1. What is GCF?
How do I apply the distributive property to express a sum of 2 whole numbers with no common factor? M06.A-N.2.2.2

2. Given the following expression (42-24), which numerical expression has the GCF factored out of the expression? Explain why the other choices are NOT correct.
2(21-12)
6(7-4)
8(6-3)
3(14-8)

3. Given the following expression (42-24), which numerical expression has the GCF factored out of the expression? Explain why the other choices are NOT correct.
2(21-12) = (2 x 21) – (2 x 12)= = 18
6(7-4)= (6x7) – (6x4) = = 18 GCF
8(6-3) = (8x6) – (8x3) = = 24
3(14-8)= (3x14) – (3x8) = 42-24= 18
42: 1x42 , 2 x 21, 3x14, 6x7
24: 1x24, 2x12, 3x8, 4x6

4. Given the following expression (56-24), which numerical expression has the GCF factored out of the expression? Explain why the other choices are NOT correct
2(23-12)
2(28-12)
8(7-3)
4(14-6)

5. Given the following expression (56-24), which numerical expression has the GCF factored out of the expression? Explain why the other choices are NOT correct
2(23-12) = (2x23)-(2x12)= = 22
2(28-12) = (2x28) – (2x12) = = 32
8(7-3) = (8x7) – (8x3) = = 32
4(14-6) = (4x14) – (4x6) = = 32
56: 1x56, 2x28, 4x14, 7x8
24: 1x24, 2x12,3x8, 4x6

6. Given the following expression with the GCF factored out, 7(9+3), which numerical expression represents the expression before the GCF was factored out? Explain why the other choices are NOT correct.
(56+21)
(21+63)
(63+14)
(21+65)

7. (56+21) = 7(8+3) (21+63) = 7(3+9) (63+14) = 7(9+2) (21+65) = (21+65)
Given the following expression with the GCF factored out, 7(9+3), which numerical expression represents the expression before the GCF was factored out? Explain why the other choices are NOT correct.
(56+21) = 7(8+3)
(21+63) = 7(3+9)
(63+14) = 7(9+2)
(21+65) = (21+65)
7(9+3)= (7x9)+ (7x3) = = 84

8. 12(6+3) Here is what was written on the board: 72 + 36
Julian’s teacher was going over homework. In the homework, the students had to factor the GCF out of the expression. After the teacher showed the work, Julian raised his hand to tell her she made a mistake. His friend said it couldn’t be a mistake because if he evaluated the expression, he would get the same answer. Julian said, “He didn’t need to calculate the answer because there was another common factor.”
Here is what was written on the board:
12(6+3)
Was Julian right to raise his hand? Did his friend evaluate the expression incorrectly? Explain your reasoning.

9. 12(6+3) Here is what was written on the board: 72 + 36
Julian’s teacher was going over homework. In the homework, the students had to factor the GCF out of the expression. After the teacher showed the work, Julian raised his hand to tell her she made a mistake. His friend said it couldn’t be a mistake because if he evaluated the expression, he would get the same answer. Julian said, “He didn’t need to calculate the answer because there was another common factor.”
Here is what was written on the board:
12(6+3)
72: 1x71,2x36, 3x24,4x18, 6x12, 8x9
36: 1x36,2x18,3x12, 4x9, 6x6
Was Julian right to raise his hand? Did his friend evaluate the expression incorrectly? Explain your reasoning. Julian was correct. 36 is the GCF of 72 and 36. So 36(2 + 1) would use the GCF.