Problem 58 - Prealgebra

Question

The gasoline tank on a car holds 18 gallons of gas. What is the volume of the tank in quarts?

Step-by-Step Solution

Answer

The volume of the tank is 72 quarts.

Step 1: Understanding the Conversion Factor

To convert gallons to quarts, we need to know the conversion factor. There are 4 quarts in a gallon. This is crucial because it tells us how to transition between these two units of measurement.

Step 2: Setting Up the Conversion

Start with the volume in gallons, which is 18. Multiply the volume in gallons by the conversion factor (4 quarts per gallon) to find the volume in quarts.

Step 3: Calculating the Volume in Quarts

Perform the multiplication: \[ 18 ext{ gallons} imes 4 ext{ quarts/gallon} = 72 ext{ quarts} \]This gives us the volume of the tank in quarts.

Key Concepts

Volume Conversion

Volume conversion is a fundamental concept in unit conversion. It allows you to express a quantity in one unit and then switch it to another. This is particularly helpful when dealing with different measurement systems or having to interpret data in various units. Understanding volume conversion is essential for solving real-world problems like converting fuel capacities or cooking measurements.

The basic idea of volume conversion is to multiply or divide the original measurement by a conversion factor. For example, converting gallons to quarts uses a conversion factor of 4, because 1 gallon equals 4 quarts. This means if you have a volume in gallons and wish to convert it to quarts, you multiply the number of gallons by 4.

Using the example from the problem, the car's gas tank holds 18 gallons. By applying the conversion factor, you multiply 18 by 4 to get 72 quarts. Remember:

• The original volume is in gallons.
• The conversion factor is a simple multiplier (4 quarts per gallon).
• The converted volume is in quarts.

This same principle applies to any unit conversion—just use the correct conversion factor for the units involved.

Measurement Units

Measurement units are standardized amounts used to quantify attributes like length, volume, and weight. They serve as a common language that allows for clear communication of quantities in daily life and scientific contexts.

The concept of a measurement unit involves both the type of quantity (like volume) and its corresponding unit (such as gallons, quarts, liters, etc.). Units like the gallon and the quart are part of the US customary system, often used in everyday contexts in the United States.

To work with these units effectively, it's vital to know their relationships. Conversion factors explain how many smaller units fit into a larger one. For example, knowing there are 4 quarts in a gallon is a key part of tackling the original exercise.

Remember, understanding measurement units and their conversions is critical not just for academic exercises, but also for practical applications in cooking, car maintenance, and any situation where accurate measurement is important.

Gallons to Quarts

Turning gallons into quarts is a straightforward conversion if you know the correct factor. The gallon and the quart are both units of volume mainly used in the United States. Knowing how to convert between them is useful, especially when dealing with fuel, liquid containers, or even beverage recipes.

To begin this conversion, recognize that:

• 1 gallon = 4 quarts

This simple relationship means that converting gallons to quarts involves multiplying the number of gallons by 4. For our specific car fuel tank example, the process would look like this: start with 18 gallons, and since each gallon equals 4 quarts, you calculate:\[18 \text{ gallons} \times 4 \text{ quarts/gallon} = 72 \text{ quarts}\]Thus, the tank holds 72 quarts of gas.

This conversion process allows for seamless transitions between different measurement units, facilitating a better understanding of quantities in practical scenarios. Whether in professional or everyday activities, converting from gallons to quarts empowers you to approach tasks with confidence.