Problem 98 - Algebra 1

Question

Evaluate the expression for the given value(s) of the variable(s). $$\frac{5}{6} a-b \text { when } a=6 \text { and } b=5$$

Step-by-Step Solution

Answer

The evaluated expression is 0

Step 1: Substitution

We replace a with 6 and b with 5 in the expression. Which gives us \( \frac {5}{6} \times 6 - 5 \)

Step 2: Perform multiplication

Multiply \(\frac{5}{6}\) by 6 to get 5. This simplifies the equation to 5 - 5

Step 3: Perform subtraction

Subtract 5 from 5 to get 0. Hence, \(\frac {5}{6} a - b = 0\) when a=6 and b=5

Key Concepts

Substitution Method

In algebra, the substitution method is a fundamental technique used to evaluate expressions. It involves replacing the variables in an expression with their given numerical values. This method is quite simple yet powerful, as it allows us to find the value of an expression for specific cases.

For instance, let’s consider the expression in our example, \( \frac{5}{6} a - b \). To evaluate this expression for \( a = 6 \) and \( b = 5 \), we use the substitution method. We substitute the given values directly into the expression: replace \( a \) with 6 and \( b \) with 5. It’s essential to follow the order of operations after substituting the values, which leads us to our next concept: carrying out basic arithmetic operations to arrive at the answer.

Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and arithmetic operations that represent a specific quantity. Expressions can be as simple as a single term or as complex as a polynomial with many terms. No matter their complexity, algebraic expressions are just instructions to perform certain operations.

In the context of our example, \( \frac{5}{6} a - b \) is an algebraic expression that includes a fraction, variables \(a\) and \(b\), and the subtraction operation. Understanding how these parts interact is crucial for evaluating the expression correctly. Also, comprehending how to manipulate these expressions is key to algebra, and this understanding will aid in tackling more advanced topics in mathematics.

Basic Arithmetic Operations

At the heart of evaluating algebraic expressions lie the basic arithmetic operations: addition, subtraction, multiplication, and division. These operations are the building blocks for all math concepts and are used in a specific order known as the order of operations.

After substitution, we conduct these operations as per the prescribed order. In our example, we multiply \( \frac{5}{6} \) by 6 first, executing the multiplication operation. The result is then used in the subtraction operation where we subtract 5. The correct sequence of these basic operations is crucial as misunderstanding the order can lead to inaccurate results. Mastering these operations and the order in which they should be executed is essential for anyone looking to succeed in algebra.