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Chapter 1: Problem 55

Write a mathematical expression for each and simplify. The product of \(-12\) and 6

Short Answer

Expert verified
The simplified expression for the product of -12 and 6 is \(-72\).

Step by step solution

01

Write the expression

Write the expression for the product of -12 and 6 as \((-12) \times 6\).
02

Perform the multiplication

Now, multiply the two numbers, \((-12) \times 6 = -72\). The simplified expression for the product of -12 and 6 is \(-72\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Negative Numbers in Multiplication
Negative numbers are numbers less than zero. When multiplying two numbers, one of which is negative, the outcome changes. Here's how it works:
  • The product of a positive number and a negative number is a negative number.
  • The product of two negative numbers is a positive number, since a negative times a negative makes a positive.
In the context of the exercise, we have a negative number (-12) being multiplied by a positive number (6). So, the result is negative:\[(-12) \times 6 = -72\]Understanding the rule of multiplying signs helps in predicting and verifying the outcomes in similar problems. By focusing on the signs of the numbers involved, you get a clearer picture of the multiplication results.
Simplification of Expressions
In algebra, simplifying an expression means breaking it down to its simplest form. This may involve:
  • Performing arithmetic operations like addition, subtraction, multiplication, and division.
  • Combining like terms, such as merging 3x and 2x into 5x.
  • Reducing fractions to their simplest form.
In the exercise given, the expression to be simplified was \((-12) \times 6\). The multiplication of these numbers results in \(-72\). This is a straightforward example of simplification because there are no other operations or terms involved. The process demonstrated here shows how simplification can make expressions more manageable and understandable.
Understanding Algebraic Expressions
An algebraic expression is a combination of numbers, variables, and arithmetic operations. Expressions can be simple, like \(3x + 4\), or complex, as in polynomial equations.Components of algebraic expressions include:
  • Constants (fixed numbers or values, such as -12 or 6).
  • Variables (letters that stand in for unknown values).
  • Coefficients (numbers multiplied by the variables, for instance, in 4x, 4 is the coefficient).
  • Operators (symbols indicating operations, like \( +, -, \times, \div \)).
In the solved exercise, \((-12) \times 6\) is an algebraic expression using constants and the multiplication operator.Simplifying such expressions often involves executing the arithmetic operation to arrive at a single number or a more reduced form. Such an understanding is crucial in algebra because it forms the basis for solving equations and performing further mathematical manipulations.

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Most popular questions from this chapter

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