Pre-Algebra Examples

$\frac{6}{a} - \frac{7}{a^{2}} \div \frac{6}{a^{3}} + \frac{7}{a}$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{6 + 7}{a} + \frac{- \frac{7}{a^{2}}}{\frac{6}{a^{3}}}$

Step 1.2

Add $6$ and $7$ .

$\frac{13}{a} + \frac{- \frac{7}{a^{2}}}{\frac{6}{a^{3}}}$

Step 2

Simplify each term.

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{13}{a} - \frac{7}{a^{2}} \cdot \frac{a^{3}}{6}$

Step 2.2

Cancel the common factor of $a^{2}$ .

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Step 2.2.1

Move the leading negative in $- \frac{7}{a^{2}}$ into the numerator.

$\frac{13}{a} + \frac{- 7}{a^{2}} \cdot \frac{a^{3}}{6}$

Step 2.2.2

Factor $a^{2}$ out of $a^{3}$ .

$\frac{13}{a} + \frac{- 7}{a^{2}} \cdot \frac{a^{2} a}{6}$

Step 2.2.3

Cancel the common factor.

$\frac{13}{a} + \frac{- 7}{a^{2}} \cdot \frac{a^{2} a}{6}$

Step 2.2.4

Rewrite the expression.

$\frac{13}{a} - 7 \frac{a}{6}$

Step 2.3

Combine $- 7$ and $\frac{a}{6}$ .

$\frac{13}{a} + \frac{- 7 a}{6}$

Step 2.4

Move the negative in front of the fraction.

$\frac{13}{a} - \frac{7 a}{6}$

Step 3

To write $\frac{13}{a}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{13}{a} \cdot \frac{6}{6} - \frac{7 a}{6}$

Step 4

To write $- \frac{7 a}{6}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$\frac{13}{a} \cdot \frac{6}{6} - \frac{7 a}{6} \cdot \frac{a}{a}$

Step 5

Write each expression with a common denominator of $a \cdot 6$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{13}{a}$ by $\frac{6}{6}$ .

$\frac{13 \cdot 6}{a \cdot 6} - \frac{7 a}{6} \cdot \frac{a}{a}$

Step 5.2

Multiply $\frac{7 a}{6}$ by $\frac{a}{a}$ .

$\frac{13 \cdot 6}{a \cdot 6} - \frac{7 a \cdot a}{6 a}$

Step 5.3

Reorder the factors of $a \cdot 6$ .

$\frac{13 \cdot 6}{6 a} - \frac{7 a \cdot a}{6 a}$

Step 6

Combine the numerators over the common denominator.

$\frac{13 \cdot 6 - 7 a \cdot a}{6 a}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $13$ by $6$ .

$\frac{78 - 7 a \cdot a}{6 a}$

Step 7.2

Multiply $a$ by $a$ by adding the exponents.

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Step 7.2.1

Move $a$ .

$\frac{78 - 7 (a \cdot a)}{6 a}$

Step 7.2.2

Multiply $a$ by $a$ .

$\frac{78 - 7 a^{2}}{6 a}$