Pre-Algebra Examples

$b = \frac{1}{3} \cdot (m (s + z) f o r s)$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot (m (s + z) f o r s) = b$ .

$\frac{1}{3} \cdot (m (s + z) f o r s) = b$

Step 2

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot (m (s + z) f o r s)) = 3 b$

Step 3

Simplify the left side.

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Step 3.1

Simplify $3 (\frac{1}{3} \cdot (m (s + z) f o r s))$ .

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Step 3.1.1

Apply the distributive property.

$3 (\frac{1}{3} \cdot ((m s + m z) f o r s)) = 3 b$

Step 3.1.2

Apply the distributive property.

$3 (\frac{1}{3} \cdot ((m s f + m z f) o r s)) = 3 b$

Step 3.1.3

Apply the distributive property.

$3 (\frac{1}{3} \cdot ((m s f o + m z f o) r s)) = 3 b$

Step 3.1.4

Apply the distributive property.

$3 (\frac{1}{3} \cdot ((m s f o r + m z f o r) s)) = 3 b$

Step 3.1.5

Apply the distributive property.

$3 (\frac{1}{3} \cdot (m s f o r s + m z f o r s)) = 3 b$

Step 3.1.6

Multiply $s$ by $s$ by adding the exponents.

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Step 3.1.6.1

Move $s$ .

$3 (\frac{1}{3} \cdot (m (s \cdot s) f o r + m z f o r s)) = 3 b$

Step 3.1.6.2

Multiply $s$ by $s$ .

$3 (\frac{1}{3} \cdot (m s^{2} f o r + m z f o r s)) = 3 b$

Step 3.1.7

Apply the distributive property.

$3 (\frac{1}{3} (m s^{2} f o r) + \frac{1}{3} (m z f o r s)) = 3 b$

Step 3.1.8

Multiply $\frac{1}{3} (m s^{2} f o r)$ .

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Step 3.1.8.1

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

$3 (\frac{m}{3} (s^{2} f o r) + \frac{1}{3} (m z f o r s)) = 3 b$

Step 3.1.8.2

Combine $s^{2}$ and $\frac{m}{3}$ .

$3 (\frac{s^{2} m}{3} (f o r) + \frac{1}{3} (m z f o r s)) = 3 b$

Step 3.1.8.3

Combine $f$ and $\frac{s^{2} m}{3}$ .

$3 (\frac{f (s^{2} m)}{3} (o r) + \frac{1}{3} (m z f o r s)) = 3 b$

Step 3.1.8.4

Combine $o$ and $\frac{f (s^{2} m)}{3}$ .

$3 (\frac{o (f (s^{2} m))}{3} r + \frac{1}{3} (m z f o r s)) = 3 b$

Step 3.1.8.5

Combine $\frac{o (f (s^{2} m))}{3}$ and $r$ .

$3 (\frac{o (f (s^{2} m)) r}{3} + \frac{1}{3} (m z f o r s)) = 3 b$

Step 3.1.9

Multiply $\frac{1}{3} (m z f o r s)$ .

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Step 3.1.9.1

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

$3 (\frac{o (f (s^{2} m)) r}{3} + \frac{m}{3} (z f o r s)) = 3 b$

Step 3.1.9.2

Combine $z$ and $\frac{m}{3}$ .

$3 (\frac{o (f (s^{2} m)) r}{3} + \frac{z m}{3} (f o r s)) = 3 b$

Step 3.1.9.3

Combine $f$ and $\frac{z m}{3}$ .

$3 (\frac{o (f (s^{2} m)) r}{3} + \frac{f (z m)}{3} (o r s)) = 3 b$

Step 3.1.9.4

Combine $o$ and $\frac{f (z m)}{3}$ .

$3 (\frac{o (f (s^{2} m)) r}{3} + \frac{o (f (z m))}{3} (r s)) = 3 b$

Step 3.1.9.5

Combine $r$ and $\frac{o (f (z m))}{3}$ .

$3 (\frac{o (f (s^{2} m)) r}{3} + \frac{r (o (f (z m)))}{3} s) = 3 b$

Step 3.1.9.6

Combine $\frac{r (o (f (z m)))}{3}$ and $s$ .

$3 (\frac{o (f (s^{2} m)) r}{3} + \frac{r (o (f (z m))) s}{3}) = 3 b$

Step 3.1.10

Remove parentheses.

$3 (\frac{o f s^{2} m r}{3} + \frac{r o f z m s}{3}) = 3 b$

Step 3.1.11

Simplify terms.

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Step 3.1.11.1

Apply the distributive property.

$3 \frac{o f s^{2} m r}{3} + 3 \frac{r o f z m s}{3} = 3 b$

Step 3.1.11.2

Cancel the common factor of $3$ .

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Step 3.1.11.2.1

Cancel the common factor.

$3 \frac{o f s^{2} m r}{3} + 3 \frac{r o f z m s}{3} = 3 b$

Step 3.1.11.2.2

Rewrite the expression.

$o f s^{2} m r + 3 \frac{r o f z m s}{3} = 3 b$

Step 3.1.11.3

Cancel the common factor of $3$ .

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Step 3.1.11.3.1

Cancel the common factor.

