https://file.aiquickdraw.com/mathbot/file/1726840990275dgde1xwk.jpg

Using the square of Fig. AS 5, show that 16 = 3 × (9 – 4) + 1. 

To demonstrate how the equation \(16 = 3 \times (9 - 4) + 1\) corresponds to the image, we will break down the mathematical expression by interpreting the visual structure of the image.

### Step-by-Step Analysis:

1. **Total number of circles**: 
   There are 16 red circles arranged in a 4x4 grid. This total corresponds to the number on the left-hand side of the equation, \(16\).

2. **Decompose the expression \(3 \times (9 - 4) + 1\)**:
   
   - The number 9 refers to a larger group of circles.
   - The number 4 refers to a smaller group that we subtract from 9.
   - The multiplication by 3 suggests repeating a pattern three times.
   - The +1 refers to an additional element after these groupings.

3. **Break down the groups**:
   Let's interpret how the circles are divided visually.

   - The 16 circles can be split into 3 sets of \( (9 - 4) \) circles each. 
   - Subtracting 4 from 9 suggests removing 4 circles from a group of 9, leaving 5 circles.
   - So, each set contains 5 circles.
   - Multiplying by 3 means we have three such sets of 5 circles, which gives us \(3 \times 5 = 15\) circles in total.
   - Adding the remaining 1 circle gives us \(15 + 1 = 16\), matching the total number of circles in the image.

### Conclusion:
Thus, the visual structure of 16 circles in the grid can be decomposed into the mathematical expression \(16 = 3 \times (9 - 4) + 1\), where groups of circles and their arrangement correspond to the numbers used in the equation.

Would you like further clarification or details on this breakdown?

Here are 5 related questions to expand on this:

1. How can this method of breaking down numbers be applied to other grid structures?
2. What are other ways to visually interpret the expression \(3 \times (9 - 4) + 1\)?
3. How would the equation change if the grid had 25 circles instead of 16?
4. Can you create a similar equation for a different arrangement of circles?
5. What is the general form of equations that describe patterns in grids like this?

**Tip**: Visual representations are often helpful in making abstract mathematical concepts easier to understand by breaking them into simpler, more tangible elements.

Using the square of Fig. AS 5, show that 16 = 3 × (9 – 4) + 1.

Explore how to break down the mathematical expression 16 = 3 × (9 – 4) + 1 using a 4x4 grid of red circles. This visual interpretation demonstrates how to apply the distributive property and arithmetic to understand the equation. Suitable for middle school students in Grades 6-8.

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