Basic Math Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Cancel the common factor of $4$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Rewrite the expression.

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

Step 2

Simplify $2 + \frac{1}{3}$ .

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Combine the numerators over the common denominator.

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

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $2$ by $3$ .

$1 + 4 c = \frac{6 + 1}{3}$

Step 2.4.2

Add $6$ and $1$ .

$1 + 4 c = \frac{7}{3}$

Step 3

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

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Step 3.1

Subtract $1$ from both sides of the equation.

$4 c = \frac{7}{3} - 1$

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 c = \frac{7}{3} - 1 \cdot \frac{3}{3}$

Step 3.3

Combine $- 1$ and $\frac{3}{3}$ .

$4 c = \frac{7}{3} + \frac{- 1 \cdot 3}{3}$

Step 3.4

Combine the numerators over the common denominator.

$4 c = \frac{7 - 1 \cdot 3}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 1$ by $3$ .

$4 c = \frac{7 - 3}{3}$

Step 3.5.2

Subtract $3$ from $7$ .

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

Step 4

Divide each term in $4 c = \frac{4}{3}$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 c = \frac{4}{3}$ by $4$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $c$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$c = \frac{4}{3} \cdot \frac{1}{4}$

Step 4.3.2

Cancel the common factor of $4$ .

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Step 4.3.2.1

Cancel the common factor.

$c = \frac{4}{3} \cdot \frac{1}{4}$

Step 4.3.2.2

Rewrite the expression.

$c = \frac{1}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$c = \frac{1}{3}$

Decimal Form:

$c = 0.\overline{3}$