Basic Math Examples

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

$7 \frac{1}{2} \cdot 3 \frac{1}{4}$

Step 1

Convert

7 \frac{1}{2}

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

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Step 1.1

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

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

$(7 + \frac{1}{2}) \cdot 3 \frac{1}{4}$

Step 1.2

Add

7

$7$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

7

$7$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

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

$(7 \cdot \frac{2}{2} + \frac{1}{2}) \cdot 3 \frac{1}{4}$

Step 1.2.2

Combine

7

$7$ and

\frac{2}{2}

$\frac{2}{2}$ .

(\frac{7 \cdot 2}{2} + \frac{1}{2}) \cdot 3 \frac{1}{4}

$(\frac{7 \cdot 2}{2} + \frac{1}{2}) \cdot 3 \frac{1}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{7 \cdot 2 + 1}{2} \cdot 3 \frac{1}{4}

$\frac{7 \cdot 2 + 1}{2} \cdot 3 \frac{1}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

7

$7$ by

2

$2$ .

\frac{14 + 1}{2} \cdot 3 \frac{1}{4}

$\frac{14 + 1}{2} \cdot 3 \frac{1}{4}$

Step 1.2.4.2

Add

14

$14$ and

1

$1$ .

\frac{15}{2} \cdot 3 \frac{1}{4}

$\frac{15}{2} \cdot 3 \frac{1}{4}$

\frac{15}{2} \cdot 3 \frac{1}{4}

$\frac{15}{2} \cdot 3 \frac{1}{4}$

\frac{15}{2} \cdot 3 \frac{1}{4}

$\frac{15}{2} \cdot 3 \frac{1}{4}$

\frac{15}{2} \cdot 3 \frac{1}{4}

$\frac{15}{2} \cdot 3 \frac{1}{4}$

Step 2

Convert

3 \frac{1}{4}

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

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Step 2.1

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

\frac{15}{2} \cdot (3 + \frac{1}{4})

$\frac{15}{2} \cdot (3 + \frac{1}{4})$

Step 2.2

Add

3

$3$ and

\frac{1}{4}

$\frac{1}{4}$ .

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Step 2.2.1

To write

3

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

\frac{4}{4}

$\frac{4}{4}$ .

\frac{15}{2} \cdot (3 \cdot \frac{4}{4} + \frac{1}{4})

$\frac{15}{2} \cdot (3 \cdot \frac{4}{4} + \frac{1}{4})$

Step 2.2.2

Combine

3

$3$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{15}{2} \cdot (\frac{3 \cdot 4}{4} + \frac{1}{4})

$\frac{15}{2} \cdot (\frac{3 \cdot 4}{4} + \frac{1}{4})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{15}{2} \cdot \frac{3 \cdot 4 + 1}{4}

$\frac{15}{2} \cdot \frac{3 \cdot 4 + 1}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

4

$4$ .

\frac{15}{2} \cdot \frac{12 + 1}{4}

$\frac{15}{2} \cdot \frac{12 + 1}{4}$

Step 2.2.4.2

Add

12

$12$ and

1

$1$ .

\frac{15}{2} \cdot \frac{13}{4}

$\frac{15}{2} \cdot \frac{13}{4}$

\frac{15}{2} \cdot \frac{13}{4}

$\frac{15}{2} \cdot \frac{13}{4}$

\frac{15}{2} \cdot \frac{13}{4}

$\frac{15}{2} \cdot \frac{13}{4}$

\frac{15}{2} \cdot \frac{13}{4}

$\frac{15}{2} \cdot \frac{13}{4}$

Step 3

Multiply

\frac{15}{2} \cdot \frac{13}{4}

$\frac{15}{2} \cdot \frac{13}{4}$ .

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Step 3.1

Multiply

\frac{15}{2}

$\frac{15}{2}$ by

\frac{13}{4}

$\frac{13}{4}$ .

\frac{15 \cdot 13}{2 \cdot 4}

$\frac{15 \cdot 13}{2 \cdot 4}$

Step 3.2

Multiply

15

$15$ by

13

$13$ .

\frac{195}{2 \cdot 4}

$\frac{195}{2 \cdot 4}$

Step 3.3

Multiply

2

$2$ by

4

$4$ .

\frac{195}{8}

$\frac{195}{8}$

\frac{195}{8}

$\frac{195}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{195}{8}

$\frac{195}{8}$

Decimal Form:

24.375

$24.375$

Mixed Number Form:

24 \frac{3}{8}

$24 \frac{3}{8}$