Pre-Algebra Examples

$F = 240000 \cdot \frac{L^{3}}{a \cdot B} \cdot ((\frac{Q + W}{3}) + (\frac{Q \cdot L}{4}))$

Step 1

Rewrite the equation as $240000 \cdot \frac{L^{3}}{a \cdot B} \cdot (\frac{Q + W}{3} + \frac{Q \cdot L}{4}) = F$ .

$\frac{240000 L^{3}}{a \cdot B} \cdot (\frac{Q + W}{3} + \frac{Q \cdot L}{4}) = F$

Step 2

Multiply each term in $\frac{240000 L^{3}}{a \cdot B} \cdot (\frac{Q + W}{3} + \frac{Q \cdot L}{4}) = F$ by $\frac{a \cdot B}{240000 L^{3}}$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{240000 L^{3}}{a \cdot B} \cdot (\frac{Q + W}{3} + \frac{Q \cdot L}{4}) = F$ by $\frac{a \cdot B}{240000 L^{3}}$ .

$\frac{240000 L^{3}}{a \cdot B} \cdot (\frac{Q + W}{3} + \frac{Q \cdot L}{4}) \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

To write $\frac{Q + W}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{240000 L^{3}}{a B} \cdot (\frac{Q + W}{3} \cdot \frac{4}{4} + \frac{Q L}{4}) \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.2

To write $\frac{Q L}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{240000 L^{3}}{a B} \cdot (\frac{Q + W}{3} \cdot \frac{4}{4} + \frac{Q L}{4} \cdot \frac{3}{3}) \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.3.1

Multiply $\frac{Q + W}{3}$ by $\frac{4}{4}$ .

$\frac{240000 L^{3}}{a B} \cdot (\frac{(Q + W) \cdot 4}{3 \cdot 4} + \frac{Q L}{4} \cdot \frac{3}{3}) \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.3.2

Multiply $3$ by $4$ .

$\frac{240000 L^{3}}{a B} \cdot (\frac{(Q + W) \cdot 4}{12} + \frac{Q L}{4} \cdot \frac{3}{3}) \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.3.3

Multiply $\frac{Q L}{4}$ by $\frac{3}{3}$ .

$\frac{240000 L^{3}}{a B} \cdot (\frac{(Q + W) \cdot 4}{12} + \frac{Q L \cdot 3}{4 \cdot 3}) \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.3.4

Multiply $4$ by $3$ .

$\frac{240000 L^{3}}{a B} \cdot (\frac{(Q + W) \cdot 4}{12} + \frac{Q L \cdot 3}{12}) \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.4

Combine the numerators over the common denominator.

$\frac{240000 L^{3}}{a B} \cdot \frac{(Q + W) \cdot 4 + Q L \cdot 3}{12} \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.5

Simplify the numerator.

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Step 2.2.5.1

Apply the distributive property.

$\frac{240000 L^{3}}{a B} \cdot \frac{Q \cdot 4 + W \cdot 4 + Q L \cdot 3}{12} \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.5.2

Move $4$ to the left of $Q$ .

$\frac{240000 L^{3}}{a B} \cdot \frac{4 \cdot Q + W \cdot 4 + Q L \cdot 3}{12} \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.5.3

Move $4$ to the left of $W$ .

$\frac{240000 L^{3}}{a B} \cdot \frac{4 \cdot Q + 4 \cdot W + Q L \cdot 3}{12} \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.5.4

Multiply $4$ by $W$ .

$\frac{240000 L^{3}}{a B} \cdot \frac{4 Q + 4 W + Q L \cdot 3}{12} \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.5.5

Move $3$ to the left of $Q L$ .

$\frac{240000 L^{3}}{a B} \cdot \frac{4 Q + 4 W + 3 Q L}{12} \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6

Simplify terms.

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Step 2.2.6.1

Cancel the common factor of $12$ .

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Step 2.2.6.1.1

Factor $12$ out of $240000 L^{3}$ .

$\frac{12 (20000 L^{3})}{a B} \cdot \frac{4 Q + 4 W + 3 Q L}{12} \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6.1.2

Cancel the common factor.

$\frac{12 (20000 L^{3})}{a B} \cdot \frac{4 Q + 4 W + 3 Q L}{12} \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6.1.3

Rewrite the expression.

