We appreciate your visit to Challenge A salon is open 5 days per week and has 42 clients per day Use the Associative Property of Multiplication to write two equivalent. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Sure! Let's solve the problem step by step.
### Step 1: Understand the Associative Property of Multiplication
The Associative Property of Multiplication states that the way numbers are grouped in a multiplication problem does not change the product. For example:
[tex]\[ (a \cdot b) \cdot c = a \cdot (b \cdot c) \][/tex]
### Step 2: Create Equivalent Expressions
Given that the salon has 42 clients per day and is open 5 days per week, the number of clients per week is:
[tex]\[ 42 \times 5 \][/tex]
To find the total number of clients in [tex]\( w \)[/tex] weeks, we multiply the weekly total by [tex]\( w \)[/tex]:
[tex]\[ 42 \cdot 5 \cdot w \][/tex]
Using the Associative Property, we can group these numbers differently to create equivalent expressions:
- [tex]\( 42 \times (5 \times w) \)[/tex]
- [tex]\( (42 \times 5) \times w \)[/tex]
Both expressions will give the same product.
### Step 3: Choose the Correct Equivalent Expressions
Based on the problem, the correct choice is:
- [tex]\( 42 \cdot (5 \cdot w) \)[/tex] and [tex]\( (42 \cdot 5) \cdot w \)[/tex]
The correct answer choice is:
B. [tex]\( 42 \cdot (5 \cdot w) \)[/tex] and [tex]\( (42 \cdot 5) \cdot w \)[/tex]
### Step 4: Calculate Clients for Specific Weeks
Now, let's calculate the total number of clients for 4 weeks and 12 weeks.
For 4 weeks:
[tex]\[ \text{Total clients in 4 weeks} = 42 \times 5 \times 4 = 210 \times 4 = 840 \][/tex]
For 12 weeks:
[tex]\[ \text{Total clients in 12 weeks} = 42 \times 5 \times 12 = 210 \times 12 = 2520 \][/tex]
So, in summary:
- Equivalent Expressions: [tex]\( 42 \cdot (5 \cdot w) \)[/tex] and [tex]\( (42 \cdot 5) \cdot w \)[/tex]
- Total clients in 4 weeks: 840
- Total clients in 12 weeks: 2520
I hope this helps! Let me know if you have any further questions.
### Step 1: Understand the Associative Property of Multiplication
The Associative Property of Multiplication states that the way numbers are grouped in a multiplication problem does not change the product. For example:
[tex]\[ (a \cdot b) \cdot c = a \cdot (b \cdot c) \][/tex]
### Step 2: Create Equivalent Expressions
Given that the salon has 42 clients per day and is open 5 days per week, the number of clients per week is:
[tex]\[ 42 \times 5 \][/tex]
To find the total number of clients in [tex]\( w \)[/tex] weeks, we multiply the weekly total by [tex]\( w \)[/tex]:
[tex]\[ 42 \cdot 5 \cdot w \][/tex]
Using the Associative Property, we can group these numbers differently to create equivalent expressions:
- [tex]\( 42 \times (5 \times w) \)[/tex]
- [tex]\( (42 \times 5) \times w \)[/tex]
Both expressions will give the same product.
### Step 3: Choose the Correct Equivalent Expressions
Based on the problem, the correct choice is:
- [tex]\( 42 \cdot (5 \cdot w) \)[/tex] and [tex]\( (42 \cdot 5) \cdot w \)[/tex]
The correct answer choice is:
B. [tex]\( 42 \cdot (5 \cdot w) \)[/tex] and [tex]\( (42 \cdot 5) \cdot w \)[/tex]
### Step 4: Calculate Clients for Specific Weeks
Now, let's calculate the total number of clients for 4 weeks and 12 weeks.
For 4 weeks:
[tex]\[ \text{Total clients in 4 weeks} = 42 \times 5 \times 4 = 210 \times 4 = 840 \][/tex]
For 12 weeks:
[tex]\[ \text{Total clients in 12 weeks} = 42 \times 5 \times 12 = 210 \times 12 = 2520 \][/tex]
So, in summary:
- Equivalent Expressions: [tex]\( 42 \cdot (5 \cdot w) \)[/tex] and [tex]\( (42 \cdot 5) \cdot w \)[/tex]
- Total clients in 4 weeks: 840
- Total clients in 12 weeks: 2520
I hope this helps! Let me know if you have any further questions.
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