Algebra Examples

$\frac{1}{3} {(1 - \frac{1}{4})}^{2}$

Step 1

Simplify the expression.

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Step 1.1

Write $1$ as a fraction with a common denominator.

$\frac{1}{3} \cdot {(\frac{4}{4} - \frac{1}{4})}^{2}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{1}{3} \cdot {(\frac{4 - 1}{4})}^{2}$

Step 1.3

Subtract $1$ from $4$ .

$\frac{1}{3} \cdot {(\frac{3}{4})}^{2}$

Step 1.4

Apply the product rule to $\frac{3}{4}$ .

$\frac{1}{3} \cdot \frac{3^{2}}{4^{2}}$

Step 2

Combine.

$\frac{1 \cdot 3^{2}}{3 \cdot 4^{2}}$

Step 3

Cancel the common factor of $3^{2}$ and $3$ .

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Step 3.1

Factor $3$ out of $1 \cdot 3^{2}$ .

$\frac{3 (1 \cdot 3)}{3 \cdot 4^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $3 \cdot 4^{2}$ .

$\frac{3 (1 \cdot 3)}{3 (4^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (1 \cdot 3)}{3 \cdot 4^{2}}$

Step 3.2.3

Rewrite the expression.

$\frac{1 \cdot 3}{4^{2}}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $3$ by $1$ .

$\frac{3}{4^{2}}$

Step 4.2

Raise $4$ to the power of $2$ .

$\frac{3}{16}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{16}$

Decimal Form:

$0.1875$