$\frac{20000 L^{3}}{a B} \cdot (4 Q + 4 W + 3 Q L) \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6.2

Multiply $\frac{20000 L^{3}}{a B}$ by $4 Q + 4 W + 3 Q L$ .

$\frac{20000 L^{3} (4 Q + 4 W + 3 Q L)}{a B} \cdot \frac{a \cdot B}{240000 L^{3}} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6.3

Combine.

$\frac{20000 L^{3} (4 Q + 4 W + 3 Q L) (a \cdot B)}{a B (240000 L^{3})} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6.4

Cancel the common factor of $20000$ and $240000$ .

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Step 2.2.6.4.1

Factor $20000$ out of $20000 L^{3} (4 Q + 4 W + 3 Q L) (a \cdot B)$ .

$\frac{20000 ((L^{3} (4 Q + 4 W + 3 Q L)) (a \cdot B))}{a B (240000 L^{3})} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6.4.2

Cancel the common factors.

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Step 2.2.6.4.2.1

Factor $20000$ out of $a B (240000 L^{3})$ .

$\frac{20000 ((L^{3} (4 Q + 4 W + 3 Q L)) (a \cdot B))}{20000 (a B (12 L^{3}))} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6.4.2.2

Cancel the common factor.

$\frac{20000 ((L^{3} (4 Q + 4 W + 3 Q L)) (a \cdot B))}{20000 (a B (12 L^{3}))} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6.4.2.3

Rewrite the expression.

$\frac{(L^{3} (4 Q + 4 W + 3 Q L)) (a \cdot B)}{a B (12 L^{3})} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6.5

Cancel the common factor of $L^{3}$ .

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Step 2.2.6.5.1

Cancel the common factor.

$\frac{L^{3} (4 Q + 4 W + 3 Q L) (a \cdot B)}{a B (12 L^{3})} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6.5.2

Rewrite the expression.

$\frac{(4 Q + 4 W + 3 Q L) (a \cdot B)}{a B \cdot (12)} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6.6

Cancel the common factor of $a$ .

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Step 2.2.6.6.1

Cancel the common factor.

$\frac{(4 Q + 4 W + 3 Q L) (a \cdot B)}{a B \cdot 12} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6.6.2

Rewrite the expression.

$\frac{(4 Q + 4 W + 3 Q L) (B)}{B \cdot (12)} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6.7

Cancel the common factor of $B$ .

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Step 2.2.6.7.1

Cancel the common factor.

$\frac{(4 Q + 4 W + 3 Q L) B}{B \cdot 12} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.2.6.7.2

Rewrite the expression.

$\frac{4 Q + 4 W + 3 Q L}{12} = F \frac{a \cdot B}{240000 L^{3}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Combine $F$ and $\frac{a B}{240000 L^{3}}$ .

$\frac{4 Q + 4 W + 3 Q L}{12} = \frac{F a B}{240000 L^{3}}$

Step 3

Multiply both sides by $12$ .

$\frac{4 Q + 4 W + 3 Q L}{12} \cdot 12 = \frac{F a B}{240000 L^{3}} \cdot 12$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{4 Q + 4 W + 3 Q L}{12} \cdot 12$ .

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Step 4.1.1.1

Cancel the common factor of $12$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{4 Q + 4 W + 3 Q L}{12} \cdot 12 = \frac{F a B}{240000 L^{3}} \cdot 12$

Step 4.1.1.1.2

Rewrite the expression.

$4 Q + 4 W + 3 Q L = \frac{F a B}{240000 L^{3}} \cdot 12$

Step 4.1.1.2

Simplify the expression.

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Step 4.1.1.2.1

Move $Q$ .

$4 Q + 4 W + 3 L Q = \frac{F a B}{240000 L^{3}} \cdot 12$

Step 4.1.1.2.2

Move $4 W$ .

$4 Q + 3 L Q + 4 W = \frac{F a B}{240000 L^{3}} \cdot 12$

Step 4.1.1.2.3

Reorder $4 Q$ and $3 L Q$ .

$3 L Q + 4 Q + 4 W = \frac{F a B}{240000 L^{3}} \cdot 12$

Step 4.2

Simplify the right side.

