Pre-Algebra Examples

$\frac{3}{2} + \frac{9}{4} + \frac{27}{8} + \frac{81}{16} + \frac{243}{32}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{3}{2}$ by $\frac{16}{16}$ .

$\frac{3}{2} \cdot \frac{16}{16} + \frac{9}{4} + \frac{27}{8} + \frac{81}{16} + \frac{243}{32}$

Step 1.2

Multiply $\frac{3}{2}$ by $\frac{16}{16}$ .

$\frac{3 \cdot 16}{2 \cdot 16} + \frac{9}{4} + \frac{27}{8} + \frac{81}{16} + \frac{243}{32}$

Step 1.3

Multiply $\frac{9}{4}$ by $\frac{8}{8}$ .

$\frac{3 \cdot 16}{2 \cdot 16} + \frac{9}{4} \cdot \frac{8}{8} + \frac{27}{8} + \frac{81}{16} + \frac{243}{32}$

Step 1.4

Multiply $\frac{9}{4}$ by $\frac{8}{8}$ .

$\frac{3 \cdot 16}{2 \cdot 16} + \frac{9 \cdot 8}{4 \cdot 8} + \frac{27}{8} + \frac{81}{16} + \frac{243}{32}$

Step 1.5

Multiply $\frac{27}{8}$ by $\frac{4}{4}$ .

$\frac{3 \cdot 16}{2 \cdot 16} + \frac{9 \cdot 8}{4 \cdot 8} + \frac{27}{8} \cdot \frac{4}{4} + \frac{81}{16} + \frac{243}{32}$

Step 1.6

Multiply $\frac{27}{8}$ by $\frac{4}{4}$ .

$\frac{3 \cdot 16}{2 \cdot 16} + \frac{9 \cdot 8}{4 \cdot 8} + \frac{27 \cdot 4}{8 \cdot 4} + \frac{81}{16} + \frac{243}{32}$

Step 1.7

Multiply $\frac{81}{16}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 16}{2 \cdot 16} + \frac{9 \cdot 8}{4 \cdot 8} + \frac{27 \cdot 4}{8 \cdot 4} + \frac{81}{16} \cdot \frac{2}{2} + \frac{243}{32}$

Step 1.8

Multiply $\frac{81}{16}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 16}{2 \cdot 16} + \frac{9 \cdot 8}{4 \cdot 8} + \frac{27 \cdot 4}{8 \cdot 4} + \frac{81 \cdot 2}{16 \cdot 2} + \frac{243}{32}$

Step 1.9

Multiply $2$ by $16$ .

$\frac{3 \cdot 16}{32} + \frac{9 \cdot 8}{4 \cdot 8} + \frac{27 \cdot 4}{8 \cdot 4} + \frac{81 \cdot 2}{16 \cdot 2} + \frac{243}{32}$

Step 1.10

Multiply $4$ by $8$ .

$\frac{3 \cdot 16}{32} + \frac{9 \cdot 8}{32} + \frac{27 \cdot 4}{8 \cdot 4} + \frac{81 \cdot 2}{16 \cdot 2} + \frac{243}{32}$

Step 1.11

Reorder the factors of $8 \cdot 4$ .

$\frac{3 \cdot 16}{32} + \frac{9 \cdot 8}{32} + \frac{27 \cdot 4}{4 \cdot 8} + \frac{81 \cdot 2}{16 \cdot 2} + \frac{243}{32}$

Step 1.12

Multiply $4$ by $8$ .

$\frac{3 \cdot 16}{32} + \frac{9 \cdot 8}{32} + \frac{27 \cdot 4}{32} + \frac{81 \cdot 2}{16 \cdot 2} + \frac{243}{32}$

Step 1.13

Reorder the factors of $16 \cdot 2$ .

$\frac{3 \cdot 16}{32} + \frac{9 \cdot 8}{32} + \frac{27 \cdot 4}{32} + \frac{81 \cdot 2}{2 \cdot 16} + \frac{243}{32}$

Step 1.14

Multiply $2$ by $16$ .

$\frac{3 \cdot 16}{32} + \frac{9 \cdot 8}{32} + \frac{27 \cdot 4}{32} + \frac{81 \cdot 2}{32} + \frac{243}{32}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 \cdot 16 + 9 \cdot 8 + 27 \cdot 4 + 81 \cdot 2 + 243}{32}$

Step 3

Simplify each term.

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Step 3.1

Multiply $3$ by $16$ .

$\frac{48 + 9 \cdot 8 + 27 \cdot 4 + 81 \cdot 2 + 243}{32}$

Step 3.2

Multiply $9$ by $8$ .

$\frac{48 + 72 + 27 \cdot 4 + 81 \cdot 2 + 243}{32}$

Step 3.3

Multiply $27$ by $4$ .

$\frac{48 + 72 + 108 + 81 \cdot 2 + 243}{32}$

Step 3.4

Multiply $81$ by $2$ .

$\frac{48 + 72 + 108 + 162 + 243}{32}$

Step 4

Simplify by adding numbers.

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Step 4.1

Add $48$ and $72$ .

$\frac{120 + 108 + 162 + 243}{32}$

Step 4.2

Add $120$ and $108$ .

$\frac{228 + 162 + 243}{32}$

Step 4.3

Add $228$ and $162$ .

$\frac{390 + 243}{32}$

Step 4.4

Add $390$ and $243$ .

$\frac{633}{32}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{633}{32}$

Decimal Form:

$19.78125$

Mixed Number Form:

$19 \frac{25}{32}$