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Chapter 1: Problem 1

perform the indicated multiplication. \(5(-9)\)

Short Answer

Expert verified
The result of the multiplication is -45.

Step by step solution

01

Identify the Numbers

Identify the two numbers that will be multiplied, in this case, it is 5 and -9.
02

Apply Multiplication Rules

The rule states that when we multiply a positive number by a negative number, the result is negative. So multiply the absolute values of the numbers (i.e., the positive forms of the numbers), which are 5 and 9. The result is 45.
03

Assign the Correct Sign to the Result

Assign the correct sign to the result. Since we are multiplying a positive number by a negative number, the result will be negative. So, the answer is -45.

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are numbers that are less than zero and are typically represented with a minus sign (-). While positive numbers show a quantity or position to the right of zero on a number line, negative numbers show a position to the left.
Negative numbers are often used to represent a loss or decrease in value, such as a debt or temperature below freezing.
  • If you owe 5 dollars, you can say you have -5 dollars.
  • If it's 5 degrees below freezing, you can say it's -5 degrees.
Understanding negative numbers is crucial because it helps in many mathematical operations, especially in multiplication. It allows us to calculate scenarios involving both increases and decreases, gains and losses.
The Concept of Absolute Value
The absolute value of a number refers to its magnitude without regard to its sign. In simple terms, it tells us how "far" a number is from zero on a number line, regardless of its positive or negative nature.
  • The absolute value of 5 is 5.
  • The absolute value of -5 is also 5.
The absolute value is denoted by two vertical lines around the number, such as \(|-5| = 5\). This concept is essential in multiplication, as it helps focus on the size of numbers involved rather than their signs. When multiplying, it is common to first consider the absolute values of the numbers and then apply the correct sign based on the multiplication rules.
Multiplication Rules with Negative Numbers
Multiplication involves understanding signs and values. When multiplying two numbers, the signs determine the result's sign. Here's a simple breakdown:
  • Positive 脳 Positive = Positive
  • Negative 脳 Negative = Positive
  • Positive 脳 Negative = Negative
  • Negative 脳 Positive = Negative
In our exercise, multiplying a positive number (5) by a negative number (-9) falls under the third rule: Positive 脳 Negative = Negative.
The absolute values (5 and 9) are multiplied first, giving 45, and then the result is given a negative sign, resulting in -45.
This is a key rule in integer multiplication that simplifies otherwise complex calculations by allowing focus on numerical operations separately from sign consideration.

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Most popular questions from this chapter

Simplify each series of additions and subtractions. $$-10-(-5)+7-2$$

Simplify each algebraic expression. $$4-6 b-8-3 b$$

Perform the indicated subtraction. $$1.4-(-1.4)$$

Simplify: \(5(3 x+2 y)+6(5 y) .\) (Section 1.4, Example 11)

Determine whether 2 is a solution of \(13 x+3=3(5 x-1)\) (Section \(1.1,\) Example 4 )
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