/*! 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 56 Determine whether each statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 56

Determine whether each statement is true or false.\(\frac{1}{2}\) is an integer.

Short Answer

Expert verified
False, \( \frac{1}{2} \) is not an integer.

Step by step solution

01

Understand the Problem

To determine if \( \frac{1}{2} \) is an integer, we need to recall the definition of an integer. Integers are whole numbers that include positive numbers, negative numbers, and zero (e.g., -3, -2, -1, 0, 1, 2, 3,...). They do not include fractions or decimals.
02

Analyze the Given Number

The number given is \( \frac{1}{2} \). This is a fraction where the numerator is 1 and the denominator is 2.
03

Compare with Integer Definition

Since \( \frac{1}{2} \) is expressed as a fraction and is not a whole number, it does not meet the criteria to be classified as an integer.

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.

Fractions
Fractions are a significant part of mathematics and everyday life. They represent parts of a whole and are written as two numbers separated by a line; for example, \( \frac{1}{2} \). The number above the line is called the numerator, and the number below is the denominator. In our example, 1 is the numerator, and 2 is the denominator.
Fractions can be
  • proper: where the numerator is smaller than the denominator, like \( \frac{1}{2} \)
  • improper: where the numerator is larger than or equal to the denominator, such as \( \frac{5}{4} \)
  • mixed numbers: a combination of whole numbers and a fraction, such as 2\( \frac{1}{3} \)
Understanding fractions is crucial because they are not whole numbers, and this distinction often creates confusion when classifying numbers. Always remember: if there's a numerator and a denominator, you're dealing with a fraction, not a whole number.
Whole Numbers
Whole numbers form the foundation of basic math. They begin at zero and include positive numbers. Examples are 0, 1, 2, 3, and so on. Unlike fractions, whole numbers do not contain any parts 鈥� they are complete by themselves.
Whole numbers are:
  • non-negative: meaning they cannot be negative
  • no fractions or decimals: whole numbers stand alone and do not have fractional or decimal parts
This is important when discussing integer classification since fractions can't fit into a whole number category. When we refer to counting numbers like 1, 2, and 3, we are essentially talking about a subset of whole numbers. Always think of whole numbers as the basic units you start counting with, simple and complete.
Number Classification
Understanding number classifications is essential to grasp the full spectrum of numbers we deal with in mathematics. Each type has distinct characteristics, including integers, whole numbers, rational numbers, and fractions.
The key classifications are:
  • Integers: Include whole numbers and their negative counterparts, such as -2, -1, 0, 1, 2. Integers do not include fractions or decimals.
  • Rational numbers: Any number that can be expressed as a fraction of two integers (e.g., \( \frac{3}{4} \)), meaning all fractions are rational numbers.
  • Whole numbers: Start from zero and include positive integers (0, 1, 2, 3,...).
Classifying numbers correctly helps avoid confusion, especially in problems like determining if \( \frac{1}{2} \) is an integer. Since integers must be whole numbers, fractions like \( \frac{1}{2} \) do not qualify. This framework is key to understanding and working with different number types in math.

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

Translate each phrase to an expression and simplify. Subtract 8 from 7 .

Simplify each expression. \(|-3|+2^{2}+[-4-(-6)]\)

Subtract. \(-\frac{3}{11}-\left(-\frac{5}{11}\right)\)

Simplify each expression. \(-16-(-3)+(-11)-14\)

Simplify each expression. \(-2+[(8-11)-(-2-9)]\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Mechanics 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.