Question

a clock chimes 4 times each hour. which expression can be used to find the number of times the clock chimes in a week?
\\(\boldsymbol{\frac{4 \text{times}}{1 \text{hour}} \times \frac{1 \text{day}}{24 \text{hours}} \times \frac{1 \text{week}}{7 \text{days}}}\\)
\\(\boldsymbol{\frac{4 \text{times}}{1 \text{hour}} \times \frac{1 \text{day}}{24 \text{hours}} \times \frac{7 \text{days}}{1 \text{week}}}\\)
\\(\boldsymbol{\frac{4 \text{times}}{1 \text{hour}} \times \frac{24 \text{hours}}{1 \text{day}} \times \frac{7 \text{days}}{1 \text{week}}}\\)
\\(\boldsymbol{\frac{4 \text{times}}{1 \text{hour}} \times \frac{24 \text{hours}}{1 \text{day}} \times \frac{1 \text{week}}{7 \text{days}}}\\)

Explanation:

Step1: Analyze the units

We need to find the number of chimes in a week. The clock chimes 4 times per hour. First, convert hours to days: there are 24 hours in a day. Then convert days to weeks: there are 7 days in a week.

Step2: Check the unit cancellation

For the correct expression, the units should cancel out to give chimes per week. Let's check each option:

• Option 1: $\frac{4 \text{ times}}{1 \text{ hour}} \times \frac{1 \text{ day}}{24 \text{ hours}} \times \frac{1 \text{ week}}{7 \text{ days}}$: Units don't cancel correctly (hours and days won't cancel to give week).
• Option 2: $\frac{4 \text{ times}}{1 \text{ hour}} \times \frac{1 \text{ day}}{24 \text{ hours}} \times \frac{7 \text{ days}}{1 \text{ week}}$: Units don't cancel correctly (hours and days won't cancel to give week).
• Option 3: $\frac{4 \text{ times}}{1 \text{ hour}} \times \frac{24 \text{ hours}}{1 \text{ day}} \times \frac{7 \text{ days}}{1 \text{ week}}$:
• Hour cancels with hour, day cancels with day, leaving times per week. Let's see: $\frac{4 \text{ times}}{\cancel{\text{hour}}} \times \frac{24 \cancel{\text{hours}}}{\cancel{\text{day}}} \times \frac{7 \cancel{\text{days}}}{1 \text{ week}} = \frac{4\times24\times7 \text{ times}}{\text{week}}$, which is correct.
• Option 4: $\frac{4 \text{ times}}{1 \text{ hour}} \times \frac{24 \text{ hours}}{1 \text{ day}} \times \frac{1 \text{ week}}{7 \text{ days}}$: Units don't cancel correctly (days and week won't cancel to give week).

Answer:

The correct expression is $\boldsymbol{\frac{4 \text{ times}}{1 \text{ hour}} \times \frac{24 \text{ hours}}{1 \text{ day}} \times \frac{7 \text{ days}}{1 \text{ week}}}$ (the third option in the given choices).