Basic Math Examples

2 \frac{1}{10} \cdot 1 \frac{2}{7}

$2 \frac{1}{10} \cdot 1 \frac{2}{7}$

Step 1

Convert

2 \frac{1}{10}

$2 \frac{1}{10}$ 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{1}{10}) \cdot 1 \frac{2}{7}

$(2 + \frac{1}{10}) \cdot 1 \frac{2}{7}$

Step 1.2

Add

2

$2$ and

\frac{1}{10}

$\frac{1}{10}$ .

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Step 1.2.1

To write

2

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

\frac{10}{10}

$\frac{10}{10}$ .

(2 \cdot \frac{10}{10} + \frac{1}{10}) \cdot 1 \frac{2}{7}

$(2 \cdot \frac{10}{10} + \frac{1}{10}) \cdot 1 \frac{2}{7}$

Step 1.2.2

Combine

2

$2$ and

\frac{10}{10}

$\frac{10}{10}$ .

(\frac{2 \cdot 10}{10} + \frac{1}{10}) \cdot 1 \frac{2}{7}

$(\frac{2 \cdot 10}{10} + \frac{1}{10}) \cdot 1 \frac{2}{7}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 10 + 1}{10} \cdot 1 \frac{2}{7}

$\frac{2 \cdot 10 + 1}{10} \cdot 1 \frac{2}{7}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

10

$10$ .

\frac{20 + 1}{10} \cdot 1 \frac{2}{7}

$\frac{20 + 1}{10} \cdot 1 \frac{2}{7}$

Step 1.2.4.2

Add

20

$20$ and

1

$1$ .

\frac{21}{10} \cdot 1 \frac{2}{7}

$\frac{21}{10} \cdot 1 \frac{2}{7}$

\frac{21}{10} \cdot 1 \frac{2}{7}

$\frac{21}{10} \cdot 1 \frac{2}{7}$

\frac{21}{10} \cdot 1 \frac{2}{7}

$\frac{21}{10} \cdot 1 \frac{2}{7}$

\frac{21}{10} \cdot 1 \frac{2}{7}

$\frac{21}{10} \cdot 1 \frac{2}{7}$

Step 2

Convert

1 \frac{2}{7}

$1 \frac{2}{7}$ to an improper fraction.

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Step 2.1

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

\frac{21}{10} \cdot (1 + \frac{2}{7})

$\frac{21}{10} \cdot (1 + \frac{2}{7})$

Step 2.2

Add

1

$1$ and

\frac{2}{7}

$\frac{2}{7}$ .

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Step 2.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{21}{10} \cdot (\frac{7}{7} + \frac{2}{7})

$\frac{21}{10} \cdot (\frac{7}{7} + \frac{2}{7})$

Step 2.2.2

Combine the numerators over the common denominator.

\frac{21}{10} \cdot \frac{7 + 2}{7}

$\frac{21}{10} \cdot \frac{7 + 2}{7}$

Step 2.2.3

Add

7

$7$ and

2

$2$ .

\frac{21}{10} \cdot \frac{9}{7}

$\frac{21}{10} \cdot \frac{9}{7}$

\frac{21}{10} \cdot \frac{9}{7}

$\frac{21}{10} \cdot \frac{9}{7}$

\frac{21}{10} \cdot \frac{9}{7}

$\frac{21}{10} \cdot \frac{9}{7}$

Step 3

Cancel the common factor of

7

$7$ .

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Step 3.1

Factor

7

$7$ out of

21

$21$ .

\frac{7 (3)}{10} \cdot \frac{9}{7}

$\frac{7 (3)}{10} \cdot \frac{9}{7}$

Step 3.2

Cancel the common factor.

$\frac{7 \cdot 3}{10} \cdot \frac{9}{7}$

Step 3.3

Rewrite the expression.

$\frac{3}{10} \cdot 9$

Step 4

Combine

$\frac{3}{10}$ and

$9$ .

$\frac{3 \cdot 9}{10}$

Step 5

Multiply

$3$ by

$9$ .

$\frac{27}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{10}$

Decimal Form:

$2.7$

Mixed Number Form:

$2 \frac{7}{10}$