Problem 39 - Basic College Mathematics

Question

To answer Exercises \(33-40\), consider the following numbers. \(\begin{array}{rrrr}305 & 313,332 & 876 & 64,000 \\ 1101 & 7624 & 1110 & 9990 \\\ 13,205 & 111,126 & 5128 & 126,111\end{array}\) Which of the above are divisible by \(10 ?\)

Step-by-Step Solution

Answer

64,000, 1110, and 9990.

Step 1: Identify divisibility rule for 10

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

Step 2: Check each number

Examine the last digit of each number given: - 305 - 313,332 - 876 - 64,000 - 1101 - 7624 - 1110 - 9990 - 13,205 - 111,126 - 5128 - 126,111.Only the numbers ending in 0 are divisible by 10.

Step 3: List the divisible numbers

From the list, the numbers ending in 0 are: - 64,000 - 1110 - 9990.

Key Concepts

divisibility by 10

Divisibility rules are shortcuts that help us determine whether a number can be divided by another number without performing the actual division. One common rule involves divisibility by 10. A number is divisible by 10 if its last digit is 0. This means you can quickly check any number just by looking at its last digit. For example:

• 305 is not divisible by 10 because its last digit is 5.
• 64,000 is divisible by 10 because its last digit is 0.

Using this rule makes it very easy to filter out numbers at a glance without having to do long division!

number properties

Understanding basic number properties is important in math. These properties help us categorize numbers and apply the right rules. A critical property when dealing with divisibility is looking at the digits of a number. For instance, to determine if a number is divisible by 10, you only need to check its last digit. Another useful property is the concept of even and odd numbers, which helps when considering divisibility by other numbers such as 2 or 5. Keep in mind:

• Numbers ending in 0 or 5 are always divisible by 5.
• Numbers ending in 0, 2, 4, 6, or 8 are divisible by 2.

By learning these properties, math becomes more manageable and intuitive.

basic arithmetic

Basic arithmetic involves operations like addition, subtraction, multiplication, and division. Having a strong understanding helps you solve more complex problems. For divisibility, division is key. Knowing how to divide numbers helps you understand why certain divisibility rules work. If we divide a number by 10 and the remainder is 0, the number is divisible by 10. Practice these foundational skills to build confidence:

• 100 ÷ 10 = 10 (0 remainder)
• 111 ÷ 10 = 11.1 (1 remainder)

Keep practicing simple arithmetic to quickly and accurately check for divisibility!