Evaluate 1-2/3+4/9-8/27

$1 - \frac{2}{3} + \frac{4}{9} - \frac{8}{27}$

Step 1

Find the common denominator.

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

$\frac{1}{1} - \frac{2}{3} + \frac{4}{9} - \frac{8}{27}$

Multiply $\frac{1}{1}$ by $\frac{27}{27}$ .

$\frac{1}{1} \cdot \frac{27}{27} - \frac{2}{3} + \frac{4}{9} - \frac{8}{27}$

Multiply $\frac{1}{1}$ by $\frac{27}{27}$ .

$\frac{27}{27} - \frac{2}{3} + \frac{4}{9} - \frac{8}{27}$

Multiply $\frac{2}{3}$ by $\frac{9}{9}$ .

$\frac{27}{27} - (\frac{2}{3} \cdot \frac{9}{9}) + \frac{4}{9} - \frac{8}{27}$

Multiply $\frac{2}{3}$ by $\frac{9}{9}$ .

$\frac{27}{27} - \frac{2 \cdot 9}{3 \cdot 9} + \frac{4}{9} - \frac{8}{27}$

Multiply $\frac{4}{9}$ by $\frac{3}{3}$ .

$\frac{27}{27} - \frac{2 \cdot 9}{3 \cdot 9} + \frac{4}{9} \cdot \frac{3}{3} - \frac{8}{27}$

Multiply $\frac{4}{9}$ by $\frac{3}{3}$ .

$\frac{27}{27} - \frac{2 \cdot 9}{3 \cdot 9} + \frac{4 \cdot 3}{9 \cdot 3} - \frac{8}{27}$

Multiply $3$ by $9$ .

$\frac{27}{27} - \frac{2 \cdot 9}{27} + \frac{4 \cdot 3}{9 \cdot 3} - \frac{8}{27}$

Reorder the factors of $9 \cdot 3$ .

$\frac{27}{27} - \frac{2 \cdot 9}{27} + \frac{4 \cdot 3}{3 \cdot 9} - \frac{8}{27}$

Multiply $3$ by $9$ .

$\frac{27}{27} - \frac{2 \cdot 9}{27} + \frac{4 \cdot 3}{27} - \frac{8}{27}$

Step 2

Combine the numerators over the common denominator.

$\frac{27 - 2 \cdot 9 + 4 \cdot 3 - 8}{27}$

Step 3

Simplify each term.

Multiply $- 2$ by $9$ .

$\frac{27 - 18 + 4 \cdot 3 - 8}{27}$

Multiply $4$ by $3$ .

$\frac{27 - 18 + 12 - 8}{27}$

Step 4

Simplify by adding and subtracting.

Subtract $18$ from $27$ .

$\frac{9 + 12 - 8}{27}$

Add $9$ and $12$ .

$\frac{21 - 8}{27}$

Subtract $8$ from $21$ .

$\frac{13}{27}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{27}$

Decimal Form:

$0.\overline{481}$

Evaluate 1-2/3+4/9-8/27

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