Basic Math Examples

$\frac{14 y}{3} \div \frac{y^{2}}{6} \cdot \frac{2}{y}$

Step 1

Combine.

$\frac{\frac{14 y}{3} \cdot 2}{\frac{y^{2}}{6} y}$

Step 2

Combine $\frac{14 y}{3}$ and $2$ .

$\frac{\frac{14 y \cdot 2}{3}}{\frac{y^{2}}{6} y}$

Step 3

Combine $\frac{y^{2}}{6}$ and $y$ .

$\frac{\frac{14 y \cdot 2}{3}}{\frac{y^{2} y}{6}}$

Step 4

Multiply $2$ by $14$ .

$\frac{\frac{28 y}{3}}{\frac{y^{2} y}{6}}$

Step 5

Multiply $y^{2}$ by $y$ by adding the exponents.

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Step 5.1

Multiply $y^{2}$ by $y$ .

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Step 5.1.1

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

$\frac{\frac{28 y}{3}}{\frac{y^{2} y^{1}}{6}}$

Step 5.1.2

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

$\frac{\frac{28 y}{3}}{\frac{y^{2 + 1}}{6}}$

Step 5.2

Add $2$ and $1$ .

$\frac{\frac{28 y}{3}}{\frac{y^{3}}{6}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{28 y}{3} \cdot \frac{6}{y^{3}}$

Step 7

Combine.

$\frac{28 y \cdot 6}{3 y^{3}}$

Step 8

Cancel the common factor of $y$ and $y^{3}$ .

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Step 8.1

Factor $y$ out of $28 y \cdot 6$ .

$\frac{y (28 \cdot 6)}{3 y^{3}}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $y$ out of $3 y^{3}$ .

$\frac{y (28 \cdot 6)}{y (3 y^{2})}$

Step 8.2.2

Cancel the common factor.

$\frac{y (28 \cdot 6)}{y (3 y^{2})}$

Step 8.2.3

Rewrite the expression.

$\frac{28 \cdot 6}{3 y^{2}}$

Step 9

Cancel the common factor of $6$ and $3$ .

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Step 9.1

Factor $3$ out of $28 \cdot 6$ .

$\frac{3 (28 \cdot 2)}{3 y^{2}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

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

$\frac{3 (28 \cdot 2)}{3 (y^{2})}$

Step 9.2.2

Cancel the common factor.

$\frac{3 (28 \cdot 2)}{3 y^{2}}$

Step 9.2.3

Rewrite the expression.

$\frac{28 \cdot 2}{y^{2}}$

Step 10

Multiply $28$ by $2$ .

$\frac{56}{y^{2}}$