Math worksheet featuring 12 exercises where students order mixed numbers and fractions from least to greatest.

To solve this worksheet, we need to order sets of mixed numbers and fractions from least to greatest.

Strategy:
1. Compare the whole numbers first. The number with the smallest whole number is the smallest overall.
2. If the whole numbers are the same, compare the fractions.
3. To compare fractions, it helps to find a common denominator or convert them to decimals. Since most denominators here are small (2, 3, 4, 5), finding a common denominator is usually easy.

Let's go through each row step-by-step.

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Row 1: $2\frac{3}{4}, \quad 1\frac{2}{3}, \quad 1\frac{1}{3}, \quad 1\frac{2}{5}$

* Whole numbers: One number has a whole part of 2 ($2\frac{3}{4}$). Three numbers have a whole part of 1.
* So, $2\frac{3}{4}$ is the largest (last).
* Now compare the ones with whole number 1: $1\frac{2}{3}, 1\frac{1}{3}, 1\frac{2}{5}$.
* Compare fractions $\frac{2}{3}, \frac{1}{3}, \frac{2}{5}$.
* $\frac{1}{3}$ is clearly smaller than $\frac{2}{3}$.
* Compare $\frac{1}{3}$ and $\frac{2}{5}$. Common denominator for 3 and 5 is 15.
* $\frac{1}{3} = \frac{5}{15}$
* $\frac{2}{5} = \frac{6}{15}$
* So $\frac{1}{3} < \frac{2}{5}$.
* Compare $\frac{2}{5}$ and $\frac{2}{3}$.
* $\frac{2}{5} = \frac{6}{15}$
* $\frac{2}{3} = \frac{10}{15}$
* So $\frac{2}{5} < \frac{2}{3}$.
* Order of fractions: $\frac{1}{3} < \frac{2}{5} < \frac{2}{3}$.
* Full order: $1\frac{1}{3}, \quad 1\frac{2}{5}, \quad 1\frac{2}{3}, \quad 2\frac{3}{4}$.

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Row 2: $1\frac{1}{2}, \quad 1, \quad 2, \quad 1\frac{1}{3}$

* Whole numbers: We have 1, 2, and mixed numbers starting with 1.
* Smallest is 1 (which is just 1).
* Next, compare numbers with whole part 1: $1\frac{1}{2}$ and $1\frac{1}{3}$.
* Compare $\frac{1}{2}$ and $\frac{1}{3}$.
* $\frac{1}{2} = \frac{3}{6}$, $\frac{1}{3} = \frac{2}{6}$. So $\frac{1}{3} < \frac{1}{2}$.
* Therefore, $1\frac{1}{3} < 1\frac{1}{2}$.
* Largest is 2.
* Full order: $1, \quad 1\frac{1}{3}, \quad 1\frac{1}{2}, \quad 2$.

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Row 3: $2, \quad 1\frac{1}{2}, \quad 1\frac{1}{3}, \quad 1\frac{1}{5}, \quad 1\frac{1}{7}$

* Smallest whole number is 1. Largest is 2.
* So 2 is last.
* Compare the rest: $1\frac{1}{2}, 1\frac{1}{3}, 1\frac{1}{5}, 1\frac{1}{7}$.
* All numerators are 1. When numerators are the same, the fraction with the larger denominator is smaller.
* Denominators: 2, 3, 5, 7.
* Largest denominator is 7 → smallest fraction is $\frac{1}{7}$.
* Next is 5 → $\frac{1}{5}$.
* Next is 3 → $\frac{1}{3}$.
* Smallest denominator is 2 → largest fraction is $\frac{1}{2}$.
* Order: $1\frac{1}{7} < 1\frac{1}{5} < 1\frac{1}{3} < 1\frac{1}{2}$.
* Full order: $1\frac{1}{7}, \quad 1\frac{1}{5}, \quad 1\frac{1}{3}, \quad 1\frac{1}{2}, \quad 2$.

