Pre-Algebra Examples

$\frac{1 + \frac{36}{49}}{1 - \frac{6}{7}}$

Step 1

Multiply the numerator and denominator of the fraction by $49$ .

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Step 1.1

Multiply $\frac{1 + \frac{36}{49}}{1 - \frac{6}{7}}$ by $\frac{49}{49}$ .

$\frac{49}{49} \cdot \frac{1 + \frac{36}{49}}{1 - \frac{6}{7}}$

Step 1.2

Combine.

$\frac{49 (1 + \frac{36}{49})}{49 (1 - \frac{6}{7})}$

Step 2

Apply the distributive property.

$\frac{49 \cdot 1 + 49 (\frac{36}{49})}{49 \cdot 1 + 49 (- \frac{6}{7})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $49$ .

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Step 3.1.1

Cancel the common factor.

$\frac{49 \cdot 1 + 49 (\frac{36}{49})}{49 \cdot 1 + 49 (- \frac{6}{7})}$

Step 3.1.2

Rewrite the expression.

$\frac{49 \cdot 1 + 36}{49 \cdot 1 + 49 (- \frac{6}{7})}$

Step 3.2

Cancel the common factor of $7$ .

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Step 3.2.1

Move the leading negative in $- \frac{6}{7}$ into the numerator.

$\frac{49 \cdot 1 + 36}{49 \cdot 1 + 49 (\frac{- 6}{7})}$

Step 3.2.2

Factor $7$ out of $49$ .

$\frac{49 \cdot 1 + 36}{49 \cdot 1 + 7 (7) \frac{- 6}{7}}$

Step 3.2.3

Cancel the common factor.

$\frac{49 \cdot 1 + 36}{49 \cdot 1 + 7 \cdot 7 \frac{- 6}{7}}$

Step 3.2.4

Rewrite the expression.

$\frac{49 \cdot 1 + 36}{49 \cdot 1 + 7 \cdot - 6}$

Step 3.3

Multiply $7$ by $- 6$ .

$\frac{49 \cdot 1 + 36}{49 \cdot 1 - 42}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $49$ by $1$ .

$\frac{49 + 36}{49 \cdot 1 - 42}$

Step 4.2

Add $49$ and $36$ .

$\frac{85}{49 \cdot 1 - 42}$

Step 5

Simplify the denominator.

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Step 5.1

Multiply $49$ by $1$ .

$\frac{85}{49 - 42}$

Step 5.2

Subtract $42$ from $49$ .

$\frac{85}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{85}{7}$

Decimal Form:

$12.14285714 \dots$

Mixed Number Form:

$12 \frac{1}{7}$