Question

exit ticket
module 2 lesson 1:
what is the side length in feet of the largest square tile that can tile a 6 - foot by 9 - foot rectangle completely? answer:

module 2 lesson 2:
the number 96 is divisible by which of the following numbers? choose all that apply. explain your reasoning for all answers choices.
a. 3
b. 4
c. 5
d. 6
e. 9
explanation:

Explanation:

Module 2 Lesson 1:

Step1: Find the GCD of 6 and 9

We need to find the greatest - common divisor (GCD) of 6 and 9. The factors of 6 are 1, 2, 3, and 6. The factors of 9 are 1, 3, and 9.

Step2: Determine the GCD value

The greatest common factor of 6 and 9 is 3.

Step1: Check divisibility by 3

To check if 96 is divisible by 3, we use the divisibility rule: the sum of the digits of 96 is \(9 + 6=15\), and 15 is divisible by 3. So \(96\div3 = 32\).

Step2: Check divisibility by 4

To check if 96 is divisible by 4, we look at the last two digits. Since 96 has the last two - digits 96 and \(96\div4 = 24\), 96 is divisible by 4.

Step3: Check divisibility by 5

A number is divisible by 5 if its last digit is either 0 or 5. Since the last digit of 96 is 6, 96 is not divisible by 5.

Step4: Check divisibility by 6

Since 96 is divisible by both 2 (it's an even number) and 3 (sum of digits is divisible by 3), it is divisible by 6. \(96\div6 = 16\).

Step5: Check divisibility by 9

To check if 96 is divisible by 9, we use the divisibility rule: the sum of the digits of 96 is 15, and 15 is not divisible by 9. So 96 is not divisible by 9.

Answer:

3

Module 2 Lesson 2: