Basic Math Examples

$12 (\frac{1}{2} m - \frac{1}{4} y) = 12 (\frac{9}{4})$

Step 1

Simplify $12 (\frac{1}{2} m - \frac{1}{4} y)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{2}$ and $m$ .

$12 (\frac{m}{2} - \frac{1}{4} y) = 12 (\frac{9}{4})$

Step 1.1.2

Combine $y$ and $\frac{1}{4}$ .

$12 (\frac{m}{2} - \frac{y}{4}) = 12 (\frac{9}{4})$

Step 1.2

Simplify terms.

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Step 1.2.1

Apply the distributive property.

$12 \frac{m}{2} + 12 (- \frac{y}{4}) = 12 (\frac{9}{4})$

Step 1.2.2

Cancel the common factor of $2$ .

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Step 1.2.2.1

Factor $2$ out of $12$ .

$2 (6) \frac{m}{2} + 12 (- \frac{y}{4}) = 12 (\frac{9}{4})$

Step 1.2.2.2

Cancel the common factor.

$2 \cdot 6 \frac{m}{2} + 12 (- \frac{y}{4}) = 12 (\frac{9}{4})$

Step 1.2.2.3

Rewrite the expression.

$6 m + 12 (- \frac{y}{4}) = 12 (\frac{9}{4})$

Step 1.2.3

Cancel the common factor of $4$ .

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Step 1.2.3.1

Move the leading negative in $- \frac{y}{4}$ into the numerator.

$6 m + 12 \frac{- y}{4} = 12 (\frac{9}{4})$

Step 1.2.3.2

Factor $4$ out of $12$ .

$6 m + 4 (3) \frac{- y}{4} = 12 (\frac{9}{4})$

Step 1.2.3.3

Cancel the common factor.

$6 m + 4 \cdot 3 \frac{- y}{4} = 12 (\frac{9}{4})$

Step 1.2.3.4

Rewrite the expression.

$6 m + 3 (- y) = 12 (\frac{9}{4})$

Step 1.2.4

Multiply $- 1$ by $3$ .

$6 m - 3 y = 12 (\frac{9}{4})$

Step 2

Simplify $12 (\frac{9}{4})$ .

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Step 2.1

Cancel the common factor of $4$ .

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Step 2.1.1

Factor $4$ out of $12$ .

$6 m - 3 y = 4 (3) \frac{9}{4}$

Step 2.1.2

Cancel the common factor.

$6 m - 3 y = 4 \cdot 3 \frac{9}{4}$

Step 2.1.3

Rewrite the expression.

$6 m - 3 y = 3 \cdot 9$

Step 2.2

Multiply $3$ by $9$ .

$6 m - 3 y = 27$

Step 3

Add $3 y$ to both sides of the equation.

$6 m = 27 + 3 y$

Step 4

Divide each term in $6 m = 27 + 3 y$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 m = 27 + 3 y$ by $6$ .

$\frac{6 m}{6} = \frac{27}{6} + \frac{3 y}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 m}{6} = \frac{27}{6} + \frac{3 y}{6}$

Step 4.2.1.2

Divide $m$ by $1$ .

$m = \frac{27}{6} + \frac{3 y}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Cancel the common factor of $27$ and $6$ .

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Step 4.3.1.1.1

Factor $3$ out of $27$ .

$m = \frac{3 (9)}{6} + \frac{3 y}{6}$

Step 4.3.1.1.2

Cancel the common factors.

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Step 4.3.1.1.2.1

Factor $3$ out of $6$ .

$m = \frac{3 \cdot 9}{3 \cdot 2} + \frac{3 y}{6}$

Step 4.3.1.1.2.2

Cancel the common factor.

$m = \frac{3 \cdot 9}{3 \cdot 2} + \frac{3 y}{6}$

Step 4.3.1.1.2.3

Rewrite the expression.

$m = \frac{9}{2} + \frac{3 y}{6}$

Step 4.3.1.2

Cancel the common factor of $3$ and $6$ .

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Step 4.3.1.2.1

Factor $3$ out of $3 y$ .

$m = \frac{9}{2} + \frac{3 (y)}{6}$

Step 4.3.1.2.2

Cancel the common factors.

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Step 4.3.1.2.2.1

Factor $3$ out of $6$ .

$m = \frac{9}{2} + \frac{3 y}{3 \cdot 2}$

Step 4.3.1.2.2.2

Cancel the common factor.

$m = \frac{9}{2} + \frac{3 y}{3 \cdot 2}$

Step 4.3.1.2.2.3

Rewrite the expression.

$m = \frac{9}{2} + \frac{y}{2}$