/*! 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 72 Simplify each numerical expressi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 72

Simplify each numerical expression. $$ (-7)(-7)-(-6)(4) $$

Short Answer

Expert verified
The simplified expression is 73.

Step by step solution

01

Multiply the First Pair of Numbers

Calculate the product of the two negative numbers: \((-7) \times (-7) = 49\). Since multiplying two negative numbers gives a positive result, the product is 49.
02

Multiply the Second Pair of Numbers

Calculate the product of the negative and positive number: \((-6) \times 4 = -24\). A negative times a positive is a negative, so the product is -24.
03

Subtract the Second Product from the First Product

Subtract the result from Step 2 from the result in Step 1:\(49 - (-24)\).Subtracting a negative is the same as adding the corresponding positive: \(49 + 24 = 73\).

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.

Multiplying Negative Numbers
Multiplying two negative numbers can sometimes be confusing, but it's a simple rule once you understand it. When two negative numbers are multiplied together, the result is always a positive number. This might seem counterintuitive at first. To visualize this, think about the rule "double negative equals a positive," which applies here too. When you multiply \(-7 \times -7\), each negative sign cancels the other out, leading to \(+49\). It's similar to the logic that subtracting a negative value ends up adding a positive value.
Understanding these basics can simplify your approach to solving many math problems.
Integer Operations
Integer operations involve adding, subtracting, multiplying, and dividing whole numbers, including both positive and negative numbers. When dealing with integer multiplication, like in the original exercise, the rules for signs are critical.
Here are some key points to remember:
  • The product of two positive numbers is positive.
  • The product of two negative numbers is positive.
  • The product of a positive and a negative number is negative.
Take the expression \((-6) \times 4\), for example. Multiplying a negative by a positive number results in a negative product, which in this case is \(-24\). Remembering these rules allows you to quickly perform and simplify integer operations.
Addition and Subtraction of Integers
Adding and subtracting integers can be particularly tricky, especially when negatives are involved. The basic rule here is that subtracting a negative number is the same as adding its opposite, or equivalent positive number. In our example, you had to tackle \((49 - (-24))\).
Since subtracting a negative is effectively addition, this simplifies to \((49 + 24)\), which gives you \73\.
To perform integer addition and subtraction smoothly, consider using a number line or think in terms of moving left (subtraction) or right (addition) on the number line. This process will help you grasp the right direction for each operation.

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

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. Ten times the difference of a number and 6

Answer the question with an algebraic expression. If \(n\) represents a whole number, what represents the next larger whole number?

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. Six more than one-third of a number

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. A number subtracted from 75

Evaluate the algebraic expressions for the given values of the variables. $$ 4 x^{2}-y^{2}, x=2 \text { and } y=-2 $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

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.