Problem 142 - Algebra A Combined Function

Question

Write each as an algebraic expression. Then simplify the expression. The difference of -9 and the product of -4 and -6

Step-by-Step Solution

Answer

The simplified expression is -33.

Step 1: Understand the Problem

The problem requires us to write an algebraic expression for 'the difference of -9 and the product of -4 and -6.', then simplify it.

Step 2: Identify Components

The key components are 'the difference' which means subtraction, '-9', and 'the product of -4 and -6' which means multiplication.

Step 3: Write the Algebraic Expression

The product of -4 and -6 can be written as \(-4 \times -6\). The expression for the difference of -9 and this product becomes:\(-9 - (-4 \times -6)\).

Step 4: Simplify the Expression

First, calculate the product: \(-4 \times -6 = 24\).Substitute the product back into the expression: \(-9 - 24\).

Step 5: Final Calculation

Perform the subtraction:\(-9 - 24 = -33\).

Key Concepts

Understanding Subtraction in Algebraic Expressions

In algebra, subtraction is a fundamental operation that involves taking away one quantity from another. When working with subtraction in algebraic expressions, it is important to clearly understand the meaning of terms like "difference." The difference between two numbers implies that you are subtracting the second number from the first number.

For the given exercise, the phrase "the difference of -9 and the product of -4 and -6" implies that you need to subtract the product (result of multiplication) from -9. Writing it in algebraic terms, the expression becomes:

• Start with -9, which is the minuend (the number from which another number is subtracted).
• Subtract the product of -4 and -6. Calculating this product is essential before performing the subtraction.

Subtraction in algebra can sometimes involve negative numbers, which can be tricky. Remember, when you subtract a negative number, it is equivalent to adding its positive counterpart. This understanding is crucial for simplifying complex expressions.

Exploring Multiplication in Algebraic Expressions

Multiplication in algebra is used to find the product of two quantities. When dealing with negative numbers, it's important to recall the rules governing their operations.

• If both numbers are negative, the product is positive.
• If one number is negative and the other is positive, the product is negative.

In the exercise, we have the product of -4 and -6. Multiplying these yields a positive 24 as both numbers are negative. This product is a key component of the expression you will subtract from -9.

To write this part of the expression:

• The multiplication is expressed as \(-4 \times -6\), resulting in 24.

Calculating the product correctly is essential since it influences the subsequent subtraction and the final simplification of the expression.

Simplification of Algebraic Expressions

Simplification is the process of reducing an expression to its simplest form. In this context, it means performing all the operations within the expression to arrive at a single numerical result or a simpler algebraic form. The aim is to make expressions easier to work with in calculations or interpretations.For the given problem, the simplified expression follows these steps:

• First, compute the multiplication to find the product: \(-4 \times -6 = 24\). This result is critical as it simplifies your expression.
• Next, substitute this product into the larger expression: \(-9 - 24\).
• Finally, carry out the subtraction: \(-9 - 24 = -33\).

It's important to process the steps in order, ensuring each operation is performed correctly. By grasping these simplification steps, you can handle more intricate algebraic expressions with confidence and accuracy.