/*! 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 67 Find each difference. $$ \fr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 67

Find each difference. $$ \frac{1}{2}-\left(-\frac{1}{4}\right) $$

Short Answer

Expert verified
The answer is \(\frac{3}{4}\).

Step by step solution

01

Identify the Operation

The given problem is to find the difference between two fractions. The expression is \(\frac{1}{2} - \big(-\frac{1}{4} \big)\). Note that subtracting a negative number is equivalent to adding its positive.
02

Rewrite the Expression

Rewrite the expression by eliminating the negative sign. \(\frac{1}{2} - \big( -\frac{1}{4} \big) = \frac{1}{2} + \frac{1}{4}\).
03

Find a Common Denominator

To add the fractions, find a common denominator. The denominators are 2 and 4. The least common denominator is 4.
04

Convert Fractions to Common Denominator

Convert \(\frac{1}{2}\) to a fraction with denominator 4. \(\frac{1}{2} = \frac{2}{4}\). Now the expression is \(\frac{2}{4} + \frac{1}{4}\).
05

Add the Fractions

Add the two fractions with the same denominator: \(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).

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
To add or subtract fractions, they must have the same denominator. The denominator is the bottom number of the fraction and tells us how many equal parts the whole is divided into.
Finding a common denominator means finding a number that both denominators can divide into without leaving a remainder. This number is often the least common multiple (LCM) of the original denominators.
In the exercise, we have denominators 2 and 4. The LCM of 2 and 4 is 4. We then convert \(\frac{1}{2}\) to \(\frac{2}{4}\) to give both fractions the same denominator. This step is crucial for proper addition or subtraction.
Adding Fractions
Once the fractions have a common denominator, adding them becomes straightforward. You simply add the numerators (the top numbers) and keep the denominator the same.
In our exercise, after converting \(\frac{1}{2}\) to \(\frac{2}{4}\), we add it to \(\frac{1}{4}\).
This looks like: \(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\)
The crucial part here is not to add the denominators, only the numerators. The denominator indicates the size of the parts we are adding, which stays the same.
Negative Numbers
Subtracting a negative number can be tricky but simpler than it sounds. The rule is straightforward: subtracting a negative number is the same as adding the positive of that number.
In our example, \(\frac{1}{2} - \big(-\frac{1}{4}\big)\) converts to \(\frac{1}{2} + \frac{1}{4}\).
This subtraction turns into an addition because a negative sign followed by another negative sign becomes positive.
This concept helps simplify many problems that involve both negative and positive numbers.

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

Use the distributive property to rewrite each expression. $$ -5.2(4 x+2.3) $$

Use the distributive property to rewrite each expression. $$ 2(6 x+5) $$

Use the distributive property to rewrite each expression. $$ 8(3 r+4 s-5 y) $$

Use the distributive property to rewrite each expression. $$ -\frac{1}{4}(8 x+3) $$

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \((6-x)(5+y)(3+a)\)
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Probability and 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.