Algebra Examples

$\frac{1}{3} + \frac{1}{6} + \frac{1}{12} + \frac{1}{24} + \frac{1}{48}$

Step 1

Find the common denominator.

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Step 1.1

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

$\frac{1}{3} \cdot \frac{16}{16} + \frac{1}{6} + \frac{1}{12} + \frac{1}{24} + \frac{1}{48}$

Step 1.2

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

$\frac{16}{3 \cdot 16} + \frac{1}{6} + \frac{1}{12} + \frac{1}{24} + \frac{1}{48}$

Step 1.3

Multiply $\frac{1}{6}$ by $\frac{8}{8}$ .

$\frac{16}{3 \cdot 16} + \frac{1}{6} \cdot \frac{8}{8} + \frac{1}{12} + \frac{1}{24} + \frac{1}{48}$

Step 1.4

Multiply $\frac{1}{6}$ by $\frac{8}{8}$ .

$\frac{16}{3 \cdot 16} + \frac{8}{6 \cdot 8} + \frac{1}{12} + \frac{1}{24} + \frac{1}{48}$

Step 1.5

Multiply $\frac{1}{12}$ by $\frac{4}{4}$ .

$\frac{16}{3 \cdot 16} + \frac{8}{6 \cdot 8} + \frac{1}{12} \cdot \frac{4}{4} + \frac{1}{24} + \frac{1}{48}$

Step 1.6

Multiply $\frac{1}{12}$ by $\frac{4}{4}$ .

$\frac{16}{3 \cdot 16} + \frac{8}{6 \cdot 8} + \frac{4}{12 \cdot 4} + \frac{1}{24} + \frac{1}{48}$

Step 1.7

Multiply $\frac{1}{24}$ by $\frac{2}{2}$ .

$\frac{16}{3 \cdot 16} + \frac{8}{6 \cdot 8} + \frac{4}{12 \cdot 4} + \frac{1}{24} \cdot \frac{2}{2} + \frac{1}{48}$

Step 1.8

Multiply $\frac{1}{24}$ by $\frac{2}{2}$ .

$\frac{16}{3 \cdot 16} + \frac{8}{6 \cdot 8} + \frac{4}{12 \cdot 4} + \frac{2}{24 \cdot 2} + \frac{1}{48}$

Step 1.9

Multiply $3$ by $16$ .

$\frac{16}{48} + \frac{8}{6 \cdot 8} + \frac{4}{12 \cdot 4} + \frac{2}{24 \cdot 2} + \frac{1}{48}$

Step 1.10

Multiply $6$ by $8$ .

$\frac{16}{48} + \frac{8}{48} + \frac{4}{12 \cdot 4} + \frac{2}{24 \cdot 2} + \frac{1}{48}$

Step 1.11

Reorder the factors of $12 \cdot 4$ .

$\frac{16}{48} + \frac{8}{48} + \frac{4}{4 \cdot 12} + \frac{2}{24 \cdot 2} + \frac{1}{48}$

Step 1.12

Multiply $4$ by $12$ .

$\frac{16}{48} + \frac{8}{48} + \frac{4}{48} + \frac{2}{24 \cdot 2} + \frac{1}{48}$

Step 1.13

Reorder the factors of $24 \cdot 2$ .

$\frac{16}{48} + \frac{8}{48} + \frac{4}{48} + \frac{2}{2 \cdot 24} + \frac{1}{48}$

Step 1.14

Multiply $2$ by $24$ .

$\frac{16}{48} + \frac{8}{48} + \frac{4}{48} + \frac{2}{48} + \frac{1}{48}$

Step 2

Combine the numerators over the common denominator.

$\frac{16 + 8 + 4 + 2 + 1}{48}$

Step 3

Simplify by adding numbers.

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Step 3.1

Add $16$ and $8$ .

$\frac{24 + 4 + 2 + 1}{48}$

Step 3.2

Add $24$ and $4$ .

$\frac{28 + 2 + 1}{48}$

Step 3.3

Add $28$ and $2$ .

$\frac{30 + 1}{48}$

Step 3.4

Add $30$ and $1$ .

$\frac{31}{48}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{31}{48}$

Decimal Form:

$0.6458\overline{3}$