Basic Math Examples

$\frac{7}{a} + 7 \div \frac{7}{a} - 7$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

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

Step 1.2

Cancel the common factor of $7$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Rewrite the expression.

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

Step 2

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Multiply $a$ by $a$ .

$\frac{7 + a^{2}}{a} - 7$

Step 5

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

$\frac{7 + a^{2}}{a} - 7 \cdot \frac{a}{a}$

Step 6

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

$\frac{7 + a^{2}}{a} + \frac{- 7 a}{a}$

Step 7

Combine the numerators over the common denominator.

$\frac{7 + a^{2} - 7 a}{a}$

Step 8

Reorder terms.

$\frac{a^{2} - 7 a + 7}{a}$