Basic Math Examples

$12 \frac{1}{2} \cdot 4 \frac{4}{5} \cdot 3 \frac{1}{3}$

Step 1

Convert $12 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$(12 + \frac{1}{2}) \cdot 4 \frac{4}{5} \cdot 3 \frac{1}{3}$

Step 1.2

Add $12$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $12$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(12 \cdot \frac{2}{2} + \frac{1}{2}) \cdot 4 \frac{4}{5} \cdot 3 \frac{1}{3}$

Step 1.2.2

Combine $12$ and $\frac{2}{2}$ .

$(\frac{12 \cdot 2}{2} + \frac{1}{2}) \cdot 4 \frac{4}{5} \cdot 3 \frac{1}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{12 \cdot 2 + 1}{2} \cdot 4 \frac{4}{5} \cdot 3 \frac{1}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $12$ by $2$ .

$\frac{24 + 1}{2} \cdot 4 \frac{4}{5} \cdot 3 \frac{1}{3}$

Step 1.2.4.2

Add $24$ and $1$ .

$\frac{25}{2} \cdot 4 \frac{4}{5} \cdot 3 \frac{1}{3}$

Step 2

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

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Step 2.1

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

$\frac{25}{2} \cdot (4 + \frac{4}{5}) \cdot 3 \frac{1}{3}$

Step 2.2

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

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Step 2.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{25}{2} \cdot (4 \cdot \frac{5}{5} + \frac{4}{5}) \cdot 3 \frac{1}{3}$

Step 2.2.2

Combine $4$ and $\frac{5}{5}$ .

$\frac{25}{2} \cdot (\frac{4 \cdot 5}{5} + \frac{4}{5}) \cdot 3 \frac{1}{3}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{25}{2} \cdot \frac{4 \cdot 5 + 4}{5} \cdot 3 \frac{1}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $5$ .

$\frac{25}{2} \cdot \frac{20 + 4}{5} \cdot 3 \frac{1}{3}$

Step 2.2.4.2

Add $20$ and $4$ .

$\frac{25}{2} \cdot \frac{24}{5} \cdot 3 \frac{1}{3}$

Step 3

Convert $3 \frac{1}{3}$ to an improper fraction.

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Step 3.1

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

$\frac{25}{2} \cdot \frac{24}{5} \cdot (3 + \frac{1}{3})$

Step 3.2

Add $3$ and $\frac{1}{3}$ .

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Step 3.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{25}{2} \cdot \frac{24}{5} \cdot (3 \cdot \frac{3}{3} + \frac{1}{3})$

Step 3.2.2

Combine $3$ and $\frac{3}{3}$ .

$\frac{25}{2} \cdot \frac{24}{5} \cdot (\frac{3 \cdot 3}{3} + \frac{1}{3})$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{25}{2} \cdot \frac{24}{5} \cdot \frac{3 \cdot 3 + 1}{3}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $3$ by $3$ .

$\frac{25}{2} \cdot \frac{24}{5} \cdot \frac{9 + 1}{3}$

Step 3.2.4.2

Add $9$ and $1$ .

$\frac{25}{2} \cdot \frac{24}{5} \cdot \frac{10}{3}$

Step 4

Cancel the common factor of $5$ .

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Step 4.1

Factor $5$ out of $25$ .

$\frac{5 (5)}{2} \cdot \frac{24}{5} \cdot \frac{10}{3}$

Step 4.2

Cancel the common factor.

$\frac{5 \cdot 5}{2} \cdot \frac{24}{5} \cdot \frac{10}{3}$

Step 4.3

Rewrite the expression.

$\frac{5}{2} \cdot 24 \cdot \frac{10}{3}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $24$ .

$\frac{5}{2} \cdot (2 (12)) \cdot \frac{10}{3}$

Step 5.2

Cancel the common factor.

$\frac{5}{2} \cdot (2 \cdot 12) \cdot \frac{10}{3}$

Step 5.3

Rewrite the expression.

$5 \cdot 12 \cdot \frac{10}{3}$

Step 6

Multiply $5$ by $12$ .

$60 \cdot \frac{10}{3}$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Factor $3$ out of $60$ .

$3 (20) \cdot \frac{10}{3}$

Step 7.2

Cancel the common factor.

$3 \cdot 20 \cdot \frac{10}{3}$

Step 7.3

Rewrite the expression.

$20 \cdot 10$

Step 8

Multiply $20$ by $10$ .

$200$