Pre-Algebra Examples

$\frac{5 k}{\frac{36 m}{\frac{15 k}{9}}}$

Step 1

Cancel the common factor of $15$ and $9$ .

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Step 1.1

Factor $3$ out of $15 k$ .

$\frac{5 k}{\frac{36 m}{\frac{3 (5 k)}{9}}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $9$ .

$\frac{5 k}{\frac{36 m}{\frac{3 (5 k)}{3 (3)}}}$

Step 1.2.2

Cancel the common factor.

$\frac{5 k}{\frac{36 m}{\frac{3 (5 k)}{3 \cdot 3}}}$

Step 1.2.3

Rewrite the expression.

$\frac{5 k}{\frac{36 m}{\frac{5 k}{3}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$5 k \frac{\frac{5 k}{3}}{36 m}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$5 k (\frac{5 k}{3} \cdot \frac{1}{36 m})$

Step 4

Multiply $\frac{5 k}{3} \cdot \frac{1}{36 m}$ .

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Step 4.1

Multiply $\frac{5 k}{3}$ by $\frac{1}{36 m}$ .

$5 k \frac{5 k}{3 (36 m)}$

Step 4.2

Multiply $36$ by $3$ .

$5 k \frac{5 k}{108 m}$

Step 5

Multiply $5 k \frac{5 k}{108 m}$ .

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Step 5.1

Combine $5$ and $\frac{5 k}{108 m}$ .

$k \frac{5 (5 k)}{108 m}$

Step 5.2

Multiply $5$ by $5$ .

$k \frac{25 k}{108 m}$

Step 5.3

Combine $k$ and $\frac{25 k}{108 m}$ .

$\frac{k (25 k)}{108 m}$

Step 5.4

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

$\frac{25 (k^{1} k)}{108 m}$

Step 5.5

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

$\frac{25 (k^{1} k^{1})}{108 m}$

Step 5.6

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

$\frac{25 k^{1 + 1}}{108 m}$

Step 5.7

Add $1$ and $1$ .

$\frac{25 k^{2}}{108 m}$