Problem 40 - Prealgebra

Question

Country - Israel Bottle size - \(350 \mathrm{mL}\) Liters in a 6 -pack ______________

Step-by-Step Solution

Answer

2.1 liters.

Step 1: Understanding Units

We are given the bottle size in milliliters (mL) and we need to convert it to liters (L) since the final answer requires the total volume in liters for a 6-pack. Remember, 1 liter equals 1000 milliliters.

Step 2: Convert Bottle Size to Liters

Convert the bottle size from milliliters to liters using the conversion factor 1 L = 1000 mL. Thus, \[ 350 ext{ mL} = \frac{350}{1000} = 0.35 ext{ L} \]

Step 3: Calculate Total Volume for a 6-Pack

A 6-pack means there are 6 bottles. Calculate the total volume by multiplying the volume of one bottle by 6. \[ ext{Total liters} = 0.35 ext{ L/bottle} imes 6 ext{ bottles} = 2.1 ext{ L} \]

Step 4: Conclusion

The total volume of a 6-pack of 350 mL bottles is 2.1 liters.

Key Concepts

Volume Calculation

Volume calculation is a fundamental concept essential for many real-world applications, from cooking to engineering. In our exercise, we're calculating the total volume of liquid in a 6-pack of 350 mL bottles.
First, it's crucial to understand that the volume of one bottle in milliliters needs to be converted to liters for simpler calculations. Given that one bottle contains 350 mL, we first need to convert this volume into liters. This is done by using the conversion factor where 1 liter is equivalent to 1000 milliliters.
By dividing the milliliters by 1000, you can convert any amount from milliliters to liters. For instance, this conversion changes 350 mL into 0.35 L. It's much easier calculating with liters when dealing with larger volumes.

• Convert mL to L for easier comprehension and calculation, especially with multiple bottles.
• Multiply the converted volume of a single bottle by the number of bottles to find the total volume.

Once converted, to find the total volume of a 6-pack, simply multiply the volume of one bottle by 6—resulting in 2.1 L. Volume calculation allows you to understand how much space a substance will occupy, an essential skill in many disciplines.

Metric System

The metric system is a standardized system of measurement used globally, especially in science and many countries around the world. It simplifies calculations and conversions because it relies on powers of ten. In this exercise, we're using the metric system to measure volume.
The metric system's units for volume include liters (L) and milliliters (mL). These are the most commonly used units and are convenient because they convert easily through simple multiplication or division by 10, 100, or 1000.

• 1 liter (L) is equivalent to 1000 milliliters (mL).
• Simplicity of conversion due to power of ten relationships.
• Used in scientific and everyday practical measurements.

When solving problems involving volume, it's often easier to use liters for larger amounts and milliliters for smaller quantities. This exercise demonstrates converting between these two units, enhancing clarity and ease of calculation.

Mathematics Education

Mathematics education involves helping students understand not only how to perform calculations, but also why and when to apply them. One of the goals is to foster strong problem-solving skills and numerical literacy.
Tackling this exercise involves understanding both unit conversion and multiplication, fundamental skills in mathematics. By first converting units, students learn how to simplify complex problems and break them into manageable parts. This process of converting and further calculating encourages logical reasoning and numerical fluency.

• Ensures students can comprehend and use different measurement units effectively.
• Encourages breaking down complex problems into simpler steps.
• Teaches the importance of precise calculations in real-world scenarios.

As students tackle exercises like this, they're also developing critical thinking and analytical skills, setting a strong foundation for future learning and application in various fields, from science to everyday life.