Basic Math Examples

$\frac{7 n}{12} \cdot (- \frac{9 n}{12})$

Step 1

Rewrite using the commutative property of multiplication.

$- \frac{7 n}{12} \cdot \frac{9 n}{12}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Move the leading negative in $- \frac{7 n}{12}$ into the numerator.

$\frac{- 7 n}{12} \cdot \frac{9 n}{12}$

Step 2.2

Factor $3$ out of $12$ .

$\frac{- 7 n}{3 (4)} \cdot \frac{9 n}{12}$

Step 2.3

Factor $3$ out of $9 n$ .

$\frac{- 7 n}{3 (4)} \cdot \frac{3 (3 n)}{12}$

Step 2.4

Cancel the common factor.

$\frac{- 7 n}{3 \cdot 4} \cdot \frac{3 (3 n)}{12}$

Step 2.5

Rewrite the expression.

$\frac{- 7 n}{4} \cdot \frac{3 n}{12}$

Step 3

Multiply $\frac{- 7 n}{4}$ by $\frac{3 n}{12}$ .

$\frac{- 7 n (3 n)}{4 \cdot 12}$

Step 4

Multiply $3$ by $- 7$ .

$\frac{- 21 n \cdot n}{4 \cdot 12}$

Step 5

Raise $n$ to the power of $1$ .

$\frac{- 21 (n^{1} n)}{4 \cdot 12}$

Step 6

Raise $n$ to the power of $1$ .

$\frac{- 21 (n^{1} n^{1})}{4 \cdot 12}$

Step 7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 21 n^{1 + 1}}{4 \cdot 12}$

Step 8

Simplify the expression.

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Step 8.1

Add $1$ and $1$ .

$\frac{- 21 n^{2}}{4 \cdot 12}$

Step 8.2

Multiply $4$ by $12$ .

$\frac{- 21 n^{2}}{48}$

Step 9

Cancel the common factor of $- 21$ and $48$ .

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Step 9.1

Factor $3$ out of $- 21 n^{2}$ .

$\frac{3 (- 7 n^{2})}{48}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $3$ out of $48$ .

$\frac{3 (- 7 n^{2})}{3 (16)}$

Step 9.2.2

Cancel the common factor.

$\frac{3 (- 7 n^{2})}{3 \cdot 16}$

Step 9.2.3

Rewrite the expression.

$\frac{- 7 n^{2}}{16}$

Step 10

Move the negative in front of the fraction.

$- \frac{7 n^{2}}{16}$