Question

math up
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representing, comparing, and ordering fractions (co

1. order the fractions in each set from least to greatest.

a) \\(\frac{3}{5}\\) \\(\frac{4}{10}\\) \\(\frac{1}{12}\\) \\(\frac{8}{9}\\)
b) \\(\frac{8}{10}\\) \\(\frac{8}{9}\\) \\(\frac{3}{8}\\) \\(\frac{2}{3}\\)

Explanation:

Part (a)

Step1: Find a common denominator

The denominators are 5, 10, 12, 9. The least common multiple (LCM) of 5, 10, 12, 9 is 180.

Step2: Convert each fraction to have denominator 180

• For $\frac{3}{5}$: $\frac{3\times36}{5\times36}=\frac{108}{180}$
• For $\frac{4}{10}$: $\frac{4\times18}{10\times18}=\frac{72}{180}$
• For $\frac{1}{12}$: $\frac{1\times15}{12\times15}=\frac{15}{180}$
• For $\frac{8}{9}$: $\frac{8\times20}{9\times20}=\frac{160}{180}$

Step3: Order the fractions by numerator

Now we have $\frac{15}{180}$ ($\frac{1}{12}$), $\frac{72}{180}$ ($\frac{4}{10}$), $\frac{108}{180}$ ($\frac{3}{5}$), $\frac{160}{180}$ ($\frac{8}{9}$). So the order from least to greatest is $\frac{1}{12}$, $\frac{4}{10}$, $\frac{3}{5}$, $\frac{8}{9}$.

Part (b)

Step1: Simplify or find common denominator

• $\frac{8}{10}=\frac{4}{5}=0.8$
• $\frac{8}{9}\approx0.888...$
• $\frac{3}{8}=0.375$
• $\frac{2}{3}\approx0.666...$

Step2: Order by decimal value

From least to greatest: $0.375$ ($\frac{3}{8}$), $0.666...$ ($\frac{2}{3}$), $0.8$ ($\frac{8}{10}$), $0.888...$ ($\frac{8}{9}$). So the order is $\frac{3}{8}$, $\frac{2}{3}$, $\frac{8}{10}$, $\frac{8}{9}$.

Answer:

a) $\frac{1}{12}$, $\frac{4}{10}$, $\frac{3}{5}$, $\frac{8}{9}$
b) $\frac{3}{8}$, $\frac{2}{3}$, $\frac{8}{10}$, $\frac{8}{9}$