/*! 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 26 Find each difference. $$-9-(-7... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 26

Find each difference. $$-9-(-7)$$

Short Answer

Expert verified
The difference is -2.

Step by step solution

01

Identify the Original Expression

The original expression given is \(-9 - (-7)\).Notice that we have a subtraction of a negative number.
02

Understand Minus and Negative Signs

Subtracting a negative number is the same as adding its positive counterpart. So, we need to remember that \(-(-7) = +7\).
03

Simplify the Expression

Replace the subtraction of the negative with the addition of the positive: \(-9 + 7\).
04

Calculate the Result

Now, compute \(-9 + 7\). Begin by thinking of a number line: move 9 units left for the -9, then 7 units right for the +7. You land at -2.

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.

Subtracting Negatives
When you encounter a mathematical expression where you need to subtract a negative number, it can initially seem confusing. However, there is an important rule that can simplify the process:
  • Subtracting a negative is the same as adding the positive of that number.
So, in the context of the given exercise \(-9 - (-7)\), the subtraction of \(-7\) becomes an addition \(+7\). This rule comes from the idea that two negative signs back to back cancel each other out, effectively switching to a positive sign.

Thinking this way can greatly simplify calculations and help avoid errors.
Integer Operations
Integer operations refer to basic math operations (such as addition, subtraction, multiplication, and division) performed on whole numbers. When working with integers:
  • Positive numbers are numbers greater than zero.
  • Negative numbers are numbers less than zero.
  • Zero itself is neutral - neither positive nor negative.
Understanding how to perform operations involving negative numbers is essential. When you have a problem like \(-9 + 7\), start by identifying the biggest number and its sign. In this case, \(-9\) is bigger than \(+7\), so the answer will be negative.

Subtract the smaller absolute value from the larger: \(9 - 7 = 2\). Then, because the larger number (9) was negative, the result is -2. This keeps the calculation straightforward and logical.
Number Line
Visualizing numbers and their operations on a number line can make understanding integer operations much easier. A number line is a straight line where we can represent integers:
  • Moving right indicates increasing or adding positive numbers.
  • Moving left indicates decreasing or adding negative numbers.
If we take the problem \(-9 + 7\), start at \(0\) and move 9 steps left to reach \(-9\). Then, move 7 steps to the right because we are adding 7. You'll find yourself at \(-2\) on the number line.

This visual approach can help solidify the understanding of how integer operations work in practical terms.

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

Graph each point. Then connect the points in alphabetical order and identify the figure. $$\begin{aligned} &A(5,8), B(1,13), C(5,18), D(9,13), E(5,8), F(5,6), G(3,7), H(3,5), I(7,7)\\\ &J(7,5), K(5,6), L(5,3), M(3,4), N(3,2), P(7,4), Q(7,2), R(5,3), S(5,1) \end{aligned}$$

Evaluate each expression. $$\frac{600}{-20}$$

Evaluate each expression. $$x \div 4, \text { if } x=-52$$

ALGEBRA Evaluate each expression if \(a=-8\) and \(b=5\) $$$2|a|$$

Simplify each expression. $$-12 m(-9 n)$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Decision 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.