Problem 47 - Elementary Algebra

Question

\(-8(9 m)\)

Step-by-Step Solution

Answer

-72m

Step 1: Understand the Problem

The given expression \(-8(9m)\) involves multiplying two numbers: \(-8\) and \(9m\).

Step 2: Multiply the Constants

Multiply the constants first: \(-8 \times 9\). This will give \-72\.

Step 3: Combine with Variable

After multiplying the constants, attach the variable \(m\) to the result. Thus, \(-72m\).

Key Concepts

algebraic expressions

An algebraic expression is a combination of numbers, variables, and arithmetic operations. For example, in the expression \(9m\), \(9\) is a constant coefficient (a number), and \(m\) is a variable, representing an unknown value. Understanding how to manipulate these expressions is a key part of algebra. When we see an expression like \(-8(9m)\), it means we need to perform the multiplication operation on the constant \(-8\) and the entire term \(9m\). This helps simplify the expression into a single term. Breaking down algebraic expressions into their parts makes them easier to understand and solve.

multiplication in algebra

In algebra, multiplication is a fundamental operation that combines terms. When multiplying coefficients and variables, it’s crucial to follow clear steps to avoid mistakes. First, multiply the constants. For instance, in the problem \(-8(9m)\):

• Start by multiplying \(-8 \times 9\). This equals \-72\.
• Next, we attach the variable \(m\) to the result, giving \-72m\.

This shows that multiplication in algebra involves both numerical and variable components, which can be handled systematically. Always keep track of your constants and don't forget to include the variable in your final answer.

negative numbers

Negative numbers can make algebra tricky. They follow specific rules that are important to understand. When multiplying, remember:

• A positive number times a negative number results in a negative number. For example, \( -8 \times 9 = -72 \).
• A negative number times a negative number results in a positive number.
• Multiplying the constants as a first step helps to organize and control these signs.

In our example, \( -8(9m) \), the multiplication of \-8\ and \9\ gives \-72\. Attaching the variable \m\ to get \-72m\ completes the process. Keep practicing with negative numbers to gain confidence in handling them in multiplication.