6}$

Decimal Form:

$284.1\overline{6}$

Mixed Number Form:

$284 \frac{1}{6}$