What is the greatest common factor (GCF) of 36 and 84?

Question

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1 point
2
3
6
12
Laura has 16 pygmy goats and 28 dairy goats. When she goes to the county fair, she needs to put them in pens with no two types of goats sharing a pen. She also needs the same number of goats in each pen. How many goats will she put in each pen?
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1 point
2 goats
4 goats
112 goats
448 goats
Use this video on the distributive property to help you. Remember to read the questions carefully.

Rewrite 135 + 45 in the form a (b + c) where a is the greatest common factor of 135 and 45.
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1 point
3 (45 + 15)
9 (15 + 5)
15 (9 + 3)
45 (3 + 1)
Rewrite the following numerical expression in an equivalent form using the distributive property: 36 + 54. Select all that apply.
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3 points
3 (12 + 18)
3 (12 + 54)
6 (6 + 9)
6 (6 + 54)
9 (4+ 6)
9 (4 + 54)
Kylie read 5 ½ books and Brady read 6 ¼ books. How many books have they read together?
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1 point
11 ¾ books
10 ½ books
11 ¼ books
12 ¾ books
Use this video on converting decimals, fractions, and percentages to help you. Remember to read the questions carefully.

0.15 is equal to what fraction?
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1 point

Option 1

Option 2

Option 3

Option 4
What is an equivalent fraction and decimal representation of 30%? Select all that apply.
3 points

Option 1

Option 2

Option 3

Option 4

Option 5
A group of middle school students was surveyed about their favorite Roblox game. Adopt Me was chosen by 0.25 of the students, Theme Park Tycoon was chosen by 1/2 of the students, Hide and Seek Extreme was chosen by 0.18 of the students, and Dragon Adventures was chosen by 7% of the students. Which game was chosen by the greatest number of students?
1 point
Adopt Me
Theme Park Tycoon
Hide and Seek Extreme
Dragon Adventures

Answer 1

Let's break this down question by question:

1. What is the greatest common factor (GCF) of 36 and 84?

   • The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
   • The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
   • Common factors: 1, 2, 3, 4, 6, 12
   • The greatest common factor is 12.

2. Laura has 16 pygmy goats and 28 dairy goats. How many goats will she put in each pen?

   • We need to find the GCF of 16 and 28.
   • The factors of 16 are: 1, 2, 4, 8, 16
   • The factors of 28 are: 1, 2, 4, 7, 14, 28
   • Common factors: 1, 2, 4
   • The greatest common factor is 4 goats.

3. Rewrite 135 + 45 in the form a(b + c) where a is the greatest common factor of 135 and 45.

   • The GCF of 135 and 45 is 45 (since 45 is the largest number that divides both).
   • We can factor this as:
     • \( 135 + 45 = 45(3 + 1) \)
   • So the answer is 45 (3 + 1).

4. Rewrite the numerical expression 36 + 54 using the distributive property:

   • The GCF of 36 and 54 is 18. Thus:
     • \( 36 + 54 = 18(2 + 3) \)
   • Also, we can show it using 9:
     • \( 36 + 54 = 9(4 + 6) \)
   • Correct options:
     • 9 (4 + 6) and 6 (6 + 9) (as 9 is a factor of 36 and 54, while 6 as well.)

5. Kylie read 5 ½ books and Brady read 6 ¼ books. How many books have they read together?

   • Convert to improper fractions or mixed numbers:
     • \( 5 ½ = \frac{11}{2} \)
     • \( 6 ¼ = \frac{25}{4} \)
   • To add these, convert \( \frac{11}{2} \) to fourths: \( \frac{22}{4} \)
   • Now add: \( \frac{22}{4} + \frac{25}{4} = \frac{47}{4} = 11 \frac{¾}{4} \)
   • The answer is 11 ¾ books.

6. What is 0.15 equal to as a fraction?

   • \( 0.15 = \frac{15}{100} = \frac{3}{20} \)

7. What is an equivalent fraction and decimal representation of 30%?

   • \( 30% = \frac{30}{100} = \frac{3}{10}\)
   • Decimal representation: \( 0.30 \)

8. Which game was chosen by the greatest number of students?

   • Adopt Me: 0.25 of students
   • Theme Park Tycoon: 1/2 = 0.50 of students
   • Hide and Seek Extreme: 0.18 of students
   • Dragon Adventures: 7% = 0.07 of students
   • The greatest number of students chose Theme Park Tycoon.

Please let me know if you need further details or have more questions!