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:

$A = 0.\overline{27}$