Basic Math Examples

$\frac{3}{2} \cdot (2 + a) = \frac{45}{8}$

Step 1

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} (\frac{3}{2} \cdot (2 + a)) = \frac{2}{3} \cdot \frac{45}{8}$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{2}{3} (\frac{3}{2} \cdot (2 + a))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{2}{3} (\frac{3}{2} \cdot 2 + \frac{3}{2} a) = \frac{2}{3} \cdot \frac{45}{8}$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{2}{3} (\frac{3}{2} \cdot 2 + \frac{3}{2} a) = \frac{2}{3} \cdot \frac{45}{8}$

Step 2.1.1.2.2

Rewrite the expression.

$\frac{2}{3} (3 + \frac{3}{2} a) = \frac{2}{3} \cdot \frac{45}{8}$

Step 2.1.1.3

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

$\frac{2}{3} (3 + \frac{3 a}{2}) = \frac{2}{3} \cdot \frac{45}{8}$

Step 2.1.1.4

Apply the distributive property.

$\frac{2}{3} \cdot 3 + \frac{2}{3} \cdot \frac{3 a}{2} = \frac{2}{3} \cdot \frac{45}{8}$

Step 2.1.1.5

Cancel the common factor of $3$ .

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Step 2.1.1.5.1

Cancel the common factor.

$\frac{2}{3} \cdot 3 + \frac{2}{3} \cdot \frac{3 a}{2} = \frac{2}{3} \cdot \frac{45}{8}$

Step 2.1.1.5.2

Rewrite the expression.

$2 + \frac{2}{3} \cdot \frac{3 a}{2} = \frac{2}{3} \cdot \frac{45}{8}$

Step 2.1.1.6

Cancel the common factor of $2$ .

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Step 2.1.1.6.1

Cancel the common factor.

$2 + \frac{2}{3} \cdot \frac{3 a}{2} = \frac{2}{3} \cdot \frac{45}{8}$

Step 2.1.1.6.2

Rewrite the expression.

$2 + \frac{1}{3} (3 a) = \frac{2}{3} \cdot \frac{45}{8}$

Step 2.1.1.7

Cancel the common factor of $3$ .

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Step 2.1.1.7.1

Factor $3$ out of $3 a$ .

$2 + \frac{1}{3} (3 (a)) = \frac{2}{3} \cdot \frac{45}{8}$

Step 2.1.1.7.2

Cancel the common factor.

$2 + \frac{1}{3} (3 a) = \frac{2}{3} \cdot \frac{45}{8}$

Step 2.1.1.7.3

Rewrite the expression.

$2 + a = \frac{2}{3} \cdot \frac{45}{8}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{2}{3} \cdot \frac{45}{8}$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Factor $2$ out of $8$ .

$2 + a = \frac{2}{3} \cdot \frac{45}{2 (4)}$

Step 2.2.1.1.2

Cancel the common factor.

$2 + a = \frac{2}{3} \cdot \frac{45}{2 \cdot 4}$

Step 2.2.1.1.3

Rewrite the expression.

$2 + a = \frac{1}{3} \cdot \frac{45}{4}$

Step 2.2.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.2.1

Factor $3$ out of $45$ .

$2 + a = \frac{1}{3} \cdot \frac{3 (15)}{4}$

Step 2.2.1.2.2

Cancel the common factor.

$2 + a = \frac{1}{3} \cdot \frac{3 \cdot 15}{4}$

Step 2.2.1.2.3

Rewrite the expression.

$2 + a = \frac{15}{4}$

Step 3

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

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Step 3.1

Subtract $2$ from both sides of the equation.

$a = \frac{15}{4} - 2$

Step 3.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$a = \frac{15}{4} - 2 \cdot \frac{4}{4}$

Step 3.3

Combine $- 2$ and $\frac{4}{4}$ .

$a = \frac{15}{4} + \frac{- 2 \cdot 4}{4}$

Step 3.4

Combine the numerators over the common denominator.

$a = \frac{15 - 2 \cdot 4}{4}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 2$ by $4$ .

$a = \frac{15 - 8}{4}$

Step 3.5.2

Subtract $8$ from $15$ .

$a = \frac{7}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{7}{4}$

Decimal Form:

$a = 1.75$

Mixed Number Form:

$a = 1 \frac{3}{4}$