Order Fractions and Mixed Numbers worksheet - Free Printable

Let's solve each of the four problems step by step. We'll compare and order the given fractions and mixed numbers.

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Problem 1: Order from least to greatest

Given:
- $ 1\frac{1}{2} $
- $ 1\frac{1}{8} $
- $ \frac{8}{7} $
- $ 1\frac{1}{5} $

#### Step 1: Convert all to improper fractions or decimals for comparison.

1. $ 1\frac{1}{2} = \frac{3}{2} = 1.5 $
2. $ 1\frac{1}{8} = \frac{9}{8} = 1.125 $
3. $ \frac{8}{7} \approx 1.1429 $
4. $ 1\frac{1}{5} = \frac{6}{5} = 1.2 $

Now compare decimal values:
- $ 1.125 $ → $ 1\frac{1}{8} $
- $ 1.1429 $ → $ \frac{8}{7} $
- $ 1.2 $ → $ 1\frac{1}{5} $
- $ 1.5 $ → $ 1\frac{1}{2} $

#### ✔ Order from least to greatest:
$$
1\frac{1}{8},\ \frac{8}{7},\ 1\frac{1}{5},\ 1\frac{1}{2}
$$

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Problem 2: Order from least to greatest

Given:
- $ 2\frac{3}{4} $
- $ 2\frac{1}{2} $
- $ \frac{12}{5} $
- $ 2\frac{5}{6} $

#### Step 1: Convert to decimals.

1. $ 2\frac{3}{4} = 2 + 0.75 = 2.75 $
2. $ 2\frac{1}{2} = 2 + 0.5 = 2.5 $
3. $ \frac{12}{5} = 2.4 $
4. $ 2\frac{5}{6} = 2 + \frac{5}{6} \approx 2 + 0.833 = 2.833 $

Now list in increasing order:
- $ 2.4 $ → $ \frac{12}{5} $
- $ 2.5 $ → $ 2\frac{1}{2} $
- $ 2.75 $ → $ 2\frac{3}{4} $
- $ 2.833 $ → $ 2\frac{5}{6} $

#### ✔ Order from least to greatest:
$$
\frac{12}{5},\ 2\frac{1}{2},\ 2\frac{3}{4},\ 2\frac{5}{6}
$$

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Problem 3: Order from greatest to least

Given:
- $ 1\frac{2}{10} $
- $ 1\frac{11}{12} $
- $ \frac{4}{4} $
- $ \frac{9}{5} $

#### Step 1: Simplify and convert to decimals.

1. $ 1\frac{2}{10} = 1 + 0.2 = 1.2 $
2. $ 1\frac{11}{12} = 1 + \frac{11}{12} \approx 1 + 0.9167 = 1.9167 $
3. $ \frac{4}{4} = 1 $
4. $ \frac{9}{5} = 1.8 $

Now list in descending order:
- $ 1.9167 $ → $ 1\frac{11}{12} $
- $ 1.8 $ → $ \frac{9}{5} $
- $ 1.2 $ → $ 1\frac{2}{10} $
- $ 1 $ → $ \frac{4}{4} $

#### ✔ Order from greatest to least:
$$
1\frac{11}{12},\ \frac{9}{5},\ 1\frac{2}{10},\ \frac{4}{4}
$$

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Problem 4: Order from greatest to least

Given:
- $ 2\frac{2}{3} $
- $ 2\frac{6}{8} $
- $ \frac{8}{6} $
- $ \frac{6}{6} $

#### Step 1: Simplify and convert to decimals.

1. $ 2\frac{2}{3} = 2 + \frac{2}{3} \approx 2 + 0.6667 = 2.6667 $
2. $ 2\frac{6}{8} = 2 + \frac{3}{4} = 2 + 0.75 = 2.75 $
3. $ \frac{8}{6} = \frac{4}{3} \approx 1.333 $
4. $ \frac{6}{6} = 1 $

Now list in descending order:
- $ 2.75 $ → $ 2\frac{6}{8} $
- $ 2.6667 $ → $ 2\frac{2}{3} $
- $ 1.333 $ → $ \frac{8}{6} $
- $ 1 $ → $ \frac{6}{6} $

#### ✔ Order from greatest to least:
$$
2\frac{6}{8},\ 2\frac{2}{3},\ \frac{8}{6},\ \frac{6}{6}
$$

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✔ Final Answers:

1. Least to greatest:
$ 1\frac{1}{8},\ \frac{8}{7},\ 1\frac{1}{5},\ 1\frac{1}{2} $

2. Least to greatest:
$ \frac{12}{5},\ 2\frac{1}{2},\ 2\frac{3}{4},\ 2\frac{5}{6} $

3. Greatest to least:
$ 1\frac{11}{12},\ \frac{9}{5},\ 1\frac{2}{10},\ \frac{4}{4} $

4. Greatest to least:
$ 2\frac{6}{8},\ 2\frac{2}{3},\ \frac{8}{6},\ \frac{6}{6} $

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Let me know if you'd like this formatted as a printable answer sheet!