Equivalent Fractions: Number Lines

**Equivalent fractions **are fractions that have the same value, even though they may look different.

π€ Here are some examples of equivalent fractions:

You already learned to find equivalent fractions using area models. π€

π In this lesson, we're going to explore how to recognize equivalent fractions using **number lines.**

Draw a number line that goes from 0 to 1.

Remember that **fractions **are values that are less than 1.

π To show a fraction, first **divide the line **into equal parts.

The **denominator **of a fraction tells about the number of equal parts that a number line should be divided into. π

The **numerator **tells about the parts we're talking about.

π Here are some of the fractions marked on a number line.

These three fractions are equivalent.

Do you want to know why? π€

First, look at the number line model for ^{2}**/**_{4}**.**

Next, look at the number line model for ^{4}**/**_{8}**.**

Then, look at the number line model for ^{3}**/**_{6}**.**

π€ Did you notice something about their lengths?

They're all the **same length!**

It's easy to **recognize equivalent fractions using number lines**** **- just check if their lengths are the same.

Let's find a fraction equivalent to ^{2}**/**_{3}.

π First, draw a number line model for **2/3****.**

π Next, draw an identical number line below it, with the same number of equal parts.

Don't label its parts yet, because you're still going to divide it further.

**Tip**: Before you move on to the next step, make sure that the two lines are of the same length. π

π Now, divide each part into smaller parts.

For our example, we'll divide each part into 2.

What fraction of the number line is colored? π€

That right! π

^{4}**/β**! Because 4 out 6 parts are colored.

π Now, compare the length of the two fractions. What did you notice?

The length of ^{2}**/**_{3}** ****is equal to the length of **^{4}**/**_{6}.

β
This means that ^{2}**/**_{3} is **equivalent** to ^{4}**/**_{6}!

Let's try another one!

Are ^{3}**/**_{4}** ** and ^{4}**/**_{6}** ** equivalent?

π First, draw the number line model for **3/4.**

π Next, draw the number line model for **4/6.**

π Place the second line below the first line.

π Compare the length of **3/4 **and **4/6.**

Are they the same length?

No, they're not!

^{3}**/**_{4} is longer than ^{4}**/**_{6}.

β This means that ^{3}**/**_{4}** **and ^{4}**/**_{6}** **are **NOT** equivalent. π

π Now you know how to recognize equivalent fractions using number lines.

Are you ready for some practice? πͺ

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