/*! 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 128 Perform these computations. $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 128

Perform these computations. $$-\frac{1}{3}-22$$

Short Answer

Expert verified
-\frac{67}{3}

Step by step solution

01

- Understand the Expression

Identify the terms in the expression. There are two terms: \[-\frac{1}{3}\] and \-22\.
02

- Convert to Common Denominator

Since \-22\ can be written as \[-\frac{66}{3}\], both terms now have the same denominator (3).
03

- Perform the Subtraction

Now subtract \[-\frac{1}{3}\] from \[-\frac{66}{3}\] to get \[-\frac{1}{3} - \frac{66}{3} = -\frac{1 + 66}{3} = -\frac{67}{3}\].
04

- Simplify the Result

Since \[-\frac{67}{3}\] is already in its simplest form, the final answer is \[-\frac{67}{3}\].

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.

common denominator
When dealing with fraction subtraction, it鈥檚 essential to make sure that the fractions involved share the same denominator. This shared denominator is called the 'common denominator.' It allows us to easily perform subtraction or addition between fractions by aligning them under the same baseline number.

In our exercise, we transformed \-22\ into its fraction equivalent, \[-\frac{66}{3}\], so it matches the denominator 3 of \-\frac{1}{3}\.

The common denominator method helps in:
  • Avoiding mistakes while subtracting or adding fractions of varying denominators.
  • Simplifying the calculation process by working within a consistent framework.
simplifying fractions
Simplifying fractions involves reducing a fraction to its simplest form where the numerator and denominator are as small as possible, but retain the same value. This is often achieved by dividing both the numerator and denominator by their greatest common divisor (GCD).

In our example, we initially transformed \-22\ into its fraction form \[-\frac{66}{3}\], and simplified the resulting subtraction without further reduction, since \[-\frac{67}{3}\] was already in its simplest form.

Key points to remember when simplifying fractions:
  • Always check if the numerator and denominator share a common divisor.
  • Always express the final answer in the simplest form.
negative fractions
Negative fractions can initially look tricky, but they follow the same basic principles as positive fractions. A negative fraction simply means that the fraction represents a value less than zero.

In the exercise, both terms \[-\frac{1}{3}\] and \[-\frac{66}{3}\] were negative. When working with negative fractions, here are some tips:

  • Always pay attention to the negative signs. Misplacing them can lead to incorrect results.
  • When performing operations like addition or subtraction, treat the negative fractions like regular fractions but remember to apply the negative rules.
Negative fractions behave like this: \[-\frac{a}{b}\] means you have a fraction \frac{a}{b} that is less than zero. This concept is vital when performing arithmetic operations with fractions.

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

Combine like terms. $$ 2 b^{2} x-16 b^{2} x $$

Combine like terms. $$ s^{4} t-5 s^{4} t $$

Find each product or quotient. $$ \frac{6 x^{3}}{2} $$

Find each product or quotient. $$ \frac{-6 x-9}{-3} $$

Simplify. $$ 2\left(x^{2}-3\right)-\left(6 x^{2}-2\right)+2\left(-7 x^{2}-4\right) $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

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.