/*! 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 81 Evaluate each expression. \(\f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 81

Evaluate each expression. \(\frac{-9(-3)}{-6}\)

Short Answer

Expert verified
The value of the expression is \(-4.5\).

Step by step solution

01

Understand the Expression

The expression given is a fraction \( \frac{-9(-3)}{-6} \). It involves multiplication in the numerator and a division operation.
02

Compute the Numerator

Multiply the numbers in the numerator: \(-9\) and \(-3\). Know that the product of two negative numbers is positive. Therefore, \(-9 \times -3 = 27\).
03

Write the Simplified Fraction

After computing the numerator, the expression becomes \( \frac{27}{-6} \).
04

Divide the Numbers

Now, divide 27 by \(-6\). The division of a positive number by a negative number yields a negative result. \( \frac{27}{-6} = -4.5 \).
05

Simplify if Necessary

Check if the result \(-4.5\) can be simplified further. In this case, \(-4.5\) is already in the simplest form.

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
When multiplying integers, especially negative ones, it's important to remember a few key rules:
  • The product of two negative numbers is positive. For example, \(-3 \times -3 = 9\).
  • The product of a positive and a negative number is negative. For instance, \(3 \times -3 = -9\).
  • The product of two positive numbers is positive, just as in standard multiplication.
In our exercise, the numbers \(-9\) and \(-3\) are both negative. Following the rule for the multiplication of two negatives, the product is positive. So, \(-9 \times -3\) results in \(27\). Understanding these rules helps to simplify complex expressions and handle integers accurately.
Division of Integers
Integer division can be a bit tricky, especially when negatives come into play. Here are some easy rules to guide you:
  • Dividing two positive numbers, or two negative numbers, results in a positive quotient. For example, \(-10 \div -5 = 2\).
  • Dividing a positive number by a negative number, or vice versa, gives a negative quotient. For example, \(20 \div -5 = -4\).
In the given exercise, the numerator \(27\) (positive) is divided by the denominator \(-6\) (negative). Applying the rule, a positive divided by a negative, yields a negative result: \(\frac{27}{-6} = -4.5\). This understanding makes it easier to handle equations involving large numbers and diverse signs.
Simplification of Fractions
Simplifying fractions is a useful skill in algebra that makes arithmetic operations and comparisons clearer. Here's how it works:
  • First, identify the greatest common divisor (GCD) of the numerator and the denominator. Use this to divide both the numerator and the denominator, simplifying the fraction to its lowest terms.
  • In cases where the fraction results in a decimal or whole number, such as \(-4.5\) in our example, check if it's already presented in the simplest form.
  • If possible, simplify further until you cannot find any common divisors other than 1.
For the fraction \(\frac{27}{-6}\), the division gives \(-4.5\), which is already simplified. It's crucial to be comfortable with rewriting fractions in simpler forms to ensure accuracy in calculations and comparisons.

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. \(5-9+(-4)-8-8\)

Subtract. \(-\frac{4}{7}-\left(-\frac{1}{7}\right)\)

Translate each phrase to an expression and simplify. Subtract -2 from 3 .

The highest point in Africa is Mt. Kilimanjaro, Tanzania, at an elevation of 19,340 feet. The lowest point is Lake Assal, Djibouti, at 512 feet below sea level. How much higher is Mt. Kilimanjaro than Lake Assal? (Source: National Geographic Society)

Translate each phrase to an expression and simplify. Find the difference between -17 and -1 .
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

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.