This worksheet provides five sets of fractions for students to arrange in ascending order, helping them visualize and compare fractional values.

Let's solve the problem step by step.

The task is to order fractions from smallest to largest. We are given several sets of fractions, and for each set, we need to compare them and arrange them in ascending order.

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🔷 Key Concept: Comparing Fractions

To compare fractions, we can:
1. Convert to decimals (easiest for most students).
2. Find a common denominator.
3. Cross-multiply.

We'll use decimal conversion here for simplicity.

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✔ Problem 1:

Fractions:
- $ \frac{4}{15} $
- $ \frac{7}{15} $
- $ \frac{3}{10} $
- $ \frac{8}{15} $
- $ \frac{13}{15} $

All have denominators of 15 or 10. Let's convert to decimals:

- $ \frac{4}{15} = 0.2667 $
- $ \frac{7}{15} = 0.4667 $
- $ \frac{3}{10} = 0.3 $
- $ \frac{8}{15} = 0.5333 $
- $ \frac{13}{15} = 0.8667 $

Now order them:

- $ 0.2667 $ → $ \frac{4}{15} $
- $ 0.3 $ → $ \frac{3}{10} $
- $ 0.4667 $ → $ \frac{7}{15} $
- $ 0.5333 $ → $ \frac{8}{15} $
- $ 0.8667 $ → $ \frac{13}{15} $

✔ Answer:
Smallest to Largest:
$ \frac{4}{15},\ \frac{3}{10},\ \frac{7}{15},\ \frac{8}{15},\ \frac{13}{15} $

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✔ Problem 2:

Fractions:
- $ \frac{9}{10} $
- $ \frac{3}{4} $
- $ \frac{4}{5} $
- $ \frac{11}{10} $
- $ \frac{2}{5} $

Convert to decimals:

- $ \frac{9}{10} = 0.9 $
- $ \frac{3}{4} = 0.75 $
- $ \frac{4}{5} = 0.8 $
- $ \frac{11}{10} = 1.1 $
- $ \frac{2}{5} = 0.4 $

Order them:

- $ 0.4 $ → $ \frac{2}{5} $
- $ 0.75 $ → $ \frac{3}{4} $
- $ 0.8 $ → $ \frac{4}{5} $
- $ 0.9 $ → $ \frac{9}{10} $
- $ 1.1 $ → $ \frac{11}{10} $

✔ Answer:
Smallest to Largest:
$ \frac{2}{5},\ \frac{3}{4},\ \frac{4}{5},\ \frac{9}{10},\ \frac{11}{10} $

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✔ Problem 3:

Fractions:
- $ \frac{1}{4} $
- $ \frac{4}{5} $
- $ \frac{1}{2} $
- $ \frac{2}{5} $
- $ \frac{3}{5} $

Convert to decimals:

- $ \frac{1}{4} = 0.25 $
- $ \frac{4}{5} = 0.8 $
- $ \frac{1}{2} = 0.5 $
- $ \frac{2}{5} = 0.4 $
- $ \frac{3}{5} = 0.6 $

Order them:

- $ 0.25 $ → $ \frac{1}{4} $
- $ 0.4 $ → $ \frac{2}{5} $
- $ 0.5 $ → $ \frac{1}{2} $
- $ 0.6 $ → $ \frac{3}{5} $
- $ 0.8 $ → $ \frac{4}{5} $

✔ Answer:
Smallest to Largest:
$ \frac{1}{4},\ \frac{2}{5},\ \frac{1}{2},\ \frac{3}{5},\ \frac{4}{5} $

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✔ Problem 4:

Fractions:
- $ \frac{5}{10} $
- $ \frac{3}{10} $
- $ \frac{1}{10} $
- $ \frac{10}{10} $
- $ \frac{2}{10} $

These all have denominator 10, so easy to compare numerators:

- $ \frac{1}{10} = 0.1 $
- $ \frac{2}{10} = 0.2 $
- $ \frac{3}{10} = 0.3 $
- $ \frac{5}{10} = 0.5 $
- $ \frac{10}{10} = 1.0 $

Order:

- $ \frac{1}{10},\ \frac{2}{10},\ \frac{3}{10},\ \frac{5}{10},\ \frac{10}{10} $

✔ Answer:
Smallest to Largest:
$ \frac{1}{10},\ \frac{2}{10},\ \frac{3}{10},\ \frac{5}{10},\ \frac{10}{10} $

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✔ Problem 5:

Fractions:
- $ \frac{1}{2} $
- $ \frac{3}{4} $
- $ \frac{3}{8} $
- $ \frac{1}{8} $
- $ \frac{4}{8} $

Convert to decimals:

- $ \frac{1}{2} = 0.5 $
- $ \frac{3}{4} = 0.75 $
- $ \frac{3}{8} = 0.375 $
- $ \frac{1}{8} = 0.125 $
- $ \frac{4}{8} = 0.5 $ → same as $ \frac{1}{2} $

Wait! $ \frac{4}{8} = \frac{1}{2} $, so it’s equal to $ \frac{1}{2} $

So now list:

- $ \frac{1}{8} = 0.125 $
- $ \frac{3}{8} = 0.375 $
- $ \frac{1}{2} = 0.5 $
- $ \frac{4}{8} = 0.5 $
- $ \frac{3}{4} = 0.75 $

Since $ \frac{1}{2} $ and $ \frac{4}{8} $ are equal, we can list either first.

✔ Answer:
Smallest to Largest:
$ \frac{1}{8},\ \frac{3}{8},\ \frac{1}{2},\ \frac{4}{8},\ \frac{3}{4} $

(Note: $ \frac{1}{2} $ and $ \frac{4}{8} $ are equivalent, so their order doesn't matter.)

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✔ Final Answers:

#### #1:
Smallest: $ \frac{4}{15},\ \frac{3}{10},\ \frac{7}{15},\ \frac{8}{15},\ \frac{13}{15} $
Largest: $ \frac{13}{15} $

#### #2:
Smallest: $ \frac{2}{5},\ \frac{3}{4},\ \frac{4}{5},\ \frac{9}{10},\ \frac{11}{10} $
Largest: $ \frac{11}{10} $

#### #3:
Smallest: $ \frac{1}{4},\ \frac{2}{5},\ \frac{1}{2},\ \frac{3}{5},\ \frac{4}{5} $
Largest: $ \frac{4}{5} $

#### #4:
Smallest: $ \frac{1}{10},\ \frac{2}{10},\ \frac{3}{10},\ \frac{5}{10},\ \frac{10}{10} $
Largest: $ \frac{10}{10} $

#### #5:
Smallest: $ \frac{1}{8},\ \frac{3}{8},\ \frac{1}{2},\ \frac{4}{8},\ \frac{3}{4} $
Largest: $ \frac{3}{4} $

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✔ Summary:
All problems solved by converting to decimals and comparing values. The key is understanding that fractions with larger numerators and smaller denominators tend to be larger, but decimal conversion ensures accuracy.

Let me know if you'd like this explained visually or using common denominators instead!