Basic Math Examples

$2 \frac{4}{5} \cdot 3 \frac{2}{7}$

Step 1

Convert

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

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Step 1.1

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

$(2 + \frac{4}{5}) \cdot 3 \frac{2}{7}$

Step 1.2

Add

$2$ and

$\frac{4}{5}$ .

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Step 1.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$(2 \cdot \frac{5}{5} + \frac{4}{5}) \cdot 3 \frac{2}{7}$

Step 1.2.2

Combine

$2$ and

$\frac{5}{5}$ .

$(\frac{2 \cdot 5}{5} + \frac{4}{5}) \cdot 3 \frac{2}{7}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 5 + 4}{5} \cdot 3 \frac{2}{7}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$5$ .

$\frac{10 + 4}{5} \cdot 3 \frac{2}{7}$

Step 1.2.4.2

Add

$10$ and

$4$ .

$\frac{14}{5} \cdot 3 \frac{2}{7}$

Step 2

Convert

$3 \frac{2}{7}$ to an improper fraction.

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Step 2.1

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

$\frac{14}{5} \cdot (3 + \frac{2}{7})$

Step 2.2

Add

$3$ and

$\frac{2}{7}$ .

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Step 2.2.1

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{7}{7}$ .

$\frac{14}{5} \cdot (3 \cdot \frac{7}{7} + \frac{2}{7})$

Step 2.2.2

Combine

$3$ and

$\frac{7}{7}$ .

$\frac{14}{5} \cdot (\frac{3 \cdot 7}{7} + \frac{2}{7})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{14}{5} \cdot \frac{3 \cdot 7 + 2}{7}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$3$ by

$7$ .

$\frac{14}{5} \cdot \frac{21 + 2}{7}$

Step 2.2.4.2

Add

$21$ and

$2$ .

$\frac{14}{5} \cdot \frac{23}{7}$

Step 3

Cancel the common factor of

$7$ .

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Step 3.1

Factor

$7$ out of

$14$ .

$\frac{7 (2)}{5} \cdot \frac{23}{7}$

Step 3.2

Cancel the common factor.

$\frac{7 \cdot 2}{5} \cdot \frac{23}{7}$

Step 3.3

Rewrite the expression.

$\frac{2}{5} \cdot 23$

Step 4

Combine

$\frac{2}{5}$ and

$23$ .

$\frac{2 \cdot 23}{5}$

Step 5

Multiply

$2$ by

$23$ .

$\frac{46}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{46}{5}$

Decimal Form:

$9.2$

Mixed Number Form:

$9 \frac{1}{5}$