Basic Math Examples

- 2 \frac{7}{6} \cdot 2 \frac{1}{3}

$- 2 \frac{7}{6} \cdot 2 \frac{1}{3}$

Step 1

Convert

2 \frac{7}{6}

$2 \frac{7}{6}$ 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{7}{6}) \cdot 2 \frac{1}{3}

$- (2 + \frac{7}{6}) \cdot 2 \frac{1}{3}$

Step 1.2

Add

2

$2$ and

\frac{7}{6}

$\frac{7}{6}$ .

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Step 1.2.1

To write

2

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

\frac{6}{6}

$\frac{6}{6}$ .

- (2 \cdot \frac{6}{6} + \frac{7}{6}) \cdot 2 \frac{1}{3}

$- (2 \cdot \frac{6}{6} + \frac{7}{6}) \cdot 2 \frac{1}{3}$

Step 1.2.2

Combine

2

$2$ and

\frac{6}{6}

$\frac{6}{6}$ .

- (\frac{2 \cdot 6}{6} + \frac{7}{6}) \cdot 2 \frac{1}{3}

$- (\frac{2 \cdot 6}{6} + \frac{7}{6}) \cdot 2 \frac{1}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

- \frac{2 \cdot 6 + 7}{6} \cdot 2 \frac{1}{3}

$- \frac{2 \cdot 6 + 7}{6} \cdot 2 \frac{1}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

6

$6$ .

- \frac{12 + 7}{6} \cdot 2 \frac{1}{3}

$- \frac{12 + 7}{6} \cdot 2 \frac{1}{3}$

Step 1.2.4.2

Add

12

$12$ and

7

$7$ .

- \frac{19}{6} \cdot 2 \frac{1}{3}

$- \frac{19}{6} \cdot 2 \frac{1}{3}$

- \frac{19}{6} \cdot 2 \frac{1}{3}

$- \frac{19}{6} \cdot 2 \frac{1}{3}$

- \frac{19}{6} \cdot 2 \frac{1}{3}

$- \frac{19}{6} \cdot 2 \frac{1}{3}$

- \frac{19}{6} \cdot 2 \frac{1}{3}

$- \frac{19}{6} \cdot 2 \frac{1}{3}$

Step 2

Convert

2 \frac{1}{3}

$2 \frac{1}{3}$ to an improper fraction.

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Step 2.1

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

- \frac{19}{6} \cdot (2 + \frac{1}{3})

$- \frac{19}{6} \cdot (2 + \frac{1}{3})$

Step 2.2

Add

2

$2$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 2.2.1

To write

2

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

\frac{3}{3}

$\frac{3}{3}$ .

- \frac{19}{6} \cdot (2 \cdot \frac{3}{3} + \frac{1}{3})

$- \frac{19}{6} \cdot (2 \cdot \frac{3}{3} + \frac{1}{3})$

Step 2.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

- \frac{19}{6} \cdot (\frac{2 \cdot 3}{3} + \frac{1}{3})

$- \frac{19}{6} \cdot (\frac{2 \cdot 3}{3} + \frac{1}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

- \frac{19}{6} \cdot \frac{2 \cdot 3 + 1}{3}

$- \frac{19}{6} \cdot \frac{2 \cdot 3 + 1}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

3

$3$ .

- \frac{19}{6} \cdot \frac{6 + 1}{3}

$- \frac{19}{6} \cdot \frac{6 + 1}{3}$

Step 2.2.4.2

Add

6

$6$ and

1

$1$ .

- \frac{19}{6} \cdot \frac{7}{3}

$- \frac{19}{6} \cdot \frac{7}{3}$

- \frac{19}{6} \cdot \frac{7}{3}

$- \frac{19}{6} \cdot \frac{7}{3}$

- \frac{19}{6} \cdot \frac{7}{3}

$- \frac{19}{6} \cdot \frac{7}{3}$

- \frac{19}{6} \cdot \frac{7}{3}

$- \frac{19}{6} \cdot \frac{7}{3}$

Step 3

Multiply

- \frac{19}{6} \cdot \frac{7}{3}

$- \frac{19}{6} \cdot \frac{7}{3}$ .

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Step 3.1

Multiply

\frac{7}{3}

$\frac{7}{3}$ by

\frac{19}{6}

$\frac{19}{6}$ .

- \frac{7 \cdot 19}{3 \cdot 6}

$- \frac{7 \cdot 19}{3 \cdot 6}$

Step 3.2

Multiply

7

$7$ by

19

$19$ .

- \frac{133}{3 \cdot 6}

$- \frac{133}{3 \cdot 6}$

Step 3.3

Multiply

3

$3$ by

6

$6$ .

- \frac{133}{18}

$- \frac{133}{18}$

- \frac{133}{18}

$- \frac{133}{18}$

Step 4

The result can be shown in multiple forms.

Exact Form:

- \frac{133}{18}

$- \frac{133}{18}$

Decimal Form:

- 7.3 ¯ 8

$- 7.3\overline{8}$

Mixed Number Form:

- 7 \frac{7}{18}

$- 7 \frac{7}{18}$