Question

question 1-1
in which situation could the product of $-15\frac{1}{2} \cdot 3\frac{1}{2}$ be used to answer the question?

• the temperature of the lake water decreased by $15\frac{1}{2} \\, ^\circ f$ per day for $3\frac{1}{2}$ days. what was the overall change in the temperature of the lake water?
• jane owed pricilla $15.50. she paid pricilla $3.50. how much does jane still owe pricilla?
• a candy jar contains $15\frac{1}{2}$ cookies. each student receives $3\frac{1}{2}$ cookies. how many students are there?
• jeffrey saved $3.50 every day for $15\frac{1}{2}$ days. how much money has jeffrey saved?

Explanation:

Step1: Analyze Option 1

The temperature decreases by \( -15\frac{1}{2}^\circ\text{F} \) per day (negative for decrease) for \( 3\frac{1}{2} \) days. Overall change is rate × time, so \( -15\frac{1}{2} \times 3\frac{1}{2} \), which matches the product.

Step2: Analyze Option 2

Jane owed $15.50 (LXI0) and paid $3.50 (\( 3\frac{1}{2} \)). The amount owed is \( 15\frac{1}{2}-3\frac{1}{2} \), not a product.

Step3: Analyze Option 3

Number of students is total cookies ÷ cookies per student, so \( 15\frac{1}{2} \div 3\frac{1}{2} \), not a product.

Step4: Analyze Option 4

Money saved is daily savings × days, so \( 3\frac{1}{2} \times 15\frac{1}{2} \), but the order is reversed, and savings are positive, so the product here would be positive \( 3\frac{1}{2} \times 15\frac{1}{2} \), not \( -15\frac{1}{2} \times 3\frac{1}{2} \).

Answer:

The temperature of the lake water decreased by \( 15\frac{1}{2}^\circ\text{F} \) per day for \( 3\frac{1}{2} \) days. What was the overall change in the temperature of the lake water?