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Chapter 1: Problem 16

Which of the following numbers is not divisible by 2? $$382, 570, 193, 196 $$

Short Answer

Expert verified
193 is not divisible by 2.

Step by step solution

01

Identify Criteria for Divisibility by 2

A number is divisible by 2 if its last digit is an even number. Even numbers end in 0, 2, 4, 6, or 8.
02

Check Each Number

Look at the last digit of each number to check divisibility: - 382 ends in 2, which is even. - 570 ends in 0, which is even. - 193 ends in 3, which is odd. - 196 ends in 6, which is even.
03

Determine the Number That Is Not Divisible by 2

Since the last digit of 193 is an odd number (3), 193 is not divisible by 2.

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Key Concepts

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

Understanding Even Numbers
In mathematics, even numbers play a vital role in exploring divisibility rules. An even number is any integer that can be divided by 2 without leaving a remainder. This means when you divide an even number by 2, the result is always a whole number.

If you glance at the number's last digit, you'll see the telltale sign of an even number. Specifically, numbers ending in 0, 2, 4, 6, or 8 are considered even.
  • A number ending in 0, like 10, is even because 10 divided by 2 equals 5.
  • Similarly, a number ending in 4, such as 24, is even, since 24 divided by 2 equals 12.
  • Recognizing these ending digits helps quickly determine if a number is even and therefore divisible by 2.
The Fundamentals of Number Operations
Performing number operations is a key skill in mathematics that allows you to solve various problems. These operations include addition, subtraction, multiplication, and division, and each has its own rules and properties.

When dealing with divisibility, you focus mainly on division. A number operation approach can help identify if numbers can be evenly divided by checking specific criteria.
  • For instance, with divisibility by 2, any number with an even last digit can undergo division by 2 effortlessly.
  • Learning these basic number operations builds a foundation to tackle more advanced problems.

Applying these operations consistently aids in identifying patterns, such as recognizing whether numbers end evenly or not.
Exploring Prealgebra Concepts
Prealgebra sets the stage for more advanced mathematical studies by introducing fundamental concepts like divisibility rules. These concepts help to develop critical thinking skills and numeric fluency.

When studying divisibility rules in prealgebra, you learn through simple procedures and guidelines. For example, understanding that a number is divisible by 2 if it ends in an even number is key.
  • As students explore these rules, they begin identifying and working with various types of numbers systematically.
  • Grasping these basic principles provides the confidence to engage with more complex algebraic operations later on.

Being well-versed in prealgebra concepts shapes the ability to tackle real-world problems mathematically, through logical reasoning and analysis.

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Most popular questions from this chapter

Simplify the given expression. $$ 20 \div 1 \cdot 4 $$

Simplify the given expression. $$ 2^{3}-1^{3} $$

Simplify the given expression. $$ 19+3\left[12-\left(2^{3}+1\right)\right] $$

Simplify the given expression. $$ 17+7\left[13-\left(2^{2}+6\right)\right] $$

Simplify the given expression. $$ 45 \div 3 \cdot 5 $$
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