Pre-Algebra Examples

$a = \frac{a + b + c}{3}$

Step 1

Multiply both sides by $3$ .

$a \cdot 3 = \frac{a + b + c}{3} \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

$3 a = \frac{a + b + c}{3} \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$3 a = \frac{a + b + c}{3} \cdot 3$

Step 2.2.1.2

Rewrite the expression.

$3 a = a + b + c$

Step 3

Solve for $a$ .

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Step 3.1

Move all terms containing $a$ to the left side of the equation.

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Step 3.1.1

Subtract $a$ from both sides of the equation.

$3 a - a = b + c$

Step 3.1.2

Subtract $a$ from $3 a$ .

$2 a = b + c$

Step 3.2

Divide each term in $2 a = b + c$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 a = b + c$ by $2$ .

$\frac{2 a}{2} = \frac{b}{2} + \frac{c}{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 a}{2} = \frac{b}{2} + \frac{c}{2}$

Step 3.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{b}{2} + \frac{c}{2}$