Basic Math Examples

\frac{1}{10} + \frac{1}{100} + \frac{1}{1000}

$\frac{1}{10} + \frac{1}{100} + \frac{1}{1000}$

Step 1

Find the common denominator.

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Step 1.1

Multiply

\frac{1}{10}

$\frac{1}{10}$ by

\frac{100}{100}

$\frac{100}{100}$ .

\frac{1}{10} \cdot \frac{100}{100} + \frac{1}{100} + \frac{1}{1000}

$\frac{1}{10} \cdot \frac{100}{100} + \frac{1}{100} + \frac{1}{1000}$

Step 1.2

Multiply

\frac{1}{10}

$\frac{1}{10}$ by

\frac{100}{100}

$\frac{100}{100}$ .

\frac{100}{10 \cdot 100} + \frac{1}{100} + \frac{1}{1000}

$\frac{100}{10 \cdot 100} + \frac{1}{100} + \frac{1}{1000}$

Step 1.3

Multiply

\frac{1}{100}

$\frac{1}{100}$ by

\frac{10}{10}

$\frac{10}{10}$ .

\frac{100}{10 \cdot 100} + \frac{1}{100} \cdot \frac{10}{10} + \frac{1}{1000}

$\frac{100}{10 \cdot 100} + \frac{1}{100} \cdot \frac{10}{10} + \frac{1}{1000}$

Step 1.4

Multiply

\frac{1}{100}

$\frac{1}{100}$ by

\frac{10}{10}

$\frac{10}{10}$ .

\frac{100}{10 \cdot 100} + \frac{10}{100 \cdot 10} + \frac{1}{1000}

$\frac{100}{10 \cdot 100} + \frac{10}{100 \cdot 10} + \frac{1}{1000}$

Step 1.5

Multiply

10

$10$ by

100

$100$ .

\frac{100}{1000} + \frac{10}{100 \cdot 10} + \frac{1}{1000}

$\frac{100}{1000} + \frac{10}{100 \cdot 10} + \frac{1}{1000}$

Step 1.6

Reorder the factors of

100 \cdot 10

$100 \cdot 10$ .

\frac{100}{1000} + \frac{10}{10 \cdot 100} + \frac{1}{1000}

$\frac{100}{1000} + \frac{10}{10 \cdot 100} + \frac{1}{1000}$

Step 1.7

Multiply

10

$10$ by

100

$100$ .

\frac{100}{1000} + \frac{10}{1000} + \frac{1}{1000}

$\frac{100}{1000} + \frac{10}{1000} + \frac{1}{1000}$

\frac{100}{1000} + \frac{10}{1000} + \frac{1}{1000}

$\frac{100}{1000} + \frac{10}{1000} + \frac{1}{1000}$

Step 2

Combine the numerators over the common denominator.

\frac{100 + 10 + 1}{1000}

$\frac{100 + 10 + 1}{1000}$

Step 3

Simplify by adding numbers.

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Step 3.1

Add

100

$100$ and

10

$10$ .

\frac{110 + 1}{1000}

$\frac{110 + 1}{1000}$

Step 3.2

Add

110

$110$ and

1

$1$ .

\frac{111}{1000}

$\frac{111}{1000}$

\frac{111}{1000}

$\frac{111}{1000}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{111}{1000}

$\frac{111}{1000}$

Decimal Form:

0.111

$0.111$