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Chapter 1: Problem 27

Fill in the blanks. An integer that cannot be evenly divided by 2 is called an _____ integer.

Short Answer

Expert verified
An integer that cannot be evenly divided by 2 is called an Odd integer.

Step by step solution

01

Understanding the Concept

An integer is a whole number, but it's not always even. If it can't be divided by 2 evenly, that means that there's a remainder after dividing by 2. This property is what distinguishes between two types of integers: even and odd.
02

Identify the Integer

The integer that cannot be divided evenly by 2 is called an odd integer. The reason is that after dividing an odd number by 2, there is always a remainder of 1.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Odd Integers
Odd integers are numbers that cannot be divided by 2 without leaving a remainder. When you divide an odd integer by 2, the result is not a whole number. For example, if you divide 7 by 2, the quotient is 3 with a remainder of 1. This remainder indicates that the number is odd.

Key features of odd integers include:
  • They end with the digits 1, 3, 5, 7, or 9.
  • The result of an odd integer plus an even integer is always odd.
  • Multiplying two odd integers results in an odd product.
Understanding these properties can help you quickly identify and work with odd integers.
Even Integers
Even integers are whole numbers that can be exactly divided by 2 without any remainder. In other words, their division by 2 results in a whole number. For example, dividing 10 by 2 results in a quotient of 5 and no remainder, making 10 an even integer.

Here are some quick facts about even integers:
  • They end with the digits 0, 2, 4, 6, or 8.
  • The sum of two even integers is always even.
  • When an odd integer is added to an even integer, the result is odd.
  • Multiplying any integer by 2 results in an even integer.
These characteristics make even integers easy to spot and manipulate in various mathematical operations.
Divisibility Rules
Divisibility rules are tools to quickly determine whether a number can be divided by another without leaving a remainder. These rules make it easier to work with large numbers without resorting to long division. Let's look at a couple of these rules:

  • Divisibility by 2: A number is divisible by 2 if its last digit is even, i.e., 0, 2, 4, 6, or 8. This rule helps identify even integers.
  • Divisibility by 3: Add all the digits in a number together. If the resulting sum is divisible by 3, then the original number is also divisible by 3.
  • Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5.
These divisibility rules can simplify calculations and are handy for quickly figuring out factors or simplifying fractions. Using these will improve your efficiency when solving math problems and help in identifying even and odd numbers easily.

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