Algebra Examples

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$

Step 1

Rewrite the equation as $\frac{P_{2} V_{2}}{T_{2}} = \frac{P_{1} V_{1}}{T_{1}}$ .

$\frac{P_{2} V_{2}}{T_{2}} = \frac{P_{1} V_{1}}{T_{1}}$

Step 2

Multiply both sides by $T_{2}$ .

$\frac{P_{2} V_{2}}{T_{2}} T_{2} = \frac{P_{1} V_{1}}{T_{1}} T_{2}$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $T_{2}$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{P_{2} V_{2}}{T_{2}} T_{2} = \frac{P_{1} V_{1}}{T_{1}} T_{2}$

Step 3.1.1.2

Rewrite the expression.

$P_{2} V_{2} = \frac{P_{1} V_{1}}{T_{1}} T_{2}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Combine $\frac{P_{1} V_{1}}{T_{1}}$ and $T_{2}$ .

$P_{2} V_{2} = \frac{P_{1} V_{1} T_{2}}{T_{1}}$

Step 4

Divide each term in $P_{2} V_{2} = \frac{P_{1} V_{1} T_{2}}{T_{1}}$ by $V_{2}$ and simplify.

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Step 4.1

Divide each term in $P_{2} V_{2} = \frac{P_{1} V_{1} T_{2}}{T_{1}}$ by $V_{2}$ .

$\frac{P_{2} V_{2}}{V_{2}} = \frac{\frac{P_{1} V_{1} T_{2}}{T_{1}}}{V_{2}}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $V_{2}$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{P_{2} V_{2}}{V_{2}} = \frac{\frac{P_{1} V_{1} T_{2}}{T_{1}}}{V_{2}}$

Step 4.2.1.2

Divide $P_{2}$ by $1$ .

$P_{2} = \frac{\frac{P_{1} V_{1} T_{2}}{T_{1}}}{V_{2}}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$P_{2} = \frac{P_{1} V_{1} T_{2}}{T_{1}} \cdot \frac{1}{V_{2}}$

Step 4.3.2

Multiply $\frac{P_{1} V_{1} T_{2}}{T_{1}}$ by $\frac{1}{V_{2}}$ .

$P_{2} = \frac{P_{1} V_{1} T_{2}}{T_{1} V_{2}}$