Discussion for Multiply Fractions & Decimals Discussion
In your journal, you explained the Associative and Commutative Properties of Multiplication to a friend. You told them that they would get the same answer every time they multiplied the numbers in the problem.
Imagine that your neighbor is scrolling through social media. Your cousin is considering making an in-app purchase. Your neighbor shows you advertisements for products that make bold claims:
“Get rich quick! Do you want to work fewer hours for the same amount of money per hour, and get even richer? Click here to see how you can relax and earn. You’ll work 10 fewer hours at the same wage, and you’ll still make more money!”
“Get hydrated now! Do you hate drinking water? Click here to see how drinking less water is actually the secret to having more water in your body. It’s the study the government doesn’t want you to see!”
Select one of the advertisements and advise your cousin:
Represent the advertisement’s claim with a sample mathematical statement.
Using the Associative and Commutative Properties of Multiplication, evaluate whether the claim is reasonable.
Explain your reasoning in your post.
Then read your peers’ advice. Respond to two of your peers:
For each post, evaluate your peer’s sample mathematical statement and determine whether it is accurate.
Tell your peers what you agree with and disagree with in their advice
Post:
Advertisement: "Get rich quick! Do you want to work fewer hours for the same amount of money per hour, and get even richer? Click here to see how you can relax and earn. You’ll work 10 fewer hours at the same wage, and you’ll still make more money!"
Sample Mathematical Statement: Let's say the cousin currently works 40 hours per week and earns $10 per hour. The claim is that by working 10 fewer hours, they will make more money.
Mathematical Statement: (40 hours * $10 per hour) - (10 hours * $10 per hour) = (30 hours * $10 per hour)
Evaluation: According to the associative and commutative properties of multiplication, the order in which the numbers are multiplied does not affect the result, and grouping the numbers differently does not change the product. In this case, whether we calculate (40 hours - 10 hours) * $10 per hour or (30 hours) * $10 per hour, we will get the same result.
Reasoning: The claim in the advertisement seems reasonable based on the associative and commutative properties of multiplication. By working 10 fewer hours, the cousin would still make the same amount per hour, resulting in more money overall.
Response to Peer 1:
The sample mathematical statement you provided accurately represents the claim made in the advertisement. I agree with your evaluation that the claim seems reasonable based on the application of the associative and commutative properties of multiplication. By working fewer hours at the same wage, the cousin should indeed make more money.
Response to Peer 2:
I noticed that in your sample mathematical statement, you used addition instead of multiplication to represent the claim in the advertisement. The claim is about working fewer hours and making more money, which aligns with the concept of multiplication. Therefore, I believe a multiplication statement would be more accurate in this scenario. However, I agree with your conclusion that the claim is reasonable based on the associative and commutative properties of multiplication.
Advertisement Claim: "Get rich quick! Do you want to work fewer hours for the same amount of money per hour, and get even richer? Click here to see how you can relax and earn. You’ll work 10 fewer hours at the same wage, and you’ll still make more money!"
Sample Mathematical Statement: If you work 10 hours less at the same wage, you will still make more money.
Evaluation:
To evaluate the claim, let's assume the wage per hour is represented by "W". If you work the regular number of hours, your earnings would be calculated as:
Regular Earnings = Regular Hours * Wage = R * W
If you work 10 hours less at the same wage, the new earnings would be calculated as:
New Earnings = (Regular Hours - 10) * Wage = (R - 10) * W
To determine whether the claim is reasonable, we can compare the two earnings:
(New Earnings) - (Regular Earnings) = (R - 10) * W - R * W
= R * W - 10 * W - R * W
= -10 * W
From the above expression, we can observe that the difference between the new earnings and the regular earnings is -10 times the wage per hour. This means that if you work 10 hours less, your earnings will decrease by 10 times the wage. Therefore, the claim is not reasonable, as you will actually make less money if you work 10 hours less at the same wage.
I agree with my peer's assessment of the claim not being reasonable. The mathematical statement accurately represents the situation, and their reasoning is clear and logical.
I disagree with my peer's advice that suggests the claim is reasonable. They state that working fewer hours at the same wage would result in more money, which contradicts the mathematical evaluation given.