To order these fractions from least to greatest, we need to compare their values. Since they have different denominators (bottom numbers), it is easiest to convert each fraction into a decimal or find a common way to compare them.
Here is the step-by-step comparison:
1.
$\frac{1}{12}$: This is a small part of a whole. $1 \div 12 \approx 0.083$
2.
$\frac{2}{9}$: $2 \div 9 \approx 0.222$
3.
$\frac{3}{8}$: $3 \div 8 = 0.375$
4.
$\frac{4}{9}$: $4 \div 9 \approx 0.444$
5.
$\frac{6}{12}$: This simplifies to $\frac{1}{2}$, which is exactly $0.5$
6.
$\frac{2}{6}$: This simplifies to $\frac{1}{3}$, which is $\approx 0.333$. Wait, let me re-check the order between $\frac{3}{8}$ and $\frac{2}{6}$.
* $\frac{2}{6} = \frac{1}{3} \approx 0.333$
* $\frac{3}{8} = 0.375$
* So, $\frac{2}{6}$ is smaller than $\frac{3}{8}$. Let's adjust the list.
Let's re-list all decimals carefully to be sure:
* $\frac{1}{12} \approx 0.083$
* $\frac{2}{9} \approx 0.222$
* $\frac{2}{6} = \frac{1}{3} \approx 0.333$
* $\frac{3}{8} = 0.375$
* $\frac{4}{9} \approx 0.444$
* $\frac{6}{12} = 0.500$
* $\frac{6}{9} = \frac{2}{3} \approx 0.666$
* $\frac{6}{8} = \frac{3}{4} = 0.750$
* $\frac{5}{6} \approx 0.833$
* $\frac{7}{9} \approx 0.777$ ... Wait, let me check $\frac{7}{9}$ vs $\frac{5}{6}$ vs $\frac{6}{8}$.
* $\frac{6}{8} = 0.75$
* $\frac{7}{9} \approx 0.777$
* $\frac{5}{6} \approx 0.833$
* So the order for the larger ones is $\frac{6}{8}$, then $\frac{7}{9}$, then $\frac{5}{6}$.
* $\frac{3}{5} = 0.600$
* $\frac{7}{7} = 1.000$
Let's put them all in order from smallest decimal to largest:
1.
$\frac{1}{12}$ ($\approx 0.08$)
2.
$\frac{2}{9}$ ($\approx 0.22$)
3.
$\frac{2}{6}$ ($\approx 0.33$)
4.
$\frac{3}{8}$ ($0.375$)
5.
$\frac{4}{9}$ ($\approx 0.44$)
6.
$\frac{3}{5}$ ($0.60$) -- *I missed this one in the first quick scan. Let's place it.*
* $\frac{6}{12} = 0.5$
* $\frac{3}{5} = 0.6$
* $\frac{6}{9} = \frac{2}{3} \approx 0.66$
* So, $\frac{6}{12}$ comes before $\frac{3}{5}$, and $\frac{3}{5}$ comes before $\frac{6}{9}$.
Let's restart the final sorted list with all 12 fractions:
1. $\frac{1}{12} \approx 0.083$
2. $\frac{2}{9} \approx 0.222$
3. $\frac{2}{6} \approx 0.333$
4. $\frac{3}{8} = 0.375$
5. $\frac{4}{9} \approx 0.444$
6. $\frac{6}{12} = 0.500$
7. $\frac{3}{5} = 0.600$
8. $\frac{6}{9} \approx 0.666$
9. $\frac{6}{8} = 0.750$
10. $\frac{7}{9} \approx 0.777$
11. $\frac{5}{6} \approx 0.833$
12. $\frac{7}{7} = 1.000$
Final Answer:
The fractions ordered from least to greatest are:
$\frac{1}{12}, \frac{2}{9}, \frac{2}{6}, \frac{3}{8}, \frac{4}{9}, \frac{6}{12}, \frac{3}{5}, \frac{6}{9}, \frac{6}{8}, \frac{7}{9}, \frac{5}{6}, \frac{7}{7}$
Parent Tip: Review the logic above to help your child master the concept of least to greatest fractions worksheet.
