Problem 10 - Basic College Mathematics

Question

For Exercises \(1-16,\) answer yes or no and give a reason based on the tests for divisibility. Determine whether 64,091 is divisible by \(10 .\)

Step-by-Step Solution

Answer

No, because the last digit is not 0.

Step 1: Identify the Divisibility Rule for 10

A number is divisible by 10 if and only if its last digit is zero.

Step 2: Check the Last Digit

Examine the last digit of the number 64,091. The last digit is 1.

Step 3: Apply the Rule

Since the last digit is not 0, 64,091 is not divisible by 10.

Key Concepts

Divisibility by 10

To determine if a number is divisible by 10, you only need to check its last digit. This rule is straightforward and very easy to apply. If the number ends in a 0, it is divisible by 10. For instance, numbers like 50, 120, and 430 all end in 0, so they are divisible by 10. Conversely, if the last digit is anything other than 0, the number is not divisible by 10.
When applying this to our example, 64,091, we see that the last digit is 1. Since this last digit is not 0, we can immediately conclude that 64,091 is not divisible by 10. This simple rule helps quickly determine divisibility and makes it easy to check large numbers.
Remembering these rules can help you in exams and everyday problem-solving. It's a basic yet powerful tool in arithmetic.

Mathematics Exercises

Mathematics exercises, like the one given, help you practice and understand core concepts. In this case, the divisibility rule for 10 is checked through a straightforward problem. Exercises typically present a problem and guide you through solving it step by step.
Engagement in such exercises fosters a deeper understanding of mathematical principles. They help you recognize patterns, apply rules, and think logically.
These exercises can range from very basic to highly complex problems. Starting with simpler problems, like checking divisibility, builds a foundation. As you progress, you can solve more intricate problems.
Regular practice through exercises is crucial. It builds confidence and reinforces your learning. Practicing divisibility rules enhances your speed and accuracy, making it easier to handle more advanced mathematics.

Step-by-Step Solution

Breaking down a problem into simple steps can make even the most complex problems much easier to understand. In our example, the solution was divided into manageable steps.

1. First, identify the rule: Check if the number ends in 0.
2. Next, examine the last digit to apply this rule.
3. Finally, draw the conclusion based on the rule.

Each step follows logically from the previous one, ensuring clarity. By focusing on one aspect at a time, you avoid feeling overwhelmed and ensure accuracy.
This approach is beneficial not only in math but in all problem-solving scenarios. It encourages thoroughness and helps you catch mistakes that you might overlook if you try to solve the problem all at once.
Remember to practice a step-by-step approach with different math problems. Soon, it will become second nature, and you'll find solving math exercises less daunting.