Basic Math Examples

$10 \frac{5}{12} \cdot 1 \frac{3}{5}$

Step 1

Convert

$10 \frac{5}{12}$ to an improper fraction.

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Step 1.1

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

$(10 + \frac{5}{12}) \cdot 1 \frac{3}{5}$

Step 1.2

Add

$10$ and

$\frac{5}{12}$ .

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Step 1.2.1

To write

$10$ as a fraction with a common denominator, multiply by

$\frac{12}{12}$ .

$(10 \cdot \frac{12}{12} + \frac{5}{12}) \cdot 1 \frac{3}{5}$

Step 1.2.2

Combine

$10$ and

$\frac{12}{12}$ .

$(\frac{10 \cdot 12}{12} + \frac{5}{12}) \cdot 1 \frac{3}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{10 \cdot 12 + 5}{12} \cdot 1 \frac{3}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$10$ by

$12$ .

$\frac{120 + 5}{12} \cdot 1 \frac{3}{5}$

Step 1.2.4.2

Add

$120$ and

$5$ .

$\frac{125}{12} \cdot 1 \frac{3}{5}$

Step 2

Convert

$1 \frac{3}{5}$ to an improper fraction.

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Step 2.1

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

$\frac{125}{12} \cdot (1 + \frac{3}{5})$

Step 2.2

Add

$1$ and

$\frac{3}{5}$ .

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Step 2.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{125}{12} \cdot (\frac{5}{5} + \frac{3}{5})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{125}{12} \cdot \frac{5 + 3}{5}$

Step 2.2.3

Add

$5$ and

$3$ .

$\frac{125}{12} \cdot \frac{8}{5}$

Step 3

Cancel the common factor of

$5$ .

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Step 3.1

Factor

$5$ out of

$125$ .

$\frac{5 (25)}{12} \cdot \frac{8}{5}$

Step 3.2

Cancel the common factor.

$\frac{5 \cdot 25}{12} \cdot \frac{8}{5}$

Step 3.3

Rewrite the expression.

$\frac{25}{12} \cdot 8$

Step 4

Cancel the common factor of

$4$ .

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Step 4.1

Factor

$4$ out of

$12$ .

$\frac{25}{4 (3)} \cdot 8$

Step 4.2

Factor

$4$ out of

$8$ .

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

Step 4.3

Cancel the common factor.

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

Step 4.4

Rewrite the expression.

$\frac{25}{3} \cdot 2$

Step 5

Combine

$\frac{25}{3}$ and

$2$ .

$\frac{25 \cdot 2}{3}$

Step 6

Multiply

$25$ by

$2$ .

$\frac{50}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{50}{3}$

Decimal Form:

$16.\overline{6}$

Mixed Number Form:

$16 \frac{2}{3}$