Problem 24 - Algebra 1

Question

\(3.67 a\) when \(a=2\)

Step-by-Step Solution

Answer

Therefore, the value of \(3.67a\) when \(a=2\) is 7.34.

Step 1: Identify the value to be substituted

First, identify the value that needs to be substituted into the equation. Here, we know that \(a=2\).

Step 2: Substitute the value into the expression

Next, replace \(a\) with 2 in the expression \(3.67 * a\) to get \(3.67 * 2\).

Step 3: Carry out the multiplication

Finally, calculate the value of \(3.67 * 2\) to find the solution to the exercise.

Key Concepts

Multiplication

Multiplication is one of the basic arithmetic operations that involves combining equal groups to find the total amount. In this exercise, you encounter the multiplication of a number with a variable. It's similar to multiplying integers or whole numbers but with an algebraic twist. When you multiply 3.67 and a variable such as \( a \), it initially looks like this: \( 3.67 \times a \). This implies that there are 3.67 groups of \( a \). If \( a \) were an integer value of 1, the result would just be 3.67, as you effectively have 3.67 of one group. However, when \( a \) takes a different value, say 2 as in this exercise, the multiplication adjusts, expanding to encompass 3.67 groups of 2, giving a substituted result of \( 3.67 \times 2 \).

This operation emphasizes the importance of accurately multiplying decimal values with integers, keeping track of the decimal precision. Using the multiplication property also helps solve algebraic equations, making this skill essential in both simple and complex mathematical contexts.

Algebraic expressions

Algebraic expressions are mathematical phrases that can include numbers, letters representing variables, and operational symbols. They form the foundation of algebra by expressing mathematical relationships in a compact form. In this exercise, the algebraic expression used is \( 3.67a \). Here, the number 3.67 is known as the coefficient, which is the constant factor that is multiplied by the variable \( a \).

• Algebraic expressions can represent real-world situations, like calculating cost, area, and more.
• The expression \( 3.67a \) implies a proportional relationship between 3.67 and \( a \).
• Understanding how to manipulate these expressions using operations like addition, subtraction, and multiplication is key to solving algebraic equations.

In our scenario, mastering this concept allows us to seamlessly substitute and simplify expressions efficiently. It's crucial to comprehend that expressions are concise tools for representing and solving mathematical problems.

Variable substitution

Variable substitution involves replacing variables in algebraic expressions with specific numerical values. This is a common practice in algebra that allows us to simplify expressions or evaluate them. In the exercise presented, the variable \( a \) is given the value of 2. By replacing every occurrence of \( a \) in the expression \( 3.67a \) with 2, we transform the expression into a simpler arithmetic equation \( 3.67 \times 2 \).

Here are some straightforward steps to perform variable substitution:

• Identify the variable and the value it should take.
• Replace the variable in the expression with the given value.
• Proceed to compute the expression following standard arithmetic rules.

This technique is incredibly useful for solving equations, modelling scenarios, and translating word problems into mathematical forms. By mastering substitution, you enhance your problem-solving toolkit and your ability to work through various algebraic challenges effectively.