Basic Math Examples

$\frac{a}{2} + \frac{a}{6} = 7$

Step 1

Simplify $\frac{a}{2} + \frac{a}{6}$ .

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Step 1.1

To write $\frac{a}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{a}{2} \cdot \frac{3}{3} + \frac{a}{6} = 7$

Step 1.2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{a}{2}$ by $\frac{3}{3}$ .

$\frac{a \cdot 3}{2 \cdot 3} + \frac{a}{6} = 7$

Step 1.2.2

Multiply $2$ by $3$ .

$\frac{a \cdot 3}{6} + \frac{a}{6} = 7$

Step 1.3

Combine the numerators over the common denominator.

$\frac{a \cdot 3 + a}{6} = 7$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Move $3$ to the left of $a$ .

$\frac{3 \cdot a + a}{6} = 7$

Step 1.4.2

Add $3 a$ and $a$ .

$\frac{4 a}{6} = 7$

Step 1.5

Cancel the common factor of $4$ and $6$ .

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Step 1.5.1

Factor $2$ out of $4 a$ .

$\frac{2 (2 a)}{6} = 7$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $2$ out of $6$ .

$\frac{2 (2 a)}{2 (3)} = 7$

Step 1.5.2.2

Cancel the common factor.

$\frac{2 (2 a)}{2 \cdot 3} = 7$

Step 1.5.2.3

Rewrite the expression.

$\frac{2 a}{3} = 7$

Step 2

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

$\frac{3}{2} \cdot \frac{2 a}{3} = \frac{3}{2} \cdot 7$

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

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Step 3.1.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 a}{3} = \frac{3}{2} \cdot 7$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 a) = \frac{3}{2} \cdot 7$

Step 3.1.1.2

Cancel the common factor of $2$ .

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Step 3.1.1.2.1

Factor $2$ out of $2 a$ .

$\frac{1}{2} (2 (a)) = \frac{3}{2} \cdot 7$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 a) = \frac{3}{2} \cdot 7$

Step 3.1.1.2.3

Rewrite the expression.

$a = \frac{3}{2} \cdot 7$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $\frac{3}{2} \cdot 7$ .

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Step 3.2.1.1

Combine $\frac{3}{2}$ and $7$ .

$a = \frac{3 \cdot 7}{2}$

Step 3.2.1.2

Multiply $3$ by $7$ .

$a = \frac{21}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{21}{2}$

Decimal Form:

$a = 10.5$

Mixed Number Form:

$a = 10 \frac{1}{2}$