Question

All of the multiples of 3 on the hundred chart are shaded. Which of the following describes the numbers shaded on the hundred chart? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Answer 1

The shaded numbers on the hundred chart are all the multiples of 3.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, and 99. These numbers are obtained by multiplying 3 by the integers from 1 to 33. They form a pattern where every third number is a multiple of 3, creating a sequence that repeats throughout the entire list up to 100.

Step-by-step explanation:

To identify the multiples of 3, we look for numbers that can be evenly divided by 3. In the given list, these numbers are 3, 6, 9, 12, and so on. Every third number is a multiple of 3. This pattern continues throughout the entire list up to 100.

Mathematically, we can express this as
`\(3 * 1, 3 * 2, 3 * 3, \ldots, 3 * 33\)`, representing the multiples of 3 within the range of 1 to 100. These are the numbers that would be shaded on the hundred chart. Understanding multiples is a fundamental concept in number theory. In this case, recognizing the multiples of 3 involves identifying the numbers that result from multiplying 3 by consecutive integers. This knowledge is essential in various mathematical applications, including factors, divisibility, and pattern recognition.

In summary, the shaded numbers on the hundred chart are precisely the multiples of 3, forming a sequence of numbers obtained by multiplying 3 by the integers from 1 to 33. This concept is foundational in number theory and provides a clear understanding of the properties of multiples in the context of the hundred chart.

Answer 2

D. All the multiples of 3.

Here's why the other options are not accurate:

A. All the even numbers: Not all even numbers are shaded. For example, 2 and 4 are even but not shaded.

B. All the odd numbers: Not all odd numbers are shaded. For example, 1 and 5 are odd but not shaded.

C. All the one-digit numbers: Not all one-digit numbers are shaded. For example, 2 and 5 are one-digit but not shaded.

Therefore, the only accurate description of the shaded numbers is that they are all multiples of 3.

Complete the image: