Problem 5 - Basic College Mathematics

Question

For Exercises \(1-16,\) answer yes or no and give a reason based on the tests for divisibility. Determine whether 671,500 is divisible by 10

Step-by-Step Solution

Answer

Yes, 671,500 is divisible by 10 because its last digit is 0.

Step 1: Understand the Divisibility Rule for 10

A number is divisible by 10 if its last digit is 0.

Step 2: Identify the Last Digit

Look at the last digit of the number 671,500. The last digit is 0.

Step 3: Apply the Rule

Since the last digit is 0, the number 671,500 meets the rule for divisibility by 10.

Step 4: Conclusion

Based on the divisibility rule for 10, verify that 671,500 is divisible by 10.

Key Concepts

divisibility by 10

To know if a number is divisible by 10, we use a simple rule: the number must end in 0. This is because 10 itself ends in 0. How does this work?
When a number ends in 0, it means there’s no remainder left when you divide it by 10. For example, 50, 120, and 670 are all divisible by 10.
On the contrary, numbers like 51, 123, and 671 are not divisible by 10. Understanding this rule helps save time and reduce mistakes in solving math problems.

last digit analysis

When analyzing the last digit of a number, you're focusing on what digit appears in the unit place. This digit determines whether a number is divisible by 2, 5, or 10.
For divisibility by 10, the last digit should be 0. Take the number 671,500: the last digit is 0. Hence, 671,500 is divisible by 10.
Learning to quickly identify this promotes better mathematical intuition and faster problem-solving skills.

mathematics education

Mathematics education is not just about memorizing rules; it's about understanding the why behind them. Teaching concepts like divisibility by 10 helps students develop logical reasoning.
When students know why the last digit matters, they can apply this knowledge to various mathematical scenarios.
Incorporating these fundamentals early on makes math less intimidating and more approachable.

number properties

Number properties help in simplifying and solving mathematical problems. Divisibility rules are a part of these properties. They allow for quicker calculations.
Understanding that a last digit of 0 makes a number divisible by 10 is one such property.
It’s a small, powerful tool that enhances computational efficiency, and provides a solid foundation for higher-level math concepts.