/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 45 Evaluate each of the following e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 45

Evaluate each of the following expressions, if possible. $$12(-8)-(-15)(-9)$$

Short Answer

Expert verified
-231

Step by step solution

01

Understand the Expression

We are given the expression: \[12(-8) - (-15)(-9)\]. This involves two multiplications and one subtraction.
02

Multiply 12 and -8

Calculate the product of 12 and -8. \[12 \times (-8) = -96\]
03

Multiply -15 and -9

Next, calculate the product of -15 and -9. Remember that the product of two negative numbers is positive. \[(-15) \times (-9) = 135\]
04

Subtract the Results

Perform the subtraction: \[-96 - 135 = -231\]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Multiplication of Integers
When multiplying integers, the rules are straightforward. The product of two positive integers is positive, and the product of two negative integers is also positive. This is crucial because multiplying two negative numbers might seem confusing at first. For example, if we consider the problem above, calculating \(12 \times (-8)\) yields \(-96\). Here, the positive and negative signs result in a negative product.

On the other hand, multiplying two negative integers, such as \((-15) \times (-9)\), gives a positive result. This is because the negatives cancel each other out, leading to a positive product, which in this case is \(135\).
Subtraction of Integers
Subtracting integers involves understanding that subtracting a negative number is the same as adding the absolute value of that number. This is because subtracting a negative is equivalent to adding its positive counterpart. In our example, we calculate \(-96 - 135\). Here, we are subtracting a positive number from a negative number, which means moving further in the negative direction on the number line.

The result of this operation is \(-96 - 135 = -231\). To break it down, you can think of it as starting at \(-96\) on the number line and then moving 135 steps further left (since subtracting a positive is like moving left on the number line), resulting in \(-231\).
Properties of Negative Numbers
Negative numbers have unique properties that affect arithmetic operations. When dealing with negative numbers, remember the following key points:

  • Adding a negative number is the same as subtracting its absolute value.
  • Subtracting a negative number is the same as adding its absolute value.
  • Multiplying two negative numbers results in a positive number, as their negative signs cancel out.
  • Multiplying a positive number by a negative number gives a negative result, as the positive and negative signs do not cancel out.
Understanding these properties helps when performing operations like the one in the example provided, where we first multiply integers, handle multiple negative signs, and then perform subtraction.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

If we denote a debt of \(\$ 15,000\) as \(-\$ 15,000,\) explain how you could use subtraction of negative numbers to represent and calculate the following: Reduce a debt of \(\$ 15,000\) by \(\$ 6,000\)

Compute the given expression. Round off your answer to two decimal places where necessary. $$12.8-9.2(3.4-1.6)$$

Evaluate the given expression. Remember to follow the order of operations. $$(30-5)(4-2)$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$5.2-1.4(2.8-0.7)$$

If possible, list three numbers that are members and three numbers that are not members of the given set. If it is not possible, explain why. \(\\{n | n \text { is a rational number but not an integer }\\}\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.