$o f s^{2} m r + 3 \frac{r o f z m s}{3} = 3 b$

Step 3.1.11.3.2

Rewrite the expression.

$o f s^{2} m r + r o f z m s = 3 b$

Step 4

Subtract $o f s^{2} m r$ from both sides of the equation.

$r o f z m s = 3 b - o f s^{2} m r$

Step 5

Divide each term in $r o f z m s = 3 b - o f s^{2} m r$ by $r o f m s$ and simplify.

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Step 5.1

Divide each term in $r o f z m s = 3 b - o f s^{2} m r$ by $r o f m s$ .

$\frac{r o f z m s}{r o f m s} = \frac{3 b}{r o f m s} + \frac{- o f s^{2} m r}{r o f m s}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $r$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{r o f z m s}{r o f m s} = \frac{3 b}{r o f m s} + \frac{- o f s^{2} m r}{r o f m s}$

Step 5.2.1.2

Rewrite the expression.

$\frac{o f z m s}{o f m s} = \frac{3 b}{r o f m s} + \frac{- o f s^{2} m r}{r o f m s}$

Step 5.2.2

Cancel the common factor of $o$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{o f z m s}{o f m s} = \frac{3 b}{r o f m s} + \frac{- o f s^{2} m r}{r o f m s}$

Step 5.2.2.2

Rewrite the expression.

$\frac{f z m s}{f m s} = \frac{3 b}{r o f m s} + \frac{- o f s^{2} m r}{r o f m s}$

Step 5.2.3

Cancel the common factor of $f$ .

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Step 5.2.3.1

Cancel the common factor.

$\frac{f z m s}{f m s} = \frac{3 b}{r o f m s} + \frac{- o f s^{2} m r}{r o f m s}$

Step 5.2.3.2

Rewrite the expression.

$\frac{z m s}{m s} = \frac{3 b}{r o f m s} + \frac{- o f s^{2} m r}{r o f m s}$

Step 5.2.4

Cancel the common factor of $m$ .

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Step 5.2.4.1

Cancel the common factor.

$\frac{z m s}{m s} = \frac{3 b}{r o f m s} + \frac{- o f s^{2} m r}{r o f m s}$

Step 5.2.4.2

Rewrite the expression.

$\frac{z s}{s} = \frac{3 b}{r o f m s} + \frac{- o f s^{2} m r}{r o f m s}$

Step 5.2.5

Cancel the common factor of $s$ .

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Step 5.2.5.1

Cancel the common factor.

$\frac{z s}{s} = \frac{3 b}{r o f m s} + \frac{- o f s^{2} m r}{r o f m s}$

Step 5.2.5.2

Divide $z$ by $1$ .

$z = \frac{3 b}{r o f m s} + \frac{- o f s^{2} m r}{r o f m s}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Cancel the common factor of $o$ .

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Step 5.3.1.1.1

Cancel the common factor.

$z = \frac{3 b}{r o f m s} + \frac{- o f s^{2} m r}{r o f m s}$

Step 5.3.1.1.2

Rewrite the expression.

$z = \frac{3 b}{r o f m s} + \frac{- 1 f s^{2} m r}{r f m s}$

Step 5.3.1.2

Cancel the common factor of $f$ .

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Step 5.3.1.2.1

Cancel the common factor.

$z = \frac{3 b}{r o f m s} + \frac{- 1 f s^{2} m r}{r f m s}$

Step 5.3.1.2.2

Rewrite the expression.

$z = \frac{3 b}{r o f m s} + \frac{- 1 s^{2} m r}{r m s}$

Step 5.3.1.3

Cancel the common factor of $s^{2}$ and $s$ .

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Step 5.3.1.3.1

Factor $s$ out of $- 1 s^{2} m r$ .

$z = \frac{3 b}{r o f m s} + \frac{s (- 1 s m r)}{r m s}$

Step 5.3.1.3.2

Cancel the common factors.

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Step 5.3.1.3.2.1

Factor $s$ out of $r m s$ .

$z = \frac{3 b}{r o f m s} + \frac{s (- 1 s m r)}{s (r m)}$

Step 5.3.1.3.2.2

Cancel the common factor.

$z = \frac{3 b}{r o f m s} + \frac{s (- 1 s m r)}{s (r m)}$

Step 5.3.1.3.2.3

Rewrite the expression.

$z = \frac{3 b}{r o f m s} + \frac{- 1 s m r}{r m}$

Step 5.3.1.4

Cancel the common factor of $m$ .

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Step 5.3.1.4.1

Cancel the common factor.

$z = \frac{3 b}{r o f m s} + \frac{- 1 s m r}{r m}$

Step 5.3.1.4.2

Rewrite the expression.

$z = \frac{3 b}{r o f m s} + \frac{- 1 s r}{r}$

Step 5.3.1.5

Cancel the common factor of $r$ .

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Step 5.3.1.5.1

Cancel the common factor.

$z = \frac{3 b}{r o f m s} + \frac{- 1 s r}{r}$

Step 5.3.1.5.2

Divide $- 1 s$ by $1$ .

$z = \frac{3 b}{r o f m s} - 1 s$

Step 5.3.1.6

Rewrite $- 1 s$ as $- s$ .

$z = \frac{3 b}{r o f m s} - s$