4. Mp Se Structure Keiko bakes two sarne-sized pies to sell at a bake sale. She sells $$ \frac{4}{6} $$ of the blueberry pie. She sells $$ \frac{2}{3} $$ of the apple pie. Are the two fractions equivalent? Draw a visual model to support your answ

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Yes, the two fractions $$ \frac{4}{6} $$ and $$ \frac{2}{3} $$ are **equivalent**. This means they represent the same portion of a whole, even though they may look different at first glance.

### **Understanding Equivalent Fractions**

To determine if two fractions are equivalent, you can simplify them to their lowest terms or find a common denominator.

1. **Simplifying $$ \frac{4}{6} $$:**
   $$
   \frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}
   $$
   So, $$ \frac{4}{6} $$ simplifies to $$ \frac{2}{3} $$.

2. **Comparing with $$ \frac{2}{3} $$:**
   Since $$ \frac{4}{6} $$ simplifies to $$ \frac{2}{3} $$, both fractions are equivalent.

### **Visual Model**

Let's use a visual representation with pies divided into equal parts to illustrate this:

#### **Blueberry Pie ($$ \frac{4}{6} $$ sold)**

Imagine the blueberry pie is divided into **6 equal slices**:

```
[ ][ ][ ][ ][ ][ ]
```

Out of these 6 slices, Keiko sells 4:

```
[S][S][S][S][ ][ ]
```

- **S** = Sold slice
- **Empty** = Unsold slice

#### **Apple Pie ($$ \frac{2}{3} $$ sold)**

Now, imagine the apple pie is divided into **3 equal slices**:

```
[ ][ ][ ]
```

Out of these 3 slices, Keiko sells 2:

```
[S][S][ ]
```

#### **Comparing Both Pies**

To easily compare the two fractions, let's adjust the apple pie to also have **6 slices** by multiplying both the numerator and the denominator by 2 (since $$ \frac{2}{3} \times \frac{2}{2} = \frac{4}{6} $$):

```
[ ][ ][ ][ ][ ][ ]
```

Keiko sells 4 out of these 6 slices:

```
[S][S][S][S][ ][ ]
```

Now, both pies visually show that Keiko sold 4 out of 6 slices, confirming that $$ \frac{4}{6} $$ and $$ \frac{2}{3} $$ are indeed equivalent.

### **Conclusion**

Both fractions represent the same portion of their respective pies:

- $$ \frac{4}{6} = \frac{2}{3} $$

Therefore, the amounts sold from both the blueberry and apple pies are equivalent.
Yes, $$ \frac{4}{6} $$ and $$ \frac{2}{3} $$ are equivalent fractions.

4. Mp Se Structure Keiko bakes two sarne-sized pies to sell at a bake sale. She sells \( \frac{4}{6} \) of the blueberry pie. She sells \( \frac{2}{3} \) of the apple pie. Are the two fractions equivalent? Draw a visual model to support your answ

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