Problem 84 - Elementary Algebra

Question

On a trip Brent bought the following amounts of gasoline: \(9.7\) gallons, \(12.3\) gallons, \(14.6\) gallons, \(12.2\) gallons, \(13.8\) gallons, and \(15.5\) gallons. How many gallons of gasoline did he purchase on the trip?

Step-by-Step Solution

Answer

Brent purchased 78.1 gallons of gasoline.

Step 1: List All Gallon Amounts

First, write down all the amounts of gasoline purchased: 9.7 gallons, 12.3 gallons, 14.6 gallons, 12.2 gallons, 13.8 gallons, and 15.5 gallons.

Step 2: Add the Gallon Amounts Together

Add the amounts together: \(9.7 + 12.3 + 14.6 + 12.2 + 13.8 + 15.5\).

Step 3: Perform the Addition

Perform the addition of the numbers: \(9.7 + 12.3 = 22.0\), then \(22.0 + 14.6 = 36.6\), then \(36.6 + 12.2 = 48.8\), then \(48.8 + 13.8 = 62.6\), and finally \(62.6 + 15.5 = 78.1\).

Step 4: Final Step: State the Total Gallons

The total amount of gasoline purchased on the trip is 78.1 gallons.

Key Concepts

Step-by-step Problem Solving

Approaching problems with a step-by-step methodology helps make complex tasks feel more manageable. When dealing with mathematical problems, especially those involving multiple numbers or operations, breaking the task down into smaller parts can facilitate better understanding and accuracy. For example, when Brent needed to find how much gasoline he purchased on his trip, a structured method was employed:

• First, list all the numbers involved—this helps to ensure none are missed.
• Next, add them in sequence, which can be managed by tackling one pair at a time.
• Finally, conclude with a clear statement of the result.

This clear and logical progression from problem to solution is the essence of step-by-step problem solving, offering clarity and reducing errors. Learning this process well can be beneficial across different types of problems.

Basic Arithmetic Operations

Basic arithmetic operations form the foundation of mathematics. These operations include addition, subtraction, multiplication, and division. In Brent's exercise, the focus is on addition. Addition combines numbers into a single total. Here's a simple breakdown of how addition helps solve problems:

• Identify the numbers to be added.
• Combine them one at a time, ensuring each sum carries over any extra into the next calculation if working with multi-decimal values.
• Maintain accuracy by double-checking each step, especially when numbers have decimals.

Mastering basic arithmetic operations like addition allows one to tackle a wide range of mathematical problems efficiently. It also serves as a building block for understanding more complex mathematical concepts.

Decimal Numbers

Decimal numbers are a form of representing numbers that are not whole, having a decimal point separating the whole part from the fractional part. They are essential in many aspects of daily life and scientific measurement because they offer a way to express precision. In arithmetic, handling decimals can be tricky without practice, but here are a few tips that help manage them:

• Always align decimal points vertically when adding or subtracting to ensure accuracy.
• If necessary, add zeros to the end of a decimal to help compare or perform operations.
• Be attentive to carrying over values, which may occur when the sum in a decimal place exceeds 10.

In the context of the exercise with Brent, each gallon measurement was a decimal number, demonstrating how decimals are frequently used in scenarios involving specific measurements. Through practice, working with decimals becomes intuitive and vital in achieving precise results in calculations.