Question
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Draw a model to show that \( x \div 3 \) is the same as \( \frac{x}{3} \)

Ask by Nguyen Burns. in the United States
Feb 26,2025

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Tutor-Verified Answer

Answer

To show that \( x \div 3 \) is the same as \( \frac{x}{3} \), imagine you have \( x \) blocks. If you divide them into groups of 3, the number of groups is \( \frac{x}{3} \). This means \( x \div 3 \) and \( \frac{x}{3} \) both represent the same division.

Solution

To show that \( x \div 3 \) is the same as \( \frac{x}{3} \), we can use a model with blocks. Let's consider a model where we have a certain number of blocks, represented by the variable \( x \). We want to divide these blocks into groups of 3. 1. Start with the blocks represented by \( x \). 2. Divide the blocks into groups of 3 by placing them in a row. 3. Count the number of groups of 3 blocks. The number of groups of 3 blocks is represented by \( \frac{x}{3} \). Therefore, \( x \div 3 \) is the same as \( \frac{x}{3} \) because both represent dividing the blocks into groups of 3.

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Extra Insights

Imagine you have a box filled with \( x \) candies, and you want to share them equally with 3 friends. To visualize this, you could draw a large box labeled \( x \) representing all your candies. Next, create three smaller boxes that represent each friend. Now, you divide the large box of \( x \) candies into the three smaller boxes. Each friend gets an equal portion of candies from the original box, which illustrates that when you divide \( x \) by 3 (or \( x \div 3 \)), you can also express this mathematically as \( \frac{x}{3} \). Both expressions result in the same amount of candies per friend, proving they are two sides of the same coin! To make it even more engaging, you could use different colors for the candies and label each small box with "Friend 1", "Friend 2", and "Friend 3", showcasing how division works in a fun and tasty context!

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