Basic Math Examples

$3 \frac{2}{3} \cdot (12 - A) = 43$

Step 1

Simplify the left side.

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Step 1.1

Simplify $3 \frac{2}{3} \cdot (12 - A)$ .

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Step 1.1.1

Convert $3 \frac{2}{3}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$(3 + \frac{2}{3}) \cdot (12 - A) = 43$

Step 1.1.1.2

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

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Step 1.1.1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(3 \cdot \frac{3}{3} + \frac{2}{3}) \cdot (12 - A) = 43$

Step 1.1.1.2.2

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

$(\frac{3 \cdot 3}{3} + \frac{2}{3}) \cdot (12 - A) = 43$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 2}{3} \cdot (12 - A) = 43$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $3$ by $3$ .

$\frac{9 + 2}{3} \cdot (12 - A) = 43$

Step 1.1.1.2.4.2

Add $9$ and $2$ .

$\frac{11}{3} \cdot (12 - A) = 43$

Step 1.1.2

Apply the distributive property.

$\frac{11}{3} \cdot 12 + \frac{11}{3} (- A) = 43$

Step 1.1.3

Cancel the common factor of $3$ .

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Step 1.1.3.1

Factor $3$ out of $12$ .

$\frac{11}{3} \cdot (3 (4)) + \frac{11}{3} (- A) = 43$

Step 1.1.3.2

Cancel the common factor.

$\frac{11}{3} \cdot (3 \cdot 4) + \frac{11}{3} (- A) = 43$

Step 1.1.3.3

Rewrite the expression.

$11 \cdot 4 + \frac{11}{3} (- A) = 43$

Step 1.1.4

Multiply $11$ by $4$ .

$44 + \frac{11}{3} (- A) = 43$

Step 1.1.5

Combine $\frac{11}{3}$ and $A$ .

$44 - \frac{11 A}{3} = 43$

Step 2

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

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Step 2.1

Subtract $44$ from both sides of the equation.

$- \frac{11 A}{3} = 43 - 44$

Step 2.2

Subtract $44$ from $43$ .

$- \frac{11 A}{3} = - 1$

Step 3

Multiply both sides of the equation by $- \frac{3}{11}$ .

$- \frac{3}{11} (- \frac{11 A}{3}) = - \frac{3}{11} \cdot - 1$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- \frac{3}{11} (- \frac{11 A}{3})$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{3}{11}$ into the numerator.

$\frac{- 3}{11} (- \frac{11 A}{3}) = - \frac{3}{11} \cdot - 1$

Step 4.1.1.1.2

Move the leading negative in $- \frac{11 A}{3}$ into the numerator.

$\frac{- 3}{11} \cdot \frac{- 11 A}{3} = - \frac{3}{11} \cdot - 1$

Step 4.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{11} \cdot \frac{- 11 A}{3} = - \frac{3}{11} \cdot - 1$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{11} \cdot \frac{- 11 A}{3} = - \frac{3}{11} \cdot - 1$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{11} (- 11 A) = - \frac{3}{11} \cdot - 1$

Step 4.1.1.2

Cancel the common factor of $11$ .

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Step 4.1.1.2.1

Factor $11$ out of $- 11 A$ .

$\frac{- 1}{11} (11 (- A)) = - \frac{3}{11} \cdot - 1$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{11} (11 (- A)) = - \frac{3}{11} \cdot - 1$

Step 4.1.1.2.3

Rewrite the expression.

$- - A = - \frac{3}{11} \cdot - 1$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 A = - \frac{3}{11} \cdot - 1$

Step 4.1.1.3.2

Multiply $A$ by $1$ .

$A = - \frac{3}{11} \cdot - 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- \frac{3}{11} \cdot - 1$ .

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Step 4.2.1.1

Multiply $- 1$ by $- 1$ .

$A = 1 (\frac{3}{11})$

Step 4.2.1.2

Multiply $\frac{3}{11}$ by $1$ .

$A = \frac{3}{11}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$A = \frac{3}{11}$

Decimal Form:

$A = 0.\overline{27}$