Pre-Algebra Examples

$\frac{1}{6} \cdot (0.1) + \frac{5}{6} \cdot (0.1)$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $0.1$ .

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Step 1.1.1

Factor $0.1$ out of $6$ .

$\frac{1}{0.1 (60)} \cdot 0.1 + \frac{5}{6} \cdot (0.1)$

Step 1.1.2

Cancel the common factor.

$\frac{1}{0.1 \cdot 60} \cdot 0.1 + \frac{5}{6} \cdot (0.1)$

Step 1.1.3

Rewrite the expression.

$\frac{1}{60} + \frac{5}{6} \cdot (0.1)$

Step 1.2

Cancel the common factor of $0.1$ .

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Step 1.2.1

Factor $0.1$ out of $6$ .

$\frac{1}{60} + \frac{5}{0.1 (60)} \cdot 0.1$

Step 1.2.2

Cancel the common factor.

$\frac{1}{60} + \frac{5}{0.1 \cdot 60} \cdot 0.1$

Step 1.2.3

Rewrite the expression.

$\frac{1}{60} + \frac{5}{60}$

Step 1.3

Cancel the common factor of $5$ and $60$ .

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Step 1.3.1

Factor $5$ out of $5$ .

$\frac{1}{60} + \frac{5 (1)}{60}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $5$ out of $60$ .

$\frac{1}{60} + \frac{5 \cdot 1}{5 \cdot 12}$

Step 1.3.2.2

Cancel the common factor.

$\frac{1}{60} + \frac{5 \cdot 1}{5 \cdot 12}$

Step 1.3.2.3

Rewrite the expression.

$\frac{1}{60} + \frac{1}{12}$

Step 2

To write $\frac{1}{12}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{60} + \frac{1}{12} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{12}$ by $\frac{5}{5}$ .

$\frac{1}{60} + \frac{5}{12 \cdot 5}$

Step 3.2

Multiply $12$ by $5$ .

$\frac{1}{60} + \frac{5}{60}$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{1 + 5}{60}$

Step 4.2

Add $1$ and $5$ .

$\frac{6}{60}$

Step 5

Cancel the common factor of $6$ and $60$ .

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Step 5.1

Factor $6$ out of $6$ .

$\frac{6 (1)}{60}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $6$ out of $60$ .

$\frac{6 \cdot 1}{6 \cdot 10}$

Step 5.2.2

Cancel the common factor.

$\frac{6 \cdot 1}{6 \cdot 10}$

Step 5.2.3

Rewrite the expression.

$\frac{1}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{10}$

Decimal Form:

$0.1$