Compare and order fractions worksheet - Free Printable

Of course! Let's solve the worksheet step by step.

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## Part 1: Comparing Fractions (Use <, =, or >)

We need to compare each pair of fractions and fill in the correct symbol.

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1. `2/3` ___ `5/6`

To compare, find a common denominator. The LCM of 3 and 6 is 6.

- `2/3 = 4/6`
- `5/6 = 5/6`

Since `4/6 < 5/6`, we write:

> `2/3 < 5/6`

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2. `1/2` ___ `2/4`

Simplify `2/4` → `1/2`

So, `1/2 = 2/4`

> `1/2 = 2/4`

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3. `2/5` ___ `5/10`

Simplify `5/10` → `1/2`

Now compare `2/5` and `1/2`.

Common denominator of 5 and 2 is 10.

- `2/5 = 4/10`
- `1/2 = 5/10`

So, `4/10 < 5/10`

> `2/5 < 5/10`

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4. `3/5` ___ `8/15`

Common denominator of 5 and 15 is 15.

- `3/5 = 9/15`
- `8/15 = 8/15`

So, `9/15 > 8/15`

> `3/5 > 8/15`

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✔ Completed Comparisons:

```
2/3 < 5/6
1/2 = 2/4
2/5 < 5/10
3/5 > 8/15
```

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## Part 2: Order these fractions from smallest to biggest

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Group 1: `2/4`, `2/6`, `5/6`, `7/12`

Let’s convert all to a common denominator. LCM of 4, 6, and 12 is 12.

- `2/4 = 6/12`
- `2/6 = 4/12`
- `5/6 = 10/12`
- `7/12 = 7/12`

Now order them by numerator:

→ `4/12` < `6/12` < `7/12` < `10/12`

Which means:

→ `2/6` < `2/4` < `7/12` < `5/6`

✔ Answer:
```
Smallest: 2/6
2/4
7/12
Biggest: 5/6
```

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Group 2: `3/4`, `5/8`, `3/8`, `1/2`

Common denominator of 4, 8, 2 is 8.

- `3/4 = 6/8`
- `5/8 = 5/8`
- `3/8 = 3/8`
- `1/2 = 4/8`

Order numerators:

→ `3/8` < `4/8` < `5/8` < `6/8`

Which means:

→ `3/8` < `1/2` < `5/8` < `3/4`

✔ Answer:
```
Smallest: 3/8
1/2
5/8
Biggest: 3/4
```

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## ✔ Final Answer Summary:

Comparisons:

- `2/3 < 5/6`
- `1/2 = 2/4`
- `2/5 < 5/10`
- `3/5 > 8/15`

Ordering Group 1 (smallest to biggest):

- Smallest: `2/6`
- Then: `2/4`
- Then: `7/12`
- Biggest: `5/6`

Ordering Group 2 (smallest to biggest):

- Smallest: `3/8`
- Then: `1/2`
- Then: `5/8`
- Biggest: `3/4`

You can now fill in the worksheet with these answers! 😊