Ordering Fractions

In the last lesson, you learned how to compare fractions.

Let's use this knowledge to **order** fractions, which means sorting them from smallest to largest. π

There are shortcuts to comparing fractions with like numerators and like denominators.

When 2 fractions have the **same numerator**, just **compare denominators**.

The **bigger the denominator**, the **smaller the fraction**.

**Remember:** The bigger the denominator, the more parts the whole is split into, so each piece is smaller.

When 2 fractions have the **same denominator**, just **compare numerators**.

The **bigger the numerator**, the **bigger the fraction**.

If fractions don't have the same numerator or denominator, find **equivalent fractions** that have either the same numerator or denominator.

When **ordering fractions with the same numerators**, look at the denominators and compare them 2 at a time.

π The fraction with the **biggest denominator **is the **smallest.**

π The fraction with the **smallest denominator **is the **biggest.**

Let's look at an example.

Order these fractions fromleasttogreatest:

The fractions have the same numerators, so you just need to compare their denominators.

**1/6 **has the **largest **denominator.

This means **1/6 ****is the smallest fraction**. π

**1/4 **has the **second largest **denominator.

This means **1/4 ****is bigger than ****1/6**. π

**1/2 **has the **smallest **denominator.

This means **1/2 ****is the biggest fraction**. π

We've re-arranged the fractions from the **least **to the **greatest**.

1/6 is the smallest, and 1/2 is the greatest. 1/4 is placed in between the two.

When **ordering fractions with the same denominators**, look at the numerators and compare them 2 at a time.

πThe fraction with the **smallest numerator **is the **smallest.**

πThe fraction with the **largest numerator **is the **biggest.**

Let's learn from an example.

Order these fractions fromleasttogreatest:

The fractions have the same denominators, so you just need to compare their numerators.

**3/8 **has the **smallest** numerator.

This means **3/8 ****is the smallest fraction**. π

**5/8 **has the **second biggest **numerator.

This means **5/8 ****is bigger than ****3/8**. π

**7/8 **has the **biggest **numerator.

This means **7/8 ****is the biggest fraction**. π

This is how we order these fractions from the **least** to the **greatest**:

When **ordering fractions **with **different** numerators and denominators, write the fractions as** equivalent fractions **with **like denominators.**

**Tip:**** Like **means **"the same"**.** Unlike** means "different".

Let's look at an example.

Order these fractions fromleasttogreatest:

π First, find some **equivalent fractions **for each fraction using **multiplication.**

π Next, pick the equivalent fractions that have the **same denominators **for all three fractions.

Be careful when picking the equivalent fractions to compare!

Make sure that they all have the **same denominators**.

**8/12**, **6/12**, and **9/12 **have the same denominators.

Now that we've found **equivalent fractions with matching denominators**, it's easy to compare them!

Just look at the **numerators**:

πThe fraction with the **smallest numerator **is the **least.**

πThe fraction with the **biggest numerator **is the **greatest.**

Can you order these fractions from least to greatest? π€

That's right!

When written in order from **least **to **greatest**, you have **6/12 **< **8/12 **< **9/12**.

Now we know that...

Great job learning how to order fractions!

Are you ready for some practice? πͺ

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