Problem 60 - Prealgebra

Question

How many 5 milliliter test tubes filled with water will it take to fill a 1 liter container?

Step-by-Step Solution

Answer

200 test tubes are needed.

Step 1: Understand Unit Conversion

First, realize that 1 liter is equivalent to 1000 milliliters. This is important because it allows us to switch between liters and milliliters easily while solving the problem.

Step 2: Set Up the Division Problem

Consider the total volume you need to fill and the capacity of each test tube. You need to know how many 5 milliliter test tubes are needed to make up 1000 milliliters. This is a division problem: 1000 milliliters divided by 5 milliliters per test tube.

Step 3: Perform the Division

Calculate the division: \( \frac{1000}{5} = 200 \). This means you need 200 test tubes to make up 1000 milliliters.

Key Concepts

Understanding Volume Measurement

Volume measurement is a critical concept in math and science. It describes the amount of three-dimensional space an object occupies. In this specific problem, we measure volume in milliliters and liters. Here's what you need to know:

• Milliliters (mL): A metric unit of volume, where 1 milliliter is one-thousandth of a liter.
• Liters (L): Another metric unit of volume, commonly used for liquids. 1 liter is equivalent to 1000 milliliters.

To solve volume measurement problems efficiently, it's important to understand unit conversions and their applications. In this problem, we start by converting 1 liter (L) into milliliters (mL). By recognizing that 1 liter equals 1000 milliliters, we can easily convert and work with smaller measurements like the 5 mL test tubes mentioned.

Setting Up a Division Problem

In this problem, once we convert the volume into milliliters, setting up a division problem becomes the logical next step. This is because we want to determine how many smaller volumes (the test tubes) are needed to make up a larger volume (1 liter).A division problem here is based on:

• Numerator: The total volume needed, which is 1000 milliliters.
• Denominator: The volume each test tube holds, which is 5 milliliters.

Division tells us how many times the denominator (volume of one test tube) fits into the numerator (total volume needed). Setting this up as a division equation allows us to calculate the number of test tubes required:\[ \text{Number of test tubes} = \frac{\text{Total volume in mL}}{\text{Volume of one test tube in mL}} \]

Approaching Math Problem Solving

Math problem solving often involves combining several concepts, like in this division problem. To solve successfully, it helps to:

• Break down the problem into simpler parts. Here, we started with converting units from liters to milliliters.
• Identify the goal of the problem. We want to find how many test tubes fill 1 liter.
• Apply mathematical operations, such as division, to reach the solution.

Executing the division helps solve the problem effectively: Calculate how many 5 mL increments fill up 1000 mL. So by dividing 1000 by 5:\[ \frac{1000}{5} = 200 \]This answer, 200, tells us you need exactly 200 test tubes of 5 milliliters to fill a 1-liter container. This approach is adaptable and can help solve numerous other math problems with similar structures.