Problem 451 - Prealgebra

Question

Contact lenses Jenna puts in a new pair of contact lenses every 14 days. How many pairs of contact lenses does she need for 365 days?

Step-by-Step Solution

Answer

Jenna needs 27 pairs of contact lenses for 365 days.

Step 1: Understand the Problem

Jenna needs to replace her contact lenses every 14 days. The goal is to determine how many pairs she will need over the course of 365 days.

Step 2: Set Up the Division Calculation

To find out how many 14-day periods are in 365 days, divide 365 days by 14 days.

Step 3: Perform the Division

365 i divided ghtml 14. This results in:

Step 4: Interpret the Quotient and Remainder

The quotient represents the number of full 14-day periods. The remainder represents the leftover days that will still require a new pair of contact lenses.

Step 5: Calculate Total Pairs Needed

Since 365 divided by 14 gives us 26 with a remainder, Jenna needs 26 pairs for the full periods and 1 additional pair for the remaining days.

Key Concepts

Division Calculation

In this problem, we use division to figure out how many pairs of contact lenses Jenna needs for 365 days. Division helps us break down a large number (like 365) into smaller, more manageable parts (like 14-day periods).

We start by dividing the total number of days Jenna needs contacts (365 days) by the number of days one pair lasts (14 days). The formula for this is:

\( \text{Number of Pairs} = \frac{365 \text{ days}}{14 \text{ days/pair}} \)

Performing the division, we get: \( \frac{365}{14} = 26 \text{ remainder } 1 \)

This means Jenna will go through 26 full periods of 14 days, but there's still 1 leftover day that needs another pair of lenses.

Real-Life Math Application

This exercise is a great example of how we use math in real life.

Here's how:

• Jenna needs to manage her contact lens usage effectively, making sure she doesn't run out.

By dividing the total number of days by the duration one pair lasts, we can plan ahead.

It helps to think about situations where you have a limited supply of something that needs regular replacement. For instance, suppose you have a subscription service that sends you a new item every month. How many items would you get in a year? Just like Jenna's contacts, you divide the total days in a year by the days in a month.

Real-life problems often require breaking down larger periods into smaller ones to make our life easier and more organized.

Understanding Remainders

One important part of division is understanding remainders. Remainders tell us what is left over after dividing a number as evenly as possible.

In Jenna's case, after dividing 365 by 14, we get a quotient of 26 and a remainder of 1.

This quotient (26) tells us that Jenna can completely use 26 pairs of contact lenses for full 14-day periods.

The remainder (1) indicates that there is 1 day left. Even though 1 day is not a full 14-day period, Jenna still needs a new pair of contacts for that leftover day.

In real life, understanding remainders is crucial when you can't simply round up or down. For tasks that need precise counts, like medication doses or budgeting, the remainder ensures accuracy and keeps us prepared.