Basic Math Examples

$7 + \frac{7}{7 + 7 \cdot 7 - 7}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $7$ and $7 + 7 \cdot 7 - 7$ .

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Step 1.1.1

Factor $7$ out of $7$ .

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

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $7$ out of $7$ .

$7 + \frac{7 \cdot 1}{7 \cdot 1 + 7 \cdot 7 - 7}$

Step 1.1.2.2

Factor $7$ out of $7 \cdot 7$ .

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

Step 1.1.2.3

Factor $7$ out of $7 (1) + 7 (7)$ .

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

Step 1.1.2.4

Factor $7$ out of $- 7$ .

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

Step 1.1.2.5

Factor $7$ out of $7 (1 + 7) + 7 \cdot - 1$ .

$7 + \frac{7 (1)}{7 (1 + 7 - 1)}$

Step 1.1.2.6

Cancel the common factor.

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

Step 1.1.2.7

Rewrite the expression.

$7 + \frac{1}{1 + 7 - 1}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

Add $1$ and $7$ .

$7 + \frac{1}{8 - 1}$

Step 1.2.2

Subtract $1$ from $8$ .

$7 + \frac{1}{7}$

Step 2

To write $7$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$7 \cdot \frac{7}{7} + \frac{1}{7}$

Step 3

Combine $7$ and $\frac{7}{7}$ .

$\frac{7 \cdot 7}{7} + \frac{1}{7}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 \cdot 7 + 1}{7}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $7$ by $7$ .

$\frac{49 + 1}{7}$

Step 5.2

Add $49$ and $1$ .

$\frac{50}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{50}{7}$

Decimal Form:

$7.\overline{142857}$

Mixed Number Form:

$7 \frac{1}{7}$