Pre-Algebra Examples

$H = \frac{1}{3} \cdot (j (c - d))$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot (j (c - d)) = H$ .

$\frac{1}{3} \cdot (j (c - d)) = H$

Step 2

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot (j (c - d))) = 3 H$

Step 3

Simplify the left side.

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Step 3.1

Simplify $3 (\frac{1}{3} \cdot (j (c - d)))$ .

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Step 3.1.1

Apply the distributive property.

$3 (\frac{1}{3} \cdot (j c + j (- d))) = 3 H$

Step 3.1.2

Rewrite using the commutative property of multiplication.

$3 (\frac{1}{3} \cdot (j c - j d)) = 3 H$

Step 3.1.3

Apply the distributive property.

$3 (\frac{1}{3} (j c) + \frac{1}{3} (- j d)) = 3 H$

Step 3.1.4

Multiply $\frac{1}{3} (j c)$ .

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Step 3.1.4.1

Combine $j$ and $\frac{1}{3}$ .

$3 (\frac{j}{3} c + \frac{1}{3} (- j d)) = 3 H$

Step 3.1.4.2

Combine $\frac{j}{3}$ and $c$ .

$3 (\frac{j c}{3} + \frac{1}{3} (- j d)) = 3 H$

Step 3.1.5

Multiply $\frac{1}{3} (- j d)$ .

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Step 3.1.5.1

Combine $\frac{1}{3}$ and $j$ .

$3 (\frac{j c}{3} - \frac{j}{3} d) = 3 H$

Step 3.1.5.2

Combine $d$ and $\frac{j}{3}$ .

$3 (\frac{j c}{3} - \frac{d j}{3}) = 3 H$

Step 3.1.6

Apply the distributive property.

$3 \frac{j c}{3} + 3 (- \frac{d j}{3}) = 3 H$

Step 3.1.7

Cancel the common factor of $3$ .

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Step 3.1.7.1

Cancel the common factor.

$3 \frac{j c}{3} + 3 (- \frac{d j}{3}) = 3 H$

Step 3.1.7.2

Rewrite the expression.

$j c + 3 (- \frac{d j}{3}) = 3 H$

Step 3.1.8

Cancel the common factor of $3$ .

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Step 3.1.8.1

Move the leading negative in $- \frac{d j}{3}$ into the numerator.

$j c + 3 \frac{- d j}{3} = 3 H$

Step 3.1.8.2

Cancel the common factor.

$j c + 3 \frac{- d j}{3} = 3 H$

Step 3.1.8.3

Rewrite the expression.

$j c - d j = 3 H$

Step 4

Add $d j$ to both sides of the equation.

$j c = 3 H + d j$

Step 5

Divide each term in $j c = 3 H + d j$ by $j$ and simplify.

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Step 5.1

Divide each term in $j c = 3 H + d j$ by $j$ .

$\frac{j c}{j} = \frac{3 H}{j} + \frac{d j}{j}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $j$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{j c}{j} = \frac{3 H}{j} + \frac{d j}{j}$

Step 5.2.1.2

Divide $c$ by $1$ .

$c = \frac{3 H}{j} + \frac{d j}{j}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $j$ .

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Step 5.3.1.1

Cancel the common factor.

$c = \frac{3 H}{j} + \frac{d j}{j}$

Step 5.3.1.2

Divide $d$ by $1$ .

$c = \frac{3 H}{j} + d$