/*! 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 29 Use any of the rules developed i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 29

Use any of the rules developed in this chapter and the rule for order of operations to simplify each of the following expressions as much as possible. [Examples 6鈥�9] $$\frac{-3(-10)}{-5}$$

Short Answer

Expert verified
The expression simplifies to \(-6\).

Step by step solution

01

Simplify the Numerator

First, focus on the numerator of the fraction \(-3(-10)\). The multiplication of two negative numbers results in a positive number. Therefore, \(-3 \times -10 = 30\).
02

Rewrite the Expression with a Simplified Numerator

Replace the original numerator with the simplified result from Step 1. The expression now becomes \(\frac{30}{-5}\).
03

Simplify the Fraction

Now, divide 30 by -5. Divide 30 by 5 to get 6, and keep the negative sign from -5 to obtain \(-6\). Thus, \(\frac{30}{-5} = -6\).

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.

Simplifying Fractions
Fractions can be tricky for many students, but simplifying them makes calculations more manageable. Simplifying fractions involves reducing them to their simplest form, where the numerator and the denominator have no common factors other than 1. In this exercise, the fraction \( \frac{30}{-5} \) was simplified using basic division, leading to an integer.
  • Identify Factors: Look at both the numerator and the denominator to see if there are any common factors. Here, 30 and 5 have the factor 5 in common.
  • Apply Division: Divide both the numerator and the denominator by their greatest common factor to simplify. Dividing 30 by 5 gives 6.
  • Sign Handling: Since the denominator is negative, the result of the fraction becomes negative as well, meaning \( \frac{30}{-5} = -6 \).
Simplifying fractions is essential for making complicated problems much more approachable.
Multiplying Integers
Understanding multiplication of integers is key to solving many math problems. When working with integers, it's important to pay attention to their signs, as they influence the result significantly.
  • Positive and Negative Integers: Remember that multiplying two negative integers results in a positive integer. This is because the negatives cancel each other out.
  • Example: In our problem, \(-3 \times -10\) equals 30. Both numbers are negative, and their multiplication yields a positive result.
  • Order of Operations: Always follow the order of operations when dealing with expressions involving integers to ensure accuracy.
By consistently applying these principles, you鈥檒l become proficient in handling integer multiplication.
Division of Integers
Division of integers is straightforward but requires careful consideration of signs. Just like with multiplication, the signs of the integers involved play a crucial role in determining the outcome.
  • Positive and Negative Results: When you divide a positive integer by a negative integer, the result is negative. Similarly, if a negative integer is divided by a positive one, the resultant is also negative.
  • Example: With \( \frac{30}{-5} = -6 \), you divide 30 (positive) by -5 (negative). The outcome is -6 since a positive number divided by a negative number gives a negative.
  • Basic Calculation: Perform the division as usual, but consider the sign of the result. Simplify this process with practice to gain confidence in recognizing how the signs affect division results.
Mastering the division of integers provides a solid foundation for more advanced mathematical concepts.

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

Add or subtract. $$12-3-7+5$$

Subtract. $$121-21$$

Profit and Loss You own a small business which provides computer support to homeowners who wish to create their own in-house computer network. In addition to setting up the network you also maintain and troubleshoot home PCs. Business gets off to a slow start. You record a profit of \(\$ 2,298\) during the first quarter of the year, a loss of \(\$ 2,854\) during the second quarter, a profit of \(\$ 3,057\) during the third quarter, and a profit of \(\$ 1,250\) for the last quarter of the year. Do you end the year with a net profit or a net loss? Represent that profit or loss as a positive or negative value.

Add or subtract. $$[3+10]+[8-2]$$

Translate each of the following and simplify the result. Subtract \(-4\) from the sum of \(-8\) and 12
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Mechanics 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.