Pre-Algebra Examples

$\frac{4 q - 6 n}{3 m} = f$

Step 1

Multiply both sides by $3 m$ .

$\frac{4 q - 6 n}{3 m} (3 m) = f (3 m)$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{4 q - 6 n}{3 m} (3 m)$ .

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Step 2.1.1.1

Rewrite using the commutative property of multiplication.

$3 \frac{4 q - 6 n}{3 m} m = f (3 m)$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Factor $3$ out of $3 m$ .

$3 \frac{4 q - 6 n}{3 (m)} m = f (3 m)$

Step 2.1.1.2.2

Cancel the common factor.

$3 \frac{4 q - 6 n}{3 m} m = f (3 m)$

Step 2.1.1.2.3

Rewrite the expression.

$\frac{4 q - 6 n}{m} m = f (3 m)$

$\frac{4 q - 6 n}{m} m = f (3 m)$

Step 2.1.1.3

Cancel the common factor of $m$ .

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Step 2.1.1.3.1

Cancel the common factor.

$\frac{4 q - 6 n}{m} m = f (3 m)$

Step 2.1.1.3.2

Rewrite the expression.

$4 q - 6 n = f (3 m)$

$4 q - 6 n = f (3 m)$

Step 2.1.1.4

Reorder $4 q$ and $- 6 n$ .

$- 6 n + 4 q = f (3 m)$

$- 6 n + 4 q = f (3 m)$

$- 6 n + 4 q = f (3 m)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$- 6 n + 4 q = 3 f m$

$- 6 n + 4 q = 3 f m$

$- 6 n + 4 q = 3 f m$

Step 3

Solve for $q$ .

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Step 3.1

Add $6 n$ to both sides of the equation.

$4 q = 3 f m + 6 n$

Step 3.2

Divide each term in $4 q = 3 f m + 6 n$ by $4$ and simplify.

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Step 3.2.1

Divide each term in $4 q = 3 f m + 6 n$ by $4$ .

$\frac{4 q}{4} = \frac{3 f m}{4} + \frac{6 n}{4}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{4 q}{4} = \frac{3 f m}{4} + \frac{6 n}{4}$

Step 3.2.2.1.2

Divide $q$ by $1$ .

$q = \frac{3 f m}{4} + \frac{6 n}{4}$

$q = \frac{3 f m}{4} + \frac{6 n}{4}$

$q = \frac{3 f m}{4} + \frac{6 n}{4}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Cancel the common factor of $6$ and $4$ .

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Step 3.2.3.1.1

Factor $2$ out of $6 n$ .

$q = \frac{3 f m}{4} + \frac{2 (3 n)}{4}$

Step 3.2.3.1.2

Cancel the common factors.

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Step 3.2.3.1.2.1

Factor $2$ out of $4$ .

$q = \frac{3 f m}{4} + \frac{2 (3 n)}{2 (2)}$

Step 3.2.3.1.2.2

Cancel the common factor.

$q = \frac{3 f m}{4} + \frac{2 (3 n)}{2 \cdot 2}$

Step 3.2.3.1.2.3

Rewrite the expression.

$q = \frac{3 f m}{4} + \frac{3 n}{2}$

$q = \frac{3 f m}{4} + \frac{3 n}{2}$

$q = \frac{3 f m}{4} + \frac{3 n}{2}$

$q = \frac{3 f m}{4} + \frac{3 n}{2}$

$q = \frac{3 f m}{4} + \frac{3 n}{2}$

$q = \frac{3 f m}{4} + \frac{3 n}{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$