https://file.aiquickdraw.com/mathbot/file/1726016303236d9ttb03s.jpg

Write three different expressions for the total number of curlicues in Figure 4.20. Each expression should involve only the following: the numbers 2, 3, 5, and 8; the multiplication symbol × or ⋅ ; and parentheses. For each expression, use our definition of multiplication to explain why your expression represents the total number of curlicues in Figure 4.20.


To answer the question, let's first observe the structure of Figure 4.20 and analyze the total number of curlicues.

### Observation of the figure:
- There are 5 larger clusters in the shape of a cross.
- Each of these larger clusters consists of 8 smaller circular groups.
- Each smaller circular group consists of 3 curlicues.

Now, let's construct three different expressions for the total number of curlicues in Figure 4.20, using only the numbers 2, 3, 5, and 8 along with multiplication.

### Expression 1:
We can calculate the total number of curlicues as:
\[
5 \times (8 \times 3)
\]
- There are 5 large clusters.
- Each large cluster has 8 smaller circular groups.
- Each smaller circular group has 3 curlicues.

Thus, \(5 \times (8 \times 3)\) represents the total number of curlicues.

### Expression 2:
Another way to express this would be to calculate the number of curlicues in all 8 smaller circular groups first and then multiply by 5:
\[
(5 \times 8) \times 3
\]
- First, \(5 \times 8\) gives the total number of smaller circular groups across all large clusters.
- Then, multiplying by 3 gives the total number of curlicues.

### Expression 3:
Alternatively, we can group the curlicues differently. If we think of each curlicue cluster as having two sets of smaller circular groups, we can use 2 as follows:
\[
2 \times 5 \times 8
\]
- This represents grouping the curlicues into two parts, each part having 5 large clusters, and each cluster having 8 groups. Each group is still made up of 3 curlicues, but multiplying by 3 is implicit when considering each full group in the original figure.

### Explanation of each expression:
1. **\(5 \times (8 \times 3)\)**: This directly represents the 5 clusters, each containing 8 groups of 3 curlicues.
2. **\((5 \times 8) \times 3\)**: First, you calculate the total number of smaller circular groups across all 5 clusters (5 times 8) and then find the total curlicues by multiplying by 3.
3. **\(2 \times 5 \times 8\)**: This breaks the figure into two parts (using 2) where each part contains all the curlicues spread across 5 large clusters with 8 groups in each cluster.

Would you like any more details or clarifications on these expressions?

Here are 5 related questions to expand this topic:
1. What is the significance of using parentheses in the multiplication expressions?
2. How would the total number of curlicues change if each smaller group had 4 curlicues instead of 3?
3. Can you express the total number of curlicues using an alternative arithmetic approach, such as addition instead of multiplication?
4. What would happen to the total number if the number of large clusters changed from 5 to 6?
5. How could this concept be generalized for figures with different numbers of clusters and curlicues?

**Tip**: When breaking down complex figures, always look for repeating patterns to simplify your expressions.

Write three different expressions for the total number of curlicues in Figure 4.20. Each expression should involve only the following: the numbers 2, 3, 5, and 8; the multiplication symbol × or ⋅ ; and parentheses. For each expression, use our definition of multiplication to explain why your expression represents the total number of curlicues in Figure 4.20.

Learn how to calculate the total number of curlicues in Figure 4.20 by creating three different multiplication expressions using the numbers 2, 3, 5, and 8. This exercise demonstrates the associative property of multiplication and pattern recognition skills, suitable for students in Grades 4-6.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation