Equivalent Fractions: Area Models

π In the previous lessons, you learned how to draw fraction models.Β Β

π€ You can use** bar models**,** area models**,** number lines**, or** set models** to draw fractions.Β

**π Drawing fraction models** can help you see whether fractions are** equivalent**.

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

π€ These fractions are actually equivalent. π

But how can they be **equivalent **if they all look different? π£

π Let's draw the** area models** for each of the fractions.

Do you remember how to draw fraction **area models**? π€

That's right!

π The first step is to draw a shape that you desire.

π Next, divide the shape into equal parts.

The **denominator **of the fraction tells you how many equal parts the shape must be divided into.

π The last step is to color or shade the parts that show the fraction.

The **numerator **tells you how many parts must be colored or shaded.

β
This is the area model for the fraction **2/4**.

β
This is the area model for the fraction **4/8**.

β
This is the area model for the fraction **3/6**.

π€ Did you notice how the** area model** for each of the fractions** are the same**?

π€ Can you think of another fraction that will be equivalent to these fractions?

π€ Study the models carefully.

For each of these models, what fraction of the squares are colored?

That's right! π

**1/2** of each model is colored. π

That means the fraction **1/2** is **also equivalent **to these fractions!

So how do you find an **equivalent fraction**? π€

Let's try to find a fraction that is equivalent to **2/3**.

π First, let's draw an** area mode**l for** 2/**3.

π Next, draw an identical model.

π€ The other model also shows the fraction** 2/3**.

π To make an** equivalent fraction**, divide each part into equal parts.

β Let's divide each part of the identical model into 2 equal parts.

What fraction does the identical model show now? π€

That's right!

π The identical model is divided into** 6 equal parts** and** 4 parts are colored**.

So the **identical model **shows the fraction **4/6**. π

Here we can see that **2/4 = 4/6**_{ }because the two fractions show the **same part of a whole**.

Let's try this example. π

Find a fraction equivalent to3/4.

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

π Next, draw an identical model.

π Now divide each part of the identical model into 2 equal parts.

What fraction does the identical model show now? π€

That's right! π

π The identical model is divided into** 8 equal parts and 6 parts are colored**.

That means the **identical model **shows the fraction **6/8**. π

β
Therefore, **3/4 = 6/8**.

π€ What about if we divide each part of the identical model into 4 equal parts?

What fraction does the identical model show now? π€

π That's right!

π The identical model is divided into** 16 equal parts and 12 parts are colored**.

So it shows the fraction **12/16**. π

β
That means **3/4 = 12/16**.

π€ We can see that:

These are all **equivalent fractions!**

**Equivalent fractions **may not look the same but as long as they refer to the **same value**, then they are **equivalent**.

π€ Tip: If you multiply the** numerator** and the** denominator** by the same number, you'll get an equivalent fraction!Β

Great! π

Are you ready for some practice? πͺ

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