Basic Math Examples

$\frac{3}{4} \cdot (6 - 9 m) = (- 9) (3 m - 2)$

Step 1

Simplify $\frac{3}{4} \cdot (6 - 9 m)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{3}{4} \cdot (6 - 9 m) = - 9 (3 m - 2)$

Step 1.2

Simplify by adding zeros.

$\frac{3}{4} \cdot (6 - 9 m) = - 9 (3 m - 2)$

Step 1.3

Apply the distributive property.

$\frac{3}{4} \cdot 6 + \frac{3}{4} (- 9 m) = - 9 (3 m - 2)$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $4$ .

$\frac{3}{2 (2)} \cdot 6 + \frac{3}{4} (- 9 m) = - 9 (3 m - 2)$

Step 1.4.2

Factor $2$ out of $6$ .

$\frac{3}{2 \cdot 2} \cdot (2 \cdot 3) + \frac{3}{4} (- 9 m) = - 9 (3 m - 2)$

Step 1.4.3

Cancel the common factor.

$\frac{3}{2 \cdot 2} \cdot (2 \cdot 3) + \frac{3}{4} (- 9 m) = - 9 (3 m - 2)$

Step 1.4.4

Rewrite the expression.

$\frac{3}{2} \cdot 3 + \frac{3}{4} (- 9 m) = - 9 (3 m - 2)$

Step 1.5

Combine $\frac{3}{2}$ and $3$ .

$\frac{3 \cdot 3}{2} + \frac{3}{4} (- 9 m) = - 9 (3 m - 2)$

Step 1.6

Multiply $3$ by $3$ .

$\frac{9}{2} + \frac{3}{4} (- 9 m) = - 9 (3 m - 2)$

Step 1.7

Multiply $\frac{3}{4} (- 9 m)$ .

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Step 1.7.1

Combine $- 9$ and $\frac{3}{4}$ .

$\frac{9}{2} + \frac{- 9 \cdot 3}{4} m = - 9 (3 m - 2)$

Step 1.7.2

Multiply $- 9$ by $3$ .

$\frac{9}{2} + \frac{- 27}{4} m = - 9 (3 m - 2)$

Step 1.7.3

Combine $\frac{- 27}{4}$ and $m$ .

$\frac{9}{2} + \frac{- 27 m}{4} = - 9 (3 m - 2)$

Step 1.8

Move the negative in front of the fraction.

$\frac{9}{2} - \frac{27 m}{4} = - 9 (3 m - 2)$

Step 2

Simplify $- 9 (3 m - 2)$ .

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Step 2.1

Apply the distributive property.

$\frac{9}{2} - \frac{27 m}{4} = - 9 (3 m) - 9 \cdot - 2$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $3$ by $- 9$ .

$\frac{9}{2} - \frac{27 m}{4} = - 27 m - 9 \cdot - 2$

Step 2.2.2

Multiply $- 9$ by $- 2$ .

$\frac{9}{2} - \frac{27 m}{4} = - 27 m + 18$

Step 3

Move all terms containing $m$ to the left side of the equation.

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Step 3.1

Add $27 m$ to both sides of the equation.

$\frac{9}{2} - \frac{27 m}{4} + 27 m = 18$

Step 3.2

To write $27 m$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9}{2} - \frac{27 m}{4} + 27 m \cdot \frac{4}{4} = 18$

Step 3.3

Combine $27 m$ and $\frac{4}{4}$ .

$\frac{9}{2} - \frac{27 m}{4} + \frac{27 m \cdot 4}{4} = 18$

Step 3.4

Combine the numerators over the common denominator.

$\frac{9}{2} + \frac{- 27 m + 27 m \cdot 4}{4} = 18$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Factor $27 m$ out of $- 27 m + 27 m \cdot 4$ .

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Step 3.5.1.1

Factor $27 m$ out of $- 27 m$ .

$\frac{9}{2} + \frac{27 m (- 1) + 27 m \cdot 4}{4} = 18$

Step 3.5.1.2

Factor $27 m$ out of $27 m \cdot 4$ .

$\frac{9}{2} + \frac{27 m (- 1) + 27 m (4)}{4} = 18$

Step 3.5.1.3

Factor $27 m$ out of $27 m (- 1) + 27 m (4)$ .

$\frac{9}{2} + \frac{27 m (- 1 + 4)}{4} = 18$

Step 3.5.2

Add $- 1$ and $4$ .

$\frac{9}{2} + \frac{27 m \cdot 3}{4} = 18$

Step 3.5.3

Multiply $3$ by $27$ .

$\frac{9}{2} + \frac{81 m}{4} = 18$

Step 4

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

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Step 4.1

Subtract $\frac{9}{2}$ from both sides of the equation.

$\frac{81 m}{4} = 18 - \frac{9}{2}$

Step 4.2

To write $18$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{81 m}{4} = 18 \cdot \frac{2}{2} - \frac{9}{2}$

Step 4.3

Combine $18$ and $\frac{2}{2}$ .

$\frac{81 m}{4} = \frac{18 \cdot 2}{2} - \frac{9}{2}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{81 m}{4} = \frac{18 \cdot 2 - 9}{2}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $18$ by $2$ .

$\frac{81 m}{4} = \frac{36 - 9}{2}$

Step 4.5.2

Subtract $9$ from $36$ .

$\frac{81 m}{4} = \frac{27}{2}$

Step 5

Multiply both sides of the equation by $\frac{4}{81}$ .

$\frac{4}{81} \cdot \frac{81 m}{4} = \frac{4}{81} \cdot \frac{27}{2}$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{4}{81} \cdot \frac{81 m}{4}$ .

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Step 6.1.1.1

Cancel the common factor of $4$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{4}{81} \cdot \frac{81 m}{4} = \frac{4}{81} \cdot \frac{27}{2}$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{81} (81 m) = \frac{4}{81} \cdot \frac{27}{2}$

Step 6.1.1.2

Cancel the common factor of $81$ .

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Step 6.1.1.2.1

Factor $81$ out of $81 m$ .

$\frac{1}{81} (81 (m)) = \frac{4}{81} \cdot \frac{27}{2}$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{81} (81 m) = \frac{4}{81} \cdot \frac{27}{2}$

Step 6.1.1.2.3

Rewrite the expression.

$m = \frac{4}{81} \cdot \frac{27}{2}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{4}{81} \cdot \frac{27}{2}$ .

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Step 6.2.1.1

Cancel the common factor of $2$ .

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Step 6.2.1.1.1

Factor $2$ out of $4$ .

$m = \frac{2 (2)}{81} \cdot \frac{27}{2}$

Step 6.2.1.1.2

Cancel the common factor.

$m = \frac{2 \cdot 2}{81} \cdot \frac{27}{2}$

Step 6.2.1.1.3

Rewrite the expression.

$m = \frac{2}{81} \cdot 27$

Step 6.2.1.2

Cancel the common factor of $27$ .

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Step 6.2.1.2.1

Factor $27$ out of $81$ .

$m = \frac{2}{27 (3)} \cdot 27$

Step 6.2.1.2.2

Cancel the common factor.

$m = \frac{2}{27 \cdot 3} \cdot 27$

Step 6.2.1.2.3

Rewrite the expression.

$m = \frac{2}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$m = \frac{2}{3}$

Decimal Form:

$m = 0.\overline{6}$