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Row 4: $1\frac{1}{2}, \quad 1\frac{1}{3}, \quad 1\frac{1}{5}, \quad 1\frac{1}{4}, \quad 1\frac{1}{6}$

* All have whole number 1. Compare fractions: $\frac{1}{2}, \frac{1}{3}, \frac{1}{5}, \frac{1}{4}, \frac{1}{6}$.
* Again, all numerators are 1. Larger denominator means smaller value.
* Denominators: 2, 3, 4, 5, 6.
* Order from largest denominator (smallest value) to smallest denominator (largest value):
* 6 → $\frac{1}{6}$
* 5 → $\frac{1}{5}$
* 4 → $\frac{1}{4}$
* 3 → $\frac{1}{3}$
* 2 → $\frac{1}{2}$
* Full order: $1\frac{1}{6}, \quad 1\frac{1}{5}, \quad 1\frac{1}{4}, \quad 1\frac{1}{3}, \quad 1\frac{1}{2}$.

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Row 5: $4\frac{1}{2}, \quad 1\frac{1}{2}, \quad 2\frac{1}{2}, \quad 3\frac{1}{2}, \quad 1\frac{1}{3}$

* Look at whole numbers: 4, 1, 2, 3, 1.
* Smallest whole numbers are 1. We have $1\frac{1}{2}$ and $1\frac{1}{3}$.
* Compare $\frac{1}{2}$ and $\frac{1}{3}$. $\frac{1}{3} < \frac{1}{2}$.
* So $1\frac{1}{3}$ is first, then $1\frac{1}{2}$.
* Next whole number is 2: $2\frac{1}{2}$.
* Next is 3: $3\frac{1}{2}$.
* Largest is 4: $4\frac{1}{2}$.
* Full order: $1\frac{1}{3}, \quad 1\frac{1}{2}, \quad 2\frac{1}{2}, \quad 3\frac{1}{2}, \quad 4\frac{1}{2}$.

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Row 6: $4\frac{1}{2}, \quad 4\frac{1}{3}, \quad 4\frac{1}{4}, \quad 4\frac{1}{5}, \quad 4\frac{1}{6}$

* All have whole number 4. Compare fractions: $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \frac{1}{6}$.
* Numerators are all 1. Larger denominator = smaller fraction.
* Denominators: 2, 3, 4, 5, 6.
* Order: $\frac{1}{6} < \frac{1}{5} < \frac{1}{4} < \frac{1}{3} < \frac{1}{2}$.
* Full order: $4\frac{1}{6}, \quad 4\frac{1}{5}, \quad 4\frac{1}{4}, \quad 4\frac{1}{3}, \quad 4\frac{1}{2}$.

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Row 7: $2\frac{1}{2}, \quad 2\frac{1}{3}, \quad 2\frac{1}{5}, \quad 2\frac{1}{4}, \quad 2\frac{1}{6}$

* All have whole number 2. Compare fractions: $\frac{1}{2}, \frac{1}{3}, \frac{1}{5}, \frac{1}{4}, \frac{1}{6}$.
* Same as Row 6 logic. Larger denominator = smaller fraction.
* Denominators: 2, 3, 4, 5, 6.
* Order: $\frac{1}{6} < \frac{1}{5} < \frac{1}{4} < \frac{1}{3} < \frac{1}{2}$.
* Full order: $2\frac{1}{6}, \quad 2\frac{1}{5}, \quad 2\frac{1}{4}, \quad 2\frac{1}{3}, \quad 2\frac{1}{2}$.

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Row 8: $14\frac{1}{10}, \quad 15\frac{1}{10}, \quad 15\frac{1}{5}, \quad 14\frac{1}{5}, \quad 16\frac{1}{10}$

* Look at whole numbers: 14, 15, 15, 14, 16.
* Smallest whole number is 14. We have $14\frac{1}{10}$ and $14\frac{1}{5}$.
* Compare $\frac{1}{10}$ and $\frac{1}{5}$.
* $\frac{1}{5} = \frac{2}{10}$. So $\frac{1}{10} < \frac{1}{5}$.
* Order: $14\frac{1}{10}, \quad 14\frac{1}{5}$.
* Next whole number is 15. We have $15\frac{1}{10}$ and $15\frac{1}{5}$.
* Same comparison: $\frac{1}{10} < \frac{1}{5}$.
* Order: $15\frac{1}{10}, \quad 15\frac{1}{5}$.
* Largest whole number is 16: $16\frac{1}{10}$.
* Full order: $14\frac{1}{10}, \quad 14\frac{1}{5}, \quad 15\frac{1}{10}, \quad 15\frac{1}{5}, \quad 16\frac{1}{10}$.

