Basic Math Examples

(1 \cdot 10) + (3 \cdot 1) + (9 \cdot \frac{1}{100})

$(1 \cdot 10) + (3 \cdot 1) + (9 \cdot \frac{1}{100})$

Step 1

Remove parentheses.

1 \cdot 10 + 3 \cdot 1 + 9 \cdot \frac{1}{100}

$1 \cdot 10 + 3 \cdot 1 + 9 \cdot \frac{1}{100}$

Step 2

Simplify each term.

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Step 2.1

Multiply

10

$10$ by

1

$1$ .

10 + 3 \cdot 1 + 9 \cdot \frac{1}{100}

$10 + 3 \cdot 1 + 9 \cdot \frac{1}{100}$

Step 2.2

Multiply

3

$3$ by

1

$1$ .

10 + 3 + 9 \cdot \frac{1}{100}

$10 + 3 + 9 \cdot \frac{1}{100}$

Step 2.3

Combine

9

$9$ and

\frac{1}{100}

$\frac{1}{100}$ .

10 + 3 + \frac{9}{100}

$10 + 3 + \frac{9}{100}$

10 + 3 + \frac{9}{100}

$10 + 3 + \frac{9}{100}$

Step 3

Find the common denominator.

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Step 3.1

Write

10

$10$ as a fraction with denominator

1

$1$ .

\frac{10}{1} + 3 + \frac{9}{100}

$\frac{10}{1} + 3 + \frac{9}{100}$

Step 3.2

Multiply

\frac{10}{1}

$\frac{10}{1}$ by

\frac{100}{100}

$\frac{100}{100}$ .

\frac{10}{1} \cdot \frac{100}{100} + 3 + \frac{9}{100}

$\frac{10}{1} \cdot \frac{100}{100} + 3 + \frac{9}{100}$

Step 3.3

Multiply

\frac{10}{1}

$\frac{10}{1}$ by

\frac{100}{100}

$\frac{100}{100}$ .

\frac{10 \cdot 100}{100} + 3 + \frac{9}{100}

$\frac{10 \cdot 100}{100} + 3 + \frac{9}{100}$

Step 3.4

Write

3

$3$ as a fraction with denominator

1

$1$ .

\frac{10 \cdot 100}{100} + \frac{3}{1} + \frac{9}{100}

$\frac{10 \cdot 100}{100} + \frac{3}{1} + \frac{9}{100}$

Step 3.5

Multiply

\frac{3}{1}

$\frac{3}{1}$ by

\frac{100}{100}

$\frac{100}{100}$ .

\frac{10 \cdot 100}{100} + \frac{3}{1} \cdot \frac{100}{100} + \frac{9}{100}

$\frac{10 \cdot 100}{100} + \frac{3}{1} \cdot \frac{100}{100} + \frac{9}{100}$

Step 3.6

Multiply

\frac{3}{1}

$\frac{3}{1}$ by

\frac{100}{100}

$\frac{100}{100}$ .

\frac{10 \cdot 100}{100} + \frac{3 \cdot 100}{100} + \frac{9}{100}

$\frac{10 \cdot 100}{100} + \frac{3 \cdot 100}{100} + \frac{9}{100}$

\frac{10 \cdot 100}{100} + \frac{3 \cdot 100}{100} + \frac{9}{100}

$\frac{10 \cdot 100}{100} + \frac{3 \cdot 100}{100} + \frac{9}{100}$

Step 4

Combine the numerators over the common denominator.

\frac{10 \cdot 100 + 3 \cdot 100 + 9}{100}

$\frac{10 \cdot 100 + 3 \cdot 100 + 9}{100}$

Step 5

Simplify each term.

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Step 5.1

Multiply

10

$10$ by

100

$100$ .

\frac{1000 + 3 \cdot 100 + 9}{100}

$\frac{1000 + 3 \cdot 100 + 9}{100}$

Step 5.2

Multiply

3

$3$ by

100

$100$ .

\frac{1000 + 300 + 9}{100}

$\frac{1000 + 300 + 9}{100}$

\frac{1000 + 300 + 9}{100}

$\frac{1000 + 300 + 9}{100}$

Step 6

Simplify by adding numbers.

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Step 6.1

Add

1000

$1000$ and

300

$300$ .

\frac{1300 + 9}{100}

$\frac{1300 + 9}{100}$

Step 6.2

Add

1300

$1300$ and

9

$9$ .

\frac{1309}{100}

$\frac{1309}{100}$

\frac{1309}{100}

$\frac{1309}{100}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{1309}{100}

$\frac{1309}{100}$

Decimal Form:

13.09

$13.09$

Mixed Number Form:

13 \frac{9}{100}

$13 \frac{9}{100}$