Basic Math Examples

$\frac{3}{4} c = \frac{1}{12} c + 2$

Step 1

Simplify $\frac{3}{4} c$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{3}{4} c = \frac{1}{12} c + 2$

Step 1.2

Simplify by adding zeros.

$\frac{3}{4} c = \frac{1}{12} c + 2$

Step 1.3

Combine $\frac{3}{4}$ and $c$ .

$\frac{3 c}{4} = \frac{1}{12} c + 2$

Step 2

Combine $\frac{1}{12}$ and $c$ .

$\frac{3 c}{4} = \frac{c}{12} + 2$

Step 3

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

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Step 3.1

Subtract $\frac{c}{12}$ from both sides of the equation.

$\frac{3 c}{4} - \frac{c}{12} = 2$

Step 3.2

To write $\frac{3 c}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 c}{4} \cdot \frac{3}{3} - \frac{c}{12} = 2$

Step 3.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{3 c}{4}$ by $\frac{3}{3}$ .

$\frac{3 c \cdot 3}{4 \cdot 3} - \frac{c}{12} = 2$

Step 3.3.2

Multiply $4$ by $3$ .

$\frac{3 c \cdot 3}{12} - \frac{c}{12} = 2$

Step 3.4

Combine the numerators over the common denominator.

$\frac{3 c \cdot 3 - c}{12} = 2$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Factor $c$ out of $3 c \cdot 3 - c$ .

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Step 3.5.1.1

Factor $c$ out of $3 c \cdot 3$ .

$\frac{c (3 \cdot 3) - c}{12} = 2$

Step 3.5.1.2

Factor $c$ out of $- c$ .

$\frac{c (3 \cdot 3) + c \cdot - 1}{12} = 2$

Step 3.5.1.3

Factor $c$ out of $c (3 \cdot 3) + c \cdot - 1$ .

$\frac{c (3 \cdot 3 - 1)}{12} = 2$

Step 3.5.2

Multiply $3$ by $3$ .

$\frac{c (9 - 1)}{12} = 2$

Step 3.5.3

Subtract $1$ from $9$ .

$\frac{c \cdot 8}{12} = 2$

Step 3.6

Cancel the common factor of $8$ and $12$ .

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Step 3.6.1

Factor $4$ out of $c \cdot 8$ .

$\frac{4 (c \cdot 2)}{12} = 2$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $4$ out of $12$ .

$\frac{4 (c \cdot 2)}{4 (3)} = 2$

Step 3.6.2.2

Cancel the common factor.

$\frac{4 (c \cdot 2)}{4 \cdot 3} = 2$

Step 3.6.2.3

Rewrite the expression.

$\frac{c \cdot 2}{3} = 2$

Step 3.7

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

$\frac{2 c}{3} = 2$

Step 4

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

$\frac{3}{2} \cdot \frac{2 c}{3} = \frac{3}{2} \cdot 2$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

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

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 c}{3} = \frac{3}{2} \cdot 2$

Step 5.1.1.1.2

Rewrite the expression.

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

Step 5.1.1.2

Cancel the common factor of $2$ .

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Step 5.1.1.2.1

Factor $2$ out of $2 c$ .

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

Step 5.1.1.2.2

Cancel the common factor.

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

Step 5.1.1.2.3

Rewrite the expression.

$c = \frac{3}{2} \cdot 2$

Step 5.2

Simplify the right side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$c = \frac{3}{2} \cdot 2$

Step 5.2.1.2

Rewrite the expression.

$c = 3$