/*! 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 6 Evaluate each of the given expre... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 6

Evaluate each of the given expressions by performing the indicated operations. $$-4+(-7)$$

Short Answer

Expert verified
The expression evaluates to \(-11\).

Step by step solution

01

Identify the Operation

In the expression \(-4 + (-7)\), we recognize that we need to perform addition between two negative numbers.
02

Combine the Negative Terms

Since both numbers are negative, you add their absolute values together. Absolute values of \(-4\) and \(-7\) are \(4\) and \(7\) respectively. So, you calculate \(4 + 7 = 11\).
03

Apply the Negative Sign

Finally, because both of the original numbers in the expression are negative, their sum will also be negative. Therefore, \(-4 + (-7) = -11\).

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.

Understanding Absolute Value
Absolute value is essentially the distance of a number from zero on the number line, regardless of direction. It's always a non-negative number. For example, the absolute value of both \(-4\) and \(-7\) is positive. In mathematical terms, we represent absolute value with two vertical bars like this: \( |-4| = 4 \).
This property helps to simplify complex problems, especially when dealing with negative numbers.
  • It turns negative numbers into positives while leaving positive numbers unchanged.
  • For instance, the absolute value of \(7\) is still \(7\), as 7 is already positive.
So, when you see an operation that requires adding negative numbers, consider their absolute values to simplify your task initially, and then take care of the sign at the end. This process is crucial for understanding how negative numbers operate in basic arithmetic.
Adding Integers
Addition of integers can be straightforward once you grasp the rules governing their interactions on the number line. Here's what you need to remember about adding integers, such as in the expression \(-4 + (-7)\).
  • When both integers are negative, as is the case here, you sum their absolute values and then affix a negative sign to the result. This means for \(-4\) and \(-7\), you calculate \(|-4| + |-7| = 4 + 7 = 11\), which becomes \(-11\) since you started with negative numbers.

  • If one integer is positive and the other is negative, you subtract the smaller absolute value from the larger and keep the sign of the integer with the larger absolute value.
This technique makes the addition of integers clearer and more manageable, helping retain accuracy in calculations.
Basic Arithmetic Operations
Basic arithmetic operations, such as addition, subtraction, multiplication, and division, form the foundation of all higher-level math problems. Understanding each operation and its rules is crucial in solving them correctly. In this context, our primary focus is on the addition of negative numbers:
  • Addition: The process of summing numbers. It often involves combining numbers to produce a larger or similar outcome, keeping rules of signs in mind.

  • Subtraction: This is essentially the addition of the opposite. If you find \(a - b\), it equals \(a + (-b)\).

  • Multiplication & Division: These operations also follow rules regarding negative signs, where a negative number times a negative number yields a positive product.
In any arithmetic calculation, remember that the signs of the numbers involved significantly impact the result. Recognizing how these operations interact feeds the problem-solving skills needed for more complex math.

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

Solve the given problems. A laptop computer has a screen that measures 15.6 in. across its diagonal. Convert this to centimeters.

Perform the indicated multiplications. In calculating the temperature variation of an industrial area, the expression \(\left(2 T^{3}+3\right)\left(T^{2}-T-3\right)\) arises. Perform the indicated multiplication.

Solve the given problems. A graphing calculator has a specific key sequence to find cube roots. Using a calculator, find \(\sqrt[3]{2140 \text { and } \sqrt[3]{-0.214}}.\)

Solve the given problems. A TV screen is 52.3 in. wide and 29.3 in. high. The length of a diagonal (the dimension used to describe it - from one corner to the opposite corner) is found by evaluating \(\sqrt{w^{2}+h^{2}}\), where \(w\) is the width and \(h\) is the height. Find the diagonal.

Perform the calculations on a calculator without rounding. Evaluate: (a) \(6.03 \div 2.25+1.77 \quad\) (b) \(6.03 \div(2.25+1.77)\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

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.