Problem 3 - Basic College Mathematics

Question

For Exercises \(1-16,\) answer yes or no and give a reason based on the tests for divisibility. Determine whether 5553 is divisible by \(5 .\)

Step-by-Step Solution

Answer

No, because 5553 does not end in 0 or 5.

Step 1 - Understand the Divisibility Rule for 5

A number is divisible by 5 if and only if its last digit is either 0 or 5.

Step 2 - Examine the Last Digit of the Given Number

Look at the last digit of the number 5553. The last digit is 3.

Step 3 - Apply the Divisibility Rule for 5

Since the last digit is 3, and 3 is neither 0 nor 5, it follows that 5553 is not divisible by 5.

Key Concepts

divisibility by 5

To determine if a number is divisible by 5, you need to check its last digit. According to the divisibility rule for 5, a number is divisible by 5 if it ends in 0 or 5. Let's take an example:

Consider the number 5553. The last digit of 5553 is 3. Since 3 is neither 0 nor 5, 5553 is not divisible by 5. This rule makes it easy to quickly assess whether a number can be divided by 5 without leaving a remainder.

In summary:

• Check the last digit
• If the last digit is 0 or 5, then the number is divisible by 5.

mathematical reasoning

Mathematical reasoning involves logical thinking and problem-solving skills. It's about understanding why a particular rule or formula works. When we see that a number like 5553 is not divisible by 5 because its last digit is 3, we are using mathematical reasoning.

By following steps:

• Identify the problem (checking divisibility by 5)
• Recall the rule (last digit must be 0 or 5)
• Apply the rule to your number (last digit of 5553 is 3)

We logically conclude that the number is not divisible by 5. This kind of reasoning helps us solve problems efficiently and correctly.

Practicing mathematical reasoning can boost your confidence and improve your ability to tackle complex problems.

number properties

Number properties are the special characteristics that numbers possess. These include divisibility rules, even and odd properties, prime numbers, and more. Understanding these properties makes it easier to work with numbers and solve mathematical problems.

For instance, knowing the property of divisibility by 5 (a number ends in 0 or 5) helps you quickly determine if a number can be divided by 5. This is a small piece of a larger set of rules and properties that govern how numbers behave.

Here are some key properties of numbers:

• Even/Odd: Even numbers end in 0, 2, 4, 6, or 8. Odd numbers end in 1, 3, 5, 7, or 9.
• Prime Numbers: These are numbers greater than 1 that have no divisors other than 1 and themselves.
• Divisibility Rules: These rules help us quickly determine if one number can be divided by another.

Understanding these properties can make math more manageable and enhance your problem-solving skills.