Basic Math Examples

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

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

Step 1

Convert

3 \frac{1}{4}

$3 \frac{1}{4}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

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

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

Step 1.2

Add

3

$3$ and

\frac{1}{4}

$\frac{1}{4}$ .

Tap for more steps...

Step 1.2.1

To write

3

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

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.2

Combine

3

$3$ and

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply

3

$3$ by

4

$4$ .

\frac{12 + 1}{4} \cdot 2 \frac{2}{3}

$\frac{12 + 1}{4} \cdot 2 \frac{2}{3}$

Step 1.2.4.2

Add

12

$12$ and

1

$1$ .

\frac{13}{4} \cdot 2 \frac{2}{3}

$\frac{13}{4} \cdot 2 \frac{2}{3}$

\frac{13}{4} \cdot 2 \frac{2}{3}

$\frac{13}{4} \cdot 2 \frac{2}{3}$

\frac{13}{4} \cdot 2 \frac{2}{3}

$\frac{13}{4} \cdot 2 \frac{2}{3}$

\frac{13}{4} \cdot 2 \frac{2}{3}

$\frac{13}{4} \cdot 2 \frac{2}{3}$

Step 2

Convert

2 \frac{2}{3}

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

Tap for more steps...

Step 2.1

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

\frac{13}{4} \cdot (2 + \frac{2}{3})

$\frac{13}{4} \cdot (2 + \frac{2}{3})$

Step 2.2

Add

2

$2$ and

\frac{2}{3}

$\frac{2}{3}$ .

Tap for more steps...

Step 2.2.1

To write

2

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

\frac{3}{3}

$\frac{3}{3}$ .

\frac{13}{4} \cdot (2 \cdot \frac{3}{3} + \frac{2}{3})

$\frac{13}{4} \cdot (2 \cdot \frac{3}{3} + \frac{2}{3})$

Step 2.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{13}{4} \cdot (\frac{2 \cdot 3}{3} + \frac{2}{3})

$\frac{13}{4} \cdot (\frac{2 \cdot 3}{3} + \frac{2}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{13}{4} \cdot \frac{2 \cdot 3 + 2}{3}

$\frac{13}{4} \cdot \frac{2 \cdot 3 + 2}{3}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply

2

$2$ by

3

$3$ .

\frac{13}{4} \cdot \frac{6 + 2}{3}

$\frac{13}{4} \cdot \frac{6 + 2}{3}$

Step 2.2.4.2

Add

6

$6$ and

2

$2$ .

\frac{13}{4} \cdot \frac{8}{3}

$\frac{13}{4} \cdot \frac{8}{3}$

\frac{13}{4} \cdot \frac{8}{3}

$\frac{13}{4} \cdot \frac{8}{3}$

\frac{13}{4} \cdot \frac{8}{3}

$\frac{13}{4} \cdot \frac{8}{3}$

\frac{13}{4} \cdot \frac{8}{3}

$\frac{13}{4} \cdot \frac{8}{3}$

Step 3

Cancel the common factor of

4

$4$ .

Tap for more steps...

Step 3.1

Factor

4

$4$ out of

8

$8$ .

\frac{13}{4} \cdot \frac{4 (2)}{3}

$\frac{13}{4} \cdot \frac{4 (2)}{3}$

Step 3.2

Cancel the common factor.

$\frac{13}{4} \cdot \frac{4 \cdot 2}{3}$

Step 3.3

Rewrite the expression.

$13 \cdot \frac{2}{3}$

Step 4

Combine

$13$ and

$\frac{2}{3}$ .

$\frac{13 \cdot 2}{3}$

Step 5

Multiply

$13$ by

$2$ .

$\frac{26}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{26}{3}$

Decimal Form:

$8.\overline{6}$

Mixed Number Form:

$8 \frac{2}{3}$