Pre-Algebra Examples

$(3 m - n) \div 6 m n \div (3 m - n) \div 6 m n$

Step 1

Rewrite the division as a fraction.

$\frac{(3 m - n) \div 6 m n \div (3 m - n)}{6 m n}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$(3 m - n) \div 6 m n \div (3 m - n) \cdot \frac{1}{6 m n}$

Step 3

Rewrite the division as a fraction.

$\frac{(3 m - n) \div 6 m n}{3 m - n} \cdot \frac{1}{6 m n}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$(3 m - n) \div 6 m n \cdot \frac{1}{3 m - n} \frac{1}{6 m n}$

Step 5

Rewrite the division as a fraction.

$\frac{3 m - n}{6 m n} \cdot \frac{1}{3 m - n} \frac{1}{6 m n}$

Step 6

Cancel the common factor of $3 m - n$ .

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Step 6.1

Cancel the common factor.

$\frac{3 m - n}{6 m n} \cdot \frac{1}{3 m - n} \frac{1}{6 m n}$

Step 6.2

Rewrite the expression.

$\frac{1}{6 m n} \cdot \frac{1}{6 m n}$

Step 7

Multiply $\frac{1}{6 m n} \cdot \frac{1}{6 m n}$ .

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Step 7.1

Multiply $\frac{1}{6 m n}$ by $\frac{1}{6 m n}$ .

$\frac{1}{6 m n (6 m n)}$

Step 7.2

Multiply $6$ by $6$ .

$\frac{1}{36 m n (m n)}$

Step 7.3

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

$\frac{1}{36 (m^{1} m) n \cdot n}$

Step 7.4

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

$\frac{1}{36 (m^{1} m^{1}) n \cdot n}$

Step 7.5

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

$\frac{1}{36 m^{1 + 1} n \cdot n}$

Step 7.6

Add $1$ and $1$ .

$\frac{1}{36 m^{2} n \cdot n}$

Step 7.7

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

$\frac{1}{36 m^{2} (n^{1} n)}$

Step 7.8

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

$\frac{1}{36 m^{2} (n^{1} n^{1})}$

Step 7.9

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

$\frac{1}{36 m^{2} n^{1 + 1}}$

Step 7.10

Add $1$ and $1$ .

$\frac{1}{36 m^{2} n^{2}}$