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Row 9: $7\frac{1}{2}, \quad 7\frac{1}{3}, \quad 7\frac{1}{5}, \quad 7\frac{1}{4}, \quad 7\frac{1}{6}$

* All have whole number 7. Compare fractions: $\frac{1}{2}, \frac{1}{3}, \frac{1}{5}, \frac{1}{4}, \frac{1}{6}$.
* Same logic as Rows 4, 6, 7. Larger denominator = smaller fraction.
* Denominators: 2, 3, 4, 5, 6.
* Order: $\frac{1}{6} < \frac{1}{5} < \frac{1}{4} < \frac{1}{3} < \frac{1}{2}$.
* Full order: $7\frac{1}{6}, \quad 7\frac{1}{5}, \quad 7\frac{1}{4}, \quad 7\frac{1}{3}, \quad 7\frac{1}{2}$.

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Row 10: $10\frac{1}{10}, \quad 9\frac{1}{10}, \quad 10\frac{1}{5}, \quad 9\frac{1}{5}, \quad 11\frac{1}{10}$

* Look at whole numbers: 10, 9, 10, 9, 11.
* Smallest whole number is 9. We have $9\frac{1}{10}$ and $9\frac{1}{5}$.
* Compare $\frac{1}{10}$ and $\frac{1}{5}$. $\frac{1}{10} < \frac{1}{5}$.
* Order: $9\frac{1}{10}, \quad 9\frac{1}{5}$.
* Next whole number is 10. We have $10\frac{1}{10}$ and $10\frac{1}{5}$.
* Same comparison: $\frac{1}{10} < \frac{1}{5}$.
* Order: $10\frac{1}{10}, \quad 10\frac{1}{5}$.
* Largest whole number is 11: $11\frac{1}{10}$.
* Full order: $9\frac{1}{10}, \quad 9\frac{1}{5}, \quad 10\frac{1}{10}, \quad 10\frac{1}{5}, \quad 11\frac{1}{10}$.

Final Answer:
1. $1\frac{1}{3}, \quad 1\frac{2}{5}, \quad 1\frac{2}{3}, \quad 2\frac{3}{4}$
2. $1, \quad 1\frac{1}{3}, \quad 1\frac{1}{2}, \quad 2$
3. $1\frac{1}{7}, \quad 1\frac{1}{5}, \quad 1\frac{1}{3}, \quad 1\frac{1}{2}, \quad 2$
4. $1\frac{1}{6}, \quad 1\frac{1}{5}, \quad 1\frac{1}{4}, \quad 1\frac{1}{3}, \quad 1\frac{1}{2}$
5. $1\frac{1}{3}, \quad 1\frac{1}{2}, \quad 2\frac{1}{2}, \quad 3\frac{1}{2}, \quad 4\frac{1}{2}$
6. $4\frac{1}{6}, \quad 4\frac{1}{5}, \quad 4\frac{1}{4}, \quad 4\frac{1}{3}, \quad 4\frac{1}{2}$
7. $2\frac{1}{6}, \quad 2\frac{1}{5}, \quad 2\frac{1}{4}, \quad 2\frac{1}{3}, \quad 2\frac{1}{2}$
8. $14\frac{1}{10}, \quad 14\frac{1}{5}, \quad 15\frac{1}{10}, \quad 15\frac{1}{5}, \quad 16\frac{1}{10}$
9. $7\frac{1}{6}, \quad 7\frac{1}{5}, \quad 7\frac{1}{4}, \quad 7\frac{1}{3}, \quad 7\frac{1}{2}$
10. $9\frac{1}{10}, \quad 9\frac{1}{5}, \quad 10\frac{1}{10}, \quad 10\frac{1}{5}, \quad 11\frac{1}{10}$