Basic Math Examples

1 \frac{1}{3} \cdot 2 \frac{3}{4}

$1 \frac{1}{3} \cdot 2 \frac{3}{4}$

Step 1

Convert

1 \frac{1}{3}

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

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Step 1.1

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

(1 + \frac{1}{3}) \cdot 2 \frac{3}{4}

$(1 + \frac{1}{3}) \cdot 2 \frac{3}{4}$

Step 1.2

Add

1

$1$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

(\frac{3}{3} + \frac{1}{3}) \cdot 2 \frac{3}{4}

$(\frac{3}{3} + \frac{1}{3}) \cdot 2 \frac{3}{4}$

Step 1.2.2

Combine the numerators over the common denominator.

\frac{3 + 1}{3} \cdot 2 \frac{3}{4}

$\frac{3 + 1}{3} \cdot 2 \frac{3}{4}$

Step 1.2.3

Add

3

$3$ and

1

$1$ .

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

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

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

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

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

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

Step 2

Convert

2 \frac{3}{4}

$2 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

\frac{4}{3} \cdot (2 + \frac{3}{4})

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

Step 2.2

Add

2

$2$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 2.2.1

To write

2

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

\frac{4}{4}

$\frac{4}{4}$ .

\frac{4}{3} \cdot (2 \cdot \frac{4}{4} + \frac{3}{4})

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

Step 2.2.2

Combine

2

$2$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{4}{3} \cdot (\frac{2 \cdot 4}{4} + \frac{3}{4})

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

Step 2.2.3

Combine the numerators over the common denominator.

\frac{4}{3} \cdot \frac{2 \cdot 4 + 3}{4}

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

4

$4$ .

\frac{4}{3} \cdot \frac{8 + 3}{4}

$\frac{4}{3} \cdot \frac{8 + 3}{4}$

Step 2.2.4.2

Add

8

$8$ and

3

$3$ .

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

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

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

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

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

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

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

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

Step 3

Cancel the common factor of

4

$4$ .

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Step 3.1

Cancel the common factor.

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

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

Step 3.2

Rewrite the expression.

\frac{1}{3} \cdot 11

$\frac{1}{3} \cdot 11$

\frac{1}{3} \cdot 11

$\frac{1}{3} \cdot 11$

Step 4

Combine

\frac{1}{3}

$\frac{1}{3}$ and

11

$11$ .

\frac{11}{3}

$\frac{11}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

\frac{11}{3}

$\frac{11}{3}$

Decimal Form:

3.\overline{6}

$3.\overline{6}$

Mixed Number Form:

3 \frac{2}{3}

$3 \frac{2}{3}$