Basic Math Examples

\frac{9}{12} \cdot 5 \frac{5}{10}

$\frac{9}{12} \cdot 5 \frac{5}{10}$

Step 1

Convert

5 \frac{5}{10}

$5 \frac{5}{10}$ to an improper fraction.

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Step 1.1

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

\frac{9}{12} \cdot (5 + \frac{5}{10})

$\frac{9}{12} \cdot (5 + \frac{5}{10})$

Step 1.2

Add

5

$5$ and

\frac{5}{10}

$\frac{5}{10}$ .

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Step 1.2.1

To write

5

$5$ as a fraction with a common denominator, multiply by

\frac{10}{10}

$\frac{10}{10}$ .

\frac{9}{12} \cdot (5 \cdot \frac{10}{10} + \frac{5}{10})

$\frac{9}{12} \cdot (5 \cdot \frac{10}{10} + \frac{5}{10})$

Step 1.2.2

Combine

5

$5$ and

\frac{10}{10}

$\frac{10}{10}$ .

\frac{9}{12} \cdot (\frac{5 \cdot 10}{10} + \frac{5}{10})

$\frac{9}{12} \cdot (\frac{5 \cdot 10}{10} + \frac{5}{10})$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{9}{12} \cdot \frac{5 \cdot 10 + 5}{10}

$\frac{9}{12} \cdot \frac{5 \cdot 10 + 5}{10}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

5

$5$ by

10

$10$ .

\frac{9}{12} \cdot \frac{50 + 5}{10}

$\frac{9}{12} \cdot \frac{50 + 5}{10}$

Step 1.2.4.2

Add

50

$50$ and

5

$5$ .

\frac{9}{12} \cdot \frac{55}{10}

$\frac{9}{12} \cdot \frac{55}{10}$

\frac{9}{12} \cdot \frac{55}{10}

$\frac{9}{12} \cdot \frac{55}{10}$

\frac{9}{12} \cdot \frac{55}{10}

$\frac{9}{12} \cdot \frac{55}{10}$

\frac{9}{12} \cdot \frac{55}{10}

$\frac{9}{12} \cdot \frac{55}{10}$

Step 2

Cancel the common factor of

9

$9$ and

12

$12$ .

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Step 2.1

Factor

3

$3$ out of

9

$9$ .

\frac{3 (3)}{12} \cdot \frac{55}{10}

$\frac{3 (3)}{12} \cdot \frac{55}{10}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor

3

$3$ out of

12

$12$ .

\frac{3 \cdot 3}{3 \cdot 4} \cdot \frac{55}{10}

$\frac{3 \cdot 3}{3 \cdot 4} \cdot \frac{55}{10}$

Step 2.2.2

Cancel the common factor.

$\frac{3 \cdot 3}{3 \cdot 4} \cdot \frac{55}{10}$

Step 2.2.3

Rewrite the expression.

$\frac{3}{4} \cdot \frac{55}{10}$

Step 3

Cancel the common factor of

$55$ and

$10$ .

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Step 3.1

Factor

$5$ out of

$55$ .

$\frac{3}{4} \cdot \frac{5 (11)}{10}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

$5$ out of

$10$ .

$\frac{3}{4} \cdot \frac{5 \cdot 11}{5 \cdot 2}$

Step 3.2.2

Cancel the common factor.

$\frac{3}{4} \cdot \frac{5 \cdot 11}{5 \cdot 2}$

Step 3.2.3

Rewrite the expression.

$\frac{3}{4} \cdot \frac{11}{2}$

Step 4

Multiply

$\frac{3}{4} \cdot \frac{11}{2}$ .

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Step 4.1

Multiply

$\frac{3}{4}$ by

$\frac{11}{2}$ .

$\frac{3 \cdot 11}{4 \cdot 2}$

Step 4.2

Multiply

$3$ by

$11$ .

$\frac{33}{4 \cdot 2}$

Step 4.3

Multiply

$4$ by

$2$ .

$\frac{33}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{33}{8}$

Decimal Form:

$4.125$

Mixed Number Form:

$4 \frac{1}{8}$