Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$5-\frac{10}{3}+\frac{20}{9}-\frac{40}{27}$$

Answer

mixed(2,11/27)

Solution


Find the Least Common Denominator (LCD) of \(\frac{10}{3},\frac{20}{9},\frac{40}{27}\). In other words, find the Least Common Multiple (LCM) of \(3,9,27\).
LCD = \(27\)
Make the denominators the same as the LCD.
\[5\times \frac{27}{27}-\frac{10\times 9}{3\times 9}+\frac{20\times 3}{9\times 3}-\frac{40}{27}\]
Simplify. Denominators are now the same.
\[\frac{135}{27}-\frac{90}{27}+\frac{60}{27}-\frac{40}{27}\]
Join the denominators.
\[\frac{135-90+60-40}{27}\]
Simplify.
\[\frac{65}{27}\]
Convert to mixed fraction.
\[2\frac{11}{27}\]

Decimal Form: 2.407407

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