/*! 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 75 Perform each indicated operation... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 75

Perform each indicated operation. \(\frac{-5(-6)}{9-(-1)}\)

Short Answer

Expert verified
The result is 3.

Step by step solution

01

Simplify the numerator

First, simplify the expression in the numerator. Here, you have \(-5(-6)\). Calculate the product of -5 and -6. \(-5(-6) = 30\)
02

Simplify the denominator

Now, simplify the expression in the denominator. Here, you have \(9 - (-1)\). Subtracting a negative number is the same as adding the positive counterpart. \(9 - (-1) = 9 + 1 = 10\)
03

Divide the results

Now, take the simplified numerator and divide it by the simplified denominator. \(\frac{30}{10} = 3\)

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
Multiplication of integers involves combining two numbers to get a product. If you multiply two positive numbers or two negative numbers, the result is positive. When you multiply a positive number and a negative number, the result is negative. For example, in the problem \(-5(-6)\), you are multiplying two negative integers. According to the rule, the product is positive. Therefore, \(-5 \times -6 = 30\).
A quick check to remember:
  • Positive \(\times\) Positive = Positive
  • Negative \(\times\) Negative = Positive
  • Positive \(\times\) Negative = Negative
  • Negative \(\times\) Positive = Negative
Simplifying Expressions
Simplifying expressions involves making them easier to work with. Let's consider the denominator, where we had \(9 - (-1)\).
When you subtract a negative number, it is the same as adding the positive equivalent. So, \(9 - (-1)\) becomes \(9 + 1\).
This makes the denominator \(10\).
Simplifying expressions like this helps reduce complex operations into simpler ones. Always look for opportunities to turn subtractions involving negatives into additions.
Division of Integers
For the division of integers, you'll need to remember a few key rules:
  • Positive \(\div\) Positive = Positive
  • Negative \(\div\) Positive = Negative
  • Positive \(\div\) Negative = Negative
  • Negative \(\div\) Negative = Positive
In the problem, we ended with \(\frac{30}{10}\). Both integers are positive, so the result is also positive:
Therefore, \(\frac{30}{10} = 3\)
This basic understanding allows you to confidently handle integer division in different scenarios.

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

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. Work Exercises 139-142 in order, to find the average of \(23,18,13,-4,\) and -8 How many numbers are in the group?

Use the distributive property to rewrite each expression. $$ -\frac{4}{3}(12 y+15 z) $$

A manufacturer has fixed costs of \(\$ 1000\) to produce gizmos. Each gizmo costs \(\$ 5\) to make. The fixed cost to produce gadgets is \(\$ 750,\) and each gadget costs \(\$ 3\) to make. Write an expression for the cost to make \(y\) gadgets.

Write a numerical expression for each phrase, and simplify the expression. 9 less than -13

Write a numerical expression for each phrase, and simplify the expression. The sum of \(\frac{3}{4}\) and \(\frac{1}{2},\) times the difference of \(\frac{2}{3}\) and \(\frac{1}{6}\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

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.