Basic Math Examples

$\frac{1}{2} \cdot (c - 2) + \frac{1}{4} \cdot (2 c + 1) = \frac{5}{4}$

Step 1

Simplify $\frac{1}{2} \cdot (c - 2) + \frac{1}{4} \cdot (2 c + 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{2} c + \frac{1}{2} \cdot - 2 + \frac{1}{4} \cdot (2 c + 1) = \frac{5}{4}$

Step 1.1.2

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

$\frac{c}{2} + \frac{1}{2} \cdot - 2 + \frac{1}{4} \cdot (2 c + 1) = \frac{5}{4}$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Factor $2$ out of $- 2$ .

$\frac{c}{2} + \frac{1}{2} \cdot (2 (- 1)) + \frac{1}{4} \cdot (2 c + 1) = \frac{5}{4}$

Step 1.1.3.2

Cancel the common factor.

$\frac{c}{2} + \frac{1}{2} \cdot (2 \cdot - 1) + \frac{1}{4} \cdot (2 c + 1) = \frac{5}{4}$

Step 1.1.3.3

Rewrite the expression.

$\frac{c}{2} - 1 + \frac{1}{4} \cdot (2 c + 1) = \frac{5}{4}$

Step 1.1.4

Apply the distributive property.

$\frac{c}{2} - 1 + \frac{1}{4} (2 c) + \frac{1}{4} \cdot 1 = \frac{5}{4}$

Step 1.1.5

Cancel the common factor of $2$ .

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Step 1.1.5.1

Factor $2$ out of $4$ .

$\frac{c}{2} - 1 + \frac{1}{2 (2)} (2 c) + \frac{1}{4} \cdot 1 = \frac{5}{4}$

Step 1.1.5.2

Factor $2$ out of $2 c$ .

$\frac{c}{2} - 1 + \frac{1}{2 (2)} (2 (c)) + \frac{1}{4} \cdot 1 = \frac{5}{4}$

Step 1.1.5.3

Cancel the common factor.

$\frac{c}{2} - 1 + \frac{1}{2 \cdot 2} (2 c) + \frac{1}{4} \cdot 1 = \frac{5}{4}$

Step 1.1.5.4

Rewrite the expression.

$\frac{c}{2} - 1 + \frac{1}{2} c + \frac{1}{4} \cdot 1 = \frac{5}{4}$

Step 1.1.6

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

$\frac{c}{2} - 1 + \frac{c}{2} + \frac{1}{4} \cdot 1 = \frac{5}{4}$

Step 1.1.7

Multiply $\frac{1}{4}$ by $1$ .

$\frac{c}{2} - 1 + \frac{c}{2} + \frac{1}{4} = \frac{5}{4}$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$- 1 + \frac{c + c}{2} + \frac{1}{4} = \frac{5}{4}$

Step 1.2.2

Add $c$ and $c$ .

$- 1 + \frac{2 c}{2} + \frac{1}{4} = \frac{5}{4}$

Step 1.2.3

Cancel the common factor of $2$ .

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Step 1.2.3.1

Cancel the common factor.

$- 1 + \frac{2 c}{2} + \frac{1}{4} = \frac{5}{4}$

Step 1.2.3.2

Divide $c$ by $1$ .

$- 1 + c + \frac{1}{4} = \frac{5}{4}$

Step 1.3

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$c - 1 \cdot \frac{4}{4} + \frac{1}{4} = \frac{5}{4}$

Step 1.4

Combine $- 1$ and $\frac{4}{4}$ .

$c + \frac{- 1 \cdot 4}{4} + \frac{1}{4} = \frac{5}{4}$

Step 1.5

Combine the numerators over the common denominator.

$c + \frac{- 1 \cdot 4 + 1}{4} = \frac{5}{4}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $- 1$ by $4$ .

$c + \frac{- 4 + 1}{4} = \frac{5}{4}$

Step 1.6.2

Add $- 4$ and $1$ .

$c + \frac{- 3}{4} = \frac{5}{4}$

Step 1.7

Move the negative in front of the fraction.

$c - \frac{3}{4} = \frac{5}{4}$

Step 2

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

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Step 2.1

Add $\frac{3}{4}$ to both sides of the equation.

$c = \frac{5}{4} + \frac{3}{4}$

Step 2.2

Combine the numerators over the common denominator.

$c = \frac{5 + 3}{4}$

Step 2.3

Add $5$ and $3$ .

$c = \frac{8}{4}$

Step 2.4

Divide $8$ by $4$ .

$c = 2$