Basic Math Examples

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

Step 1

Convert $1 \frac{1}{3}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

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

Step 1.2

Add $1$ and $\frac{1}{3}$ .

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $3$ and $1$ .

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

Step 2

Simplify each term.

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Step 2.1

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

$\frac{1}{16} + \frac{1}{4} \cdot \frac{4}{3}$

Step 2.2

Cancel the common factor of $4$ .

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Step 2.2.1

Cancel the common factor.

$\frac{1}{16} + \frac{1}{4} \cdot \frac{4}{3}$

Step 2.2.2

Rewrite the expression.

$\frac{1}{16} + \frac{1}{3}$

Step 3

To write $\frac{1}{16}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{16} \cdot \frac{3}{3} + \frac{1}{3}$

Step 4

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\frac{1}{16} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{16}{16}$

Step 5

Write each expression with a common denominator of $48$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{1}{16}$ by $\frac{3}{3}$ .

$\frac{3}{16 \cdot 3} + \frac{1}{3} \cdot \frac{16}{16}$

Step 5.2

Multiply $16$ by $3$ .

$\frac{3}{48} + \frac{1}{3} \cdot \frac{16}{16}$

Step 5.3

Multiply $\frac{1}{3}$ by $\frac{16}{16}$ .

$\frac{3}{48} + \frac{16}{3 \cdot 16}$

Step 5.4

Multiply $3$ by $16$ .

$\frac{3}{48} + \frac{16}{48}$

Step 6

Combine the numerators over the common denominator.

$\frac{3 + 16}{48}$

Step 7

Add $3$ and $16$ .

$\frac{19}{48}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{48}$

Decimal Form:

$0.3958\overline{3}$