/*! 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 54 In the following exercises, simp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 54

In the following exercises, simplify. $$ \frac{1}{2}+\frac{7}{8}+\left(-\frac{1}{2}\right) $$

Short Answer

Expert verified
\(\frac{7}{8} \)

Step by step solution

01

- Simplify the Sum

Combine the fractions \(\frac{1}{2} \) and \(-\frac{1}{2} \). Since they are opposites, \(\frac{1}{2} + (-\frac{1}{2}) = 0 \).
02

- Add the Remaining Fraction

Now, add \(\frac{7}{8} \) to the result from Step 1. Since the result from Step 1 is 0, we have \(\frac{7}{8} + 0 = \frac{7}{8} \).

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.

Combining Fractions
When working with fractions, combining them accurately is fundamental. This involves adding or subtracting fractions, which requires a common denominator. In our exercise, we started with three fractions: \(\frac{1}{2}\), \(\frac{7}{8}\), and \(-\frac{1}{2}\).

Notice that \(\frac{1}{2}\) and \(-\frac{1}{2}\) already have common denominators. By adding these, they cancel each other out, equating to zero. Now, we only need to deal with \(\frac{7}{8}\).

To recap:
  • Align the fractions to have the same denominators.
  • Simplify or combine fractions where possible.
  • Proceed step-by-step to avoid errors.
Simplifying Expressions
Simplifying expressions involves reducing them to their simplest form. This makes the math quicker and the expressions easier to understand.

In our problem, after combining \(\frac{1}{2}\) and \(-\frac{1}{2}\), the result is zero. By isolating \(\frac{7}{8}\), we effectively simplified our initial expression.

Here's what we did: \[ \frac{1}{2} + (-\frac{1}{2}) = 0 \] \[ 0 + \frac{7}{8} = \frac{7}{8} \]

Key steps to take:
  • Identify terms that can be combined.
  • Add or subtract similar terms.
  • Simplify the result.
Remember, simplifying means making expressions as straightforward as possible.
Negative Fractions
Negative fractions are essential in algebra and arithmetic. They can seem tricky, but handling them follows the same basic rules as any other number. In our example, \(-\frac{1}{2}\) is a negative fraction.

By adding \(\frac{1}{2}\) and \(-\frac{1}{2}\), the positives and negatives cancel out. This is fundamental to understanding how opposites interact in math.

Important points to remember:
  • When adding a fraction to its negative, the result is zero.
  • Always pay attention to the signs.
  • Treat negative fractions like their positive counterparts but account for the negative sign in arithmetic operations.

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

In the following exercises, convert between metric units. Donna is 1.7 meters tall. Convert her height to centimeters.

In the following exercises, solve, and state your answer in mixed units. John caught 4 lobsters. The weights of the lobsters were 1 pound 9 ounces, 1 pound 12 ounces, 4 pounds 2 ounces, and 2 pounds 15 ounces. What was the total weight of the lobsters?

In the following exercises, evaluate each expression for the given value. If \(m=-13,\) evaluate: $$ (a)-\frac{2}{5}\left(\frac{5}{2} m\right) $$ $$ (b)\left(-\frac{2}{5} \cdot \frac{5}{2}\right) m $$

In the following exercises, evaluate using the distributive property. If \(d=14,\) evaluate $$ (a)-100(0.1 d+0.35) $$ $$ \begin{array}{l}{\text { (b) }-100 \cdot(0.1 d)+(-100)(0.35)} \\ {\text { to } \operatorname{show}} \\ {-100(0.1 d+0.35)=-100 \cdot(0.1 d)+(-100)(0.35)}\end{array} $$

In the following exercises, simplify. $$ 43+39+(-43) $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

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.