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Step 4.2.1

Cancel the common factor of $12$ .

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Step 4.2.1.1

Factor $12$ out of $240000 L^{3}$ .

$3 L Q + 4 Q + 4 W = \frac{F a B}{12 (20000 L^{3})} \cdot 12$

Step 4.2.1.2

Cancel the common factor.

$3 L Q + 4 Q + 4 W = \frac{F a B}{12 (20000 L^{3})} \cdot 12$

Step 4.2.1.3

Rewrite the expression.

$3 L Q + 4 Q + 4 W = \frac{F a B}{20000 L^{3}}$

Step 5

Solve for $W$ .

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Step 5.1

Move all terms not containing $W$ to the right side of the equation.

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Step 5.1.1

Subtract $3 L Q$ from both sides of the equation.

$4 Q + 4 W = \frac{F a B}{20000 L^{3}} - 3 L Q$

Step 5.1.2

Subtract $4 Q$ from both sides of the equation.

$4 W = \frac{F a B}{20000 L^{3}} - 3 L Q - 4 Q$

Step 5.2

Divide each term in $4 W = \frac{F a B}{20000 L^{3}} - 3 L Q - 4 Q$ by $4$ and simplify.

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Step 5.2.1

Divide each term in $4 W = \frac{F a B}{20000 L^{3}} - 3 L Q - 4 Q$ by $4$ .

$\frac{4 W}{4} = \frac{\frac{F a B}{20000 L^{3}}}{4} + \frac{- 3 L Q}{4} + \frac{- 4 Q}{4}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $4$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{4 W}{4} = \frac{\frac{F a B}{20000 L^{3}}}{4} + \frac{- 3 L Q}{4} + \frac{- 4 Q}{4}$

Step 5.2.2.1.2

Divide $W$ by $1$ .

$W = \frac{\frac{F a B}{20000 L^{3}}}{4} + \frac{- 3 L Q}{4} + \frac{- 4 Q}{4}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Simplify each term.

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Step 5.2.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$W = \frac{F a B}{20000 L^{3}} \cdot \frac{1}{4} + \frac{- 3 L Q}{4} + \frac{- 4 Q}{4}$

Step 5.2.3.1.2

Combine.

$W = \frac{F a B \cdot 1}{20000 L^{3} \cdot 4} + \frac{- 3 L Q}{4} + \frac{- 4 Q}{4}$

Step 5.2.3.1.3

Multiply $F$ by $1$ .

$W = \frac{F a B}{20000 L^{3} \cdot 4} + \frac{- 3 L Q}{4} + \frac{- 4 Q}{4}$

Step 5.2.3.1.4

Multiply $4$ by $20000$ .

$W = \frac{F a B}{80000 L^{3}} + \frac{- 3 L Q}{4} + \frac{- 4 Q}{4}$

Step 5.2.3.1.5

Move the negative in front of the fraction.

$W = \frac{F a B}{80000 L^{3}} - \frac{3 L Q}{4} + \frac{- 4 Q}{4}$

Step 5.2.3.1.6

Cancel the common factor of $- 4$ and $4$ .

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Step 5.2.3.1.6.1

Factor $4$ out of $- 4 Q$ .

$W = \frac{F a B}{80000 L^{3}} - \frac{3 L Q}{4} + \frac{4 (- Q)}{4}$

Step 5.2.3.1.6.2

Cancel the common factors.

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Step 5.2.3.1.6.2.1

Factor $4$ out of $4$ .

$W = \frac{F a B}{80000 L^{3}} - \frac{3 L Q}{4} + \frac{4 (- Q)}{4 (1)}$

Step 5.2.3.1.6.2.2

Cancel the common factor.

$W = \frac{F a B}{80000 L^{3}} - \frac{3 L Q}{4} + \frac{4 (- Q)}{4 \cdot 1}$

Step 5.2.3.1.6.2.3

Rewrite the expression.

$W = \frac{F a B}{80000 L^{3}} - \frac{3 L Q}{4} + \frac{- Q}{1}$

Step 5.2.3.1.6.2.4

Divide $- Q$ by $1$ .

$W = \frac{F a B}{80000 L^{3}} - \frac{3 L Q}{4} - Q$