Question

Is 1,000 a multiple of \(3 ?\) How do you know?

Short answer

No, 1,000 is not a multiple of 3 because the sum of its digits is 1, which is not divisible by 3.

Step-by-step solution

- Understand the concept of multiples

A number is a multiple of another number if it can be expressed as the product of that number and an integer. For instance, for a number to be a multiple of 3, it should be expressible as 3 times some integer.

- Use the divisibility rule for 3

One quick way to check if a number is a multiple of 3 is to use the divisibility rule for 3. According to this rule, a number is divisible by 3 if the sum of its digits is divisible by 3.

- Sum the digits of 1,000

Add the digits of 1,000: 1 + 0 + 0 + 0 = 1

- Check divisibility

Now, check if the sum (1) is divisible by 3. Since 1 is not divisible by 3, 1,000 is not a multiple of 3.

Key concepts

multiples

Multiples are numbers that result from multiplying a given number by integers. Think of multiples as the products you get when you multiply a number by 1, 2, 3, and so on. For example, the multiples of 3 include 3, 6, 9, 12, and many more.

If you have a number and you want to check if it is a multiple of another number, you can see if you can express it as the other number times an integer. This is a very helpful process in math.

In our exercise, we checked if 1,000 is a multiple of 3. To do that, we used a neat trick called the divisibility rule for 3, which will be explained next.

divisibility by 3

Checking if a number is divisible by 3 can be easily done using a simple rule.

The divisibility rule for 3 says that a number is divisible by 3 if the sum of its digits is divisible by 3. Let's break this down with an example.

Imagine you have the number 1,236. To see if it's divisible by 3, you add its digits: 1 + 2 + 3 + 6. This equals 12. Now, you check if 12 is divisible by 3. Since 12 divided by 3 equals 4, it is divisible by 3. Therefore, 1,236 is also divisible by 3.

In the exercise, we did the same with 1,000. We summed its digits: 1 + 0 + 0 + 0, which equals 1. Since 1 is not divisible by 3, 1,000 is not a multiple of 3.

math problem solving

Solving math problems often involves breaking them down into smaller, more manageable steps. Let's revisit our exercise.

First, we identified the key concept: checking if a number is a multiple of another number. This involves knowing what multiples are. Next, we applied a specific rule — the divisibility rule for 3 — that simplifies the process. By summing the digits and checking the sum's divisibility, we reached our conclusion.

This structured approach (understanding the problem, applying relevant rules or formulas, and working step by step) makes math problems easier to tackle. Always remember to:

• Understand the core concept.
• Use any rules or shortcuts available.
• Take it step by step.

This strategy can be used for various math problems, not just those involving multiples or divisibility.