Problem 75 - Intermediate Algebra

Question

Simplify each numerical expression. $$ (6-11)(4-9) $$

Step-by-Step Solution

Answer

25

Step 1: Simplify the First Expression

Begin by simplifying the expression inside the first set of parentheses: \(6 - 11\). Calculating \(6 - 11\) results in \(-5\).

Step 2: Simplify the Second Expression

Next, simplify the expression inside the second set of parentheses: \(4 - 9\). Calculating \(4 - 9\) results in \(-5\).

Step 3: Multiply the Results

Combine the simplified results by multiplying them. Multiply \(-5\) by \(-5\), which equals \(25\).

Key Concepts

Algebra

Algebra often involves working with variables, constants, and the basic operations: addition, subtraction, multiplication, and division. It helps us describe patterns and solve equations, providing a foundation for understanding higher level math.
To solve the given problem, we are focusing on simplifying the expression and multiplying the resulting terms. Algebra teaches us to break down expressions into more manageable parts and understand how numbers relate to each other. For example, in this context, we're applying the distributive property, which allows us to handle operations within parentheses effectively.
When working with algebraic expressions, it's important to carefully follow the structure of the expression. Identify which parts of the expression to simplify and in what order. This approach prevents errors and helps in reaching the correct answer systematically.

Numerical Expressions

Numerical expressions are mathematical phrases that use only numbers and operations. They're basic building blocks in math. Unlike algebraic expressions, they don't include variables, making them simpler to handle. In our task, the expression is \((6-11)(4-9)\). Our goal was to simplify and then perform the operation to find the product.
Simplification is key. Start with evaluating expressions inside parentheses. It follows the order of operations, also known by PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. Applying this rule, simplify what's inside the parentheses first: \((6-11) = -5\) and \((4-9) = -5\).
After evaluating these, you're left with \((-5)(-5)\). This clear approach turns a daunting expression into a straightforward operation, eventually leading to the final result: 25.

Step-by-Step Solutions

Step-by-step solutions are incredibly useful in mathematics. They serve as a map to navigate through complex problems. This approach involves breaking down the problem into smaller, more manageable parts, making it easier to follow and understand.
For the problem at hand, we proceeded with a clear strategy: simplify first, then multiply.

• Step 1: Simplify each numerical expression within the parentheses. For this exercise: \(6-11\) simplifies to \(-5\) and \(4-9\) simplifies to \(-5\).
• Step 2: Multiply the results. Multiply \(-5\) by \(-5\), which equals \(25\).

Breaking down math problems like this not only leads to the correct answer but also builds a strong foundation for approaching more complex mathematical tasks in the future. Following these steps ensures clarity and accuracy in solving expressions.