/*! 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 71 Fill in the blanks with \(<,&... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 71

Fill in the blanks with \(<,>,\) or \(=\). $$-\frac{3}{12} \square-\frac{2}{8}$$

Short Answer

Expert verified
-\frac{3}{12} = -\frac{2}{8}

Step by step solution

01

Simplify the Fractions

First, simplify both fractions to their lowest terms. For \(-\frac{3}{12}\), divide the numerator and the denominator by their greatest common divisor, which is 3. \(-\frac{3}{12} = -\frac{1}{4}\). For \(-\frac{2}{8}\), divide the numerator and the denominator by their greatest common divisor, which is 2. \(-\frac{2}{8} = -\frac{1}{4}\).
02

Compare Simplified Fractions

Now compare \(-\frac{1}{4}\) to \(-\frac{1}{4}\). Since both fractions are equal, the relationship is \(=\).

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
Simplifying fractions means reducing them to their lowest terms. This makes it easier to compare them.

Here's how to simplify any fraction:
  • 1. Find the greatest common divisor (GCD) of the numerator and the denominator.
  • 2. Divide both the numerator and the denominator by this GCD.

For example, if we start with \(-\frac{3}{12}\), we can simplify it by finding the GCD of 3 and 12, which is 3. Dividing both terms by 3, we get \(-\frac{1}{4}\).
Similarly, for \(-\frac{2}{8}\), the GCD of 2 and 8 is 2. Dividing both terms by 2, we obtain \(-\frac{1}{4}\).
Sometimes, finding the GCD can be tricky, but a simple way to approach it is to break down the numbers into their prime factors. The GCD will be the product of the lowest power of common prime factors.
Comparing Fractions
Comparing fractions involves more than just looking at the numerators or denominators. It's important to understand the value represented by each fraction.
  • If the fractions have the same denominators, compare the numerators directly.
  • If they have different denominators, you may need to bring both fractions to a common denominator before comparing.

In our exercise, after simplifying both fractions to \(-\frac{1}{4}\), it becomes clear that \'-1' in both fractions signifies that they are equivalent. Therefore, \(-\frac{1}{4} = -\frac{1}{4}\).
Generally speaking, for fractions with the same denominator, the fraction with the larger numerator is the larger fraction, and vice versa. With fractions having different denominators, finding a common denominator helps lay the groundwork for a fair comparison.
Negative Fractions
Negative fractions can sometimes be confusing, but they follow the same rules as positive fractions鈥攐nly the direction of inequality changes.
  • A fraction with a larger negative numerator (in absolute value) is smaller.
  • For example, \-\frac{1}{4}\ is larger than \-\frac{2}{4}\.

In our exercise, \(-\frac{3}{12}\) and \(-\frac{2}{8}\) simplified to \-\frac{1}{4}\ respectively, indicating they are equal.
Moreover, if we were comparing \-\frac{1}{3}\ and \-\frac{1}{4}\, \-\frac{1}{4}\ would be the larger fraction as \(-\frac{1}{4}\) is closer to 0 on the number line than \(-\frac{1}{3}\).
Remember this rule, and negative fractions will become much less intimidating to handle.

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

Which expressions are equivalent to \(\frac{-9}{10} ?\) \(\begin{array}{cccc}\text { a. } \frac{9}{10} & \text { b. }-\frac{9}{10} & \text { c. } \frac{9}{-10} & \text { d. } \frac{-9}{-10}\end{array}\)

Simplify. $$-\left(-\frac{1}{4}\right)$$

For Exercises 33鈥�38, label the fraction as proper or improper. $$\frac{7}{8}$$

True or false? Suppose \(m\) and \(n\) are nonzero numbers, where \(m>n .\) Then \(\frac{m}{n}\) is an improper fraction.

Simplify the fraction to lowest terms. Write the answer as a fraction or a whole number. $$\frac{69}{92}$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

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.