Question

Mr. French's students are working on finding numbers less than 100 that are multiples of given one-digit numbers. When Mr. French asks them how they know when a number is a multiple of 6, one student, Crystal, says, ""Even numbers are multiples of 6!""

Mr. French wants to use two numbers to show Crystal that her description of multiples of 6 is incomplete and needs to be refined.
Which of the following numbers are best for Mr. French to use for this purpose?

a) 16 and 20
b) 12 and 18
c) 24 and 30
d) 14 and 22

Answer 1

The numbers 14 and 22 are the best examples to show that not all even numbers are multiples of 6. Both numbers are even, which aligns with the student's initial belief, but as they are not divisible by 3, they are not multiples of 6, thereby correcting the misconception.

Step-by-step explanation:

Mr. French is looking to correct Crystal’s understanding that not all even numbers are multiples of 6. To do this, presenting two numbers that are even but not multiples of 6 would be the most effective. The numbers should be even to align with Crystal’s assumption but should not be divisible by 6 to show the inaccuracy in her statement.

The best numbers for Mr. French to use would be 14 and 22. These numbers are both even (ending in 4 and 2, respectively), which satisfies Crystal’s initial claim. However, neither 14 nor 22 is a multiple of 6, as 14 divided by 6 leaves a remainder of 2, and 22 divided by 6 leaves a remainder of 4. This demonstrates that while being even is a necessary condition for being a multiple of 6, it is not a sufficient one. Numbers must also satisfy the condition of being divisible by 3 to be a multiple of 6, which neither 14 nor 22 do.