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Chapter 1: Problem 30

Multiply or divide as indicated. See Examples 4 and 5 . $$ (-0.9)(-0.5) $$

Short Answer

Expert verified
The product is 0.45.

Step by step solution

01

Understand the Operation

We are instructed to multiply two negative numbers: \(-0.9\) and \(-0.5\). Multiplying two negative numbers will result in a positive product.
02

Multiply the Two Numbers

Calculate the product of \(0.9\) and \(0.5\). Multiply 0.9 by 0.5 to get 0.45. As both numbers are negative, their product is positive.
03

Determine the Sign

Remember that multiplying two negative numbers results in a positive product. Therefore, \((-0.9)(-0.5)\) equals 0.45.

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Key Concepts

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

Positive Product
When multiplying two negative numbers, a useful outcome unfolds 鈥� the product becomes positive. This may seem counterintuitive at first, but it is a fundamental property of multiplication. To grasp this better, think of multiplying negatives as flipping signs.

Here鈥檚 how:
  • A negative number can be visualized as pointing in the opposite direction of a positive number.
  • When you multiply two negative directions, they amplify and reverse each other to make a positive direction.
  • So, \((-0.9) \times (-0.5)\) equals 0.45, a positive product.
This principle is key and frequently appears in math problems involving negative numbers. Remember, two negatives make a positive when multiplied.
Negative Numbers
Negative numbers represent values less than zero. They are essential in various mathematical and real-world contexts. They appear frequently, especially in topics like debts or measuring temperatures below freezing. Understanding them helps in recognizing patterns in different scenarios.

Dealing with negative numbers involves visualization and rule application:
  • Consider a number line where anything left of zero is negative.
  • Negatives can symbolize a lack (like debt) or decrease compared to a reference.
  • These numbers adhere to specific rules when performing operations, especially in multiplication.
With practice, interpreting and using negative numbers becomes second nature. For instance, the exercise \((-0.9)\) and \((-0.5)\) gives meaningful results, turning negative descriptions into positive outcomes through multiplication.
Multiplication Rules
Multiplication rules form the foundation of calculating products, ensuring accurate outcomes.

Here are some core rules related to multiplying numbers:
  • If both numbers are positive, the product is positive.
  • If one number is negative and the other is positive, the product is negative.
  • If both numbers are negative, the product is positive 鈥� as we see with \((-0.9) \times (-0.5)\) = 0.45.
Utilizing these rules simplifies complex calculations and reduces errors. Remember, multiplication鈥檚 symmetry makes it predictable. Knowing the rule set allows quick determination of a product's sign and offers insights into broader mathematical situations. Practicing these helps reinforce foundational understanding, aiding in tackling more challenging problems.

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Most popular questions from this chapter

Translating Write each phrase as an algebraic expression. Use the variable \(x\) to represent each unknown number. See Example 8 . Eight times the difference of a number and nine.

Evaluate each expression when \(x=9\) and \(y=-2 .\) See Example 12 $$ \frac{5+2|y-x|}{x+6 y} $$

Complete the statement to illustrate the given property. \(4(x+3)=\)_____Distributive property.

Find the value of the expression when \(x_{1}=2, x_{2}=4, y_{1}=-3\) \(y_{2}=2\) $$ \frac{y_{2}-y_{1}}{x_{2}-x_{1}} $$

Translating Write each phrase as an algebraic expression. Use the variable \(x\) to represent each unknown number. See Example 8 . Twice the sum of a number and three.
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