/*! 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 56 Perform each indicated operation... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 56

Perform each indicated operation. $$ -5(4-7) $$

Short Answer

Expert verified
15

Step by step solution

01

- Identify the Expression Inside the Parentheses

Note the operation inside the parentheses. Here, you have the expression: \[ 4 - 7 \]
02

- Simplify Inside the Parentheses

Perform the subtraction operation inside the parentheses: \[ 4 - 7 = -3 \]
03

- Multiply the Result by -5

Now, multiply the result from Step 2 by -5: \[ -5 \times (-3) = 15 \]

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 Order of Operations
Mathematics often involves performing several operations within a single expression. To solve these expressions correctly, it's essential to follow the 'order of operations.'

This order can be remembered by the acronym PEMDAS, which stands for:
\begin{itemize} \begin{scriptsize}
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
    • \begin{scriptsize>

    In our example, \(-5(4 - 7)\) we first had to handle the operation inside the parentheses \((4 - 7)\). The subtraction within the parentheses is performed first as per the rules of PEMDAS.
    Simplification Techniques
    Simplification means making a math expression easier to work with by performing operations step-by-step. In our example: \begin{aligned} -5(4 - 7) \begin{aligned} We first simplified the expression in parentheses. Performing \(4 - 7\) gave us \(-3\).
    A step-by-step approach often makes complex problems easier to handle. Each step should be verified to ensure the simplification process is correct. For instance, after simplifying \(4 - 7\), we replaced it with \(-3\) and our expression became \(-5(-3)\). Checking each step helps to avoid mistakes.
    Multiplication of Integers
    Multiplication of integers is another fundamental concept, especially when dealing with positive and negative numbers.
    Here, we multiplied \(-5 \times -3\). Remember some key rules for multiplication of integers:
    \begin{itemize} \begin{scriptsize}
  • Positive x Positive = Positive: \((3 \times 2 = 6)\)
  • Negative x Negative = Positive: \((-3 \times -2 = 6)\)
  • Positive x Negative = Negative: \((3 \times -2 = -6)\)
  • Negative x Positive = Negative: \((-3 \times 2 = -6)\)
    • Using these rules, \(-5\) multiplied by \(-3\) becomes \(15\), because a negative times a negative equals a positive. Hence, our final answer is \(15\).

    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

    Simplify each expression. $$ 100[0.06(x+5)] $$

    A manufacturer has fixed costs of \(\$ 1000\) to produce widgets. Each widget costs \(\$ 5\) to make. The fixed cast to produce gadgets is \(\$ 750,\) and each gadget costs \(\$ 3\) to make . Write an expression for the cost to make \(x\) widgets. (Hint: The cost will be the sum of the fixed cost and the cost per item times the number of items.)

    Write a numerical expression for each phrase and simplify. The product of \(-9\) and \(2,\) added to 9

    Simplify each expression. $$ -\frac{4}{3}+2 t+\frac{1}{3} t-8-\frac{8}{3} t $$

    Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. A number multiplied by \(-7,\) subtracted from the sum of 13 and six times the number
    See all solutions

    Recommended explanations on Math Textbooks

    Theoretical and Mathematical Physics

    Read Explanation

    Probability and Statistics

    Read Explanation

    Discrete Mathematics

    Read Explanation

    Logic and Functions

    Read Explanation

    Mechanics Maths

    Read Explanation

    Calculus

    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.