Basic Math Examples

$\frac{1}{2} a + a = 24$

Step 1

Simplify $\frac{1}{2} a + a$ .

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Step 1.1

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

$\frac{a}{2} + a = 24$

Step 1.2

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

$\frac{a}{2} + a \cdot \frac{2}{2} = 24$

Step 1.3

Simplify terms.

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Step 1.3.1

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

$\frac{a}{2} + \frac{a \cdot 2}{2} = 24$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{a + a \cdot 2}{2} = 24$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Move $2$ to the left of $a$ .

$\frac{a + 2 \cdot a}{2} = 24$

Step 1.4.2

Add $a$ and $2 a$ .

$\frac{3 a}{2} = 24$

Step 2

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

$\frac{2}{3} \cdot \frac{3 a}{2} = \frac{2}{3} \cdot 24$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{2}{3} \cdot \frac{3 a}{2}$ .

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Step 3.1.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 a}{2} = \frac{2}{3} \cdot 24$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 a) = \frac{2}{3} \cdot 24$

Step 3.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.2.1

Factor $3$ out of $3 a$ .

$\frac{1}{3} (3 (a)) = \frac{2}{3} \cdot 24$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 a) = \frac{2}{3} \cdot 24$

Step 3.1.1.2.3

Rewrite the expression.

$a = \frac{2}{3} \cdot 24$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{2}{3} \cdot 24$ .

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Step 3.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Factor $3$ out of $24$ .

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

Step 3.2.1.1.2

Cancel the common factor.

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

Step 3.2.1.1.3

Rewrite the expression.

$a = 2 \cdot 8$

Step 3.2.1.2

Multiply $2$ by $8$ .

$a = 16$