Basic Math Examples

$D = \frac{F - S}{S} \cdot 100$

Step 1

Rewrite the equation as $\frac{F - S}{S} \cdot 100 = D$ .

$\frac{F - S}{S} \cdot 100 = D$

Step 2

Combine $\frac{F - S}{S}$ and $100$ .

$\frac{(F - S) \cdot 100}{S} = D$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$S, 1$

Step 3.2

The LCM of one and any expression is the expression.

$S$

Step 4

Multiply each term in $\frac{(F - S) \cdot 100}{S} = D$ by $S$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{(F - S) \cdot 100}{S} = D$ by $S$ .

$\frac{(F - S) \cdot 100}{S} S = D S$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $S$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{(F - S) \cdot 100}{S} S = D S$

Step 4.2.1.2

Rewrite the expression.

$(F - S) \cdot 100 = D S$

Step 4.2.2

Apply the distributive property.

$F \cdot 100 - S \cdot 100 = D S$

Step 4.2.3

Simplify the expression.

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Step 4.2.3.1

Move $100$ to the left of $F$ .

$100 \cdot F - S \cdot 100 = D S$

Step 4.2.3.2

Multiply $100$ by $- 1$ .

$100 F - 100 S = D S$

Step 5

Solve the equation.

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Step 5.1

Subtract $D S$ from both sides of the equation.

$100 F - 100 S - D S = 0$

Step 5.2

Subtract $100 F$ from both sides of the equation.

$- 100 S - D S = - 100 F$

Step 5.3

Factor $S$ out of $- 100 S - D S$ .

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Step 5.3.1

Factor $S$ out of $- 100 S$ .

$S \cdot - 100 - D S = - 100 F$

Step 5.3.2

Factor $S$ out of $- D S$ .

$S \cdot - 100 + S (- D) = - 100 F$

Step 5.3.3

Factor $S$ out of $S \cdot - 100 + S (- D)$ .

$S (- 100 - D) = - 100 F$

Step 5.4

Divide each term in $S (- 100 - D) = - 100 F$ by $- 100 - D$ and simplify.

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Step 5.4.1

Divide each term in $S (- 100 - D) = - 100 F$ by $- 100 - D$ .

$\frac{S (- 100 - D)}{- 100 - D} = \frac{- 100 F}{- 100 - D}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of $- 100 - D$ .

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Step 5.4.2.1.1

Cancel the common factor.

$\frac{S (- 100 - D)}{- 100 - D} = \frac{- 100 F}{- 100 - D}$

Step 5.4.2.1.2

Divide $S$ by $1$ .

$S = \frac{- 100 F}{- 100 - D}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Move the negative in front of the fraction.

$S = - \frac{100 F}{- 100 - D}$

Step 5.4.3.2

Rewrite $- 100$ as $- 1 (100)$ .

$S = - \frac{100 F}{- 1 (100) - D}$

Step 5.4.3.3

Factor $- 1$ out of $- D$ .

$S = - \frac{100 F}{- 1 (100) - (D)}$

Step 5.4.3.4

Factor $- 1$ out of $- 1 (100) - (D)$ .

$S = - \frac{100 F}{- 1 (100 + D)}$

Step 5.4.3.5

Simplify the expression.

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Step 5.4.3.5.1

Move the negative in front of the fraction.

$S = - - \frac{100 F}{100 + D}$

Step 5.4.3.5.2

Multiply $- 1$ by $- 1$ .

$S = 1 \frac{100 F}{100 + D}$

Step 5.4.3.5.3

Multiply $\frac{100 F}{100 + D}$ by $1$ .

$S = \frac{100 F}{100 + D}$