Name _______________________________________ Date ____________________Mrs. Labuski / Mrs. Portsmore Period ________ Unit 4 Lesson 6 GCF & Distributive

OC 3-5Essential Question: How can using properties help you to represent mathematical relationships?Objective: Students need to express a sum of two whole numbers as two factors with a common factor as a multiple of the sum of two whole numbers with no common factor by applying the Distributive Property.

Example: 36 + 8 as 4(9 + 2). Step 1: Find the GCF of the numbers in the sum. GCF of 36 and 8 is 4.

Step 2: Replace each number by a product of the GCF and its other factor.36 + 8 = 4 9 + 4 2

Step 3: Replace the sum of the products by two factors with the GCF as a multiple of the sum of two whole numbers. 36 + 8 = 4 9 + 4 2 = 4(9 + 2)Write each of the following sums as two factors of their GCF and a sum:

1) 24 + 16 (GCF=_____) 2) 25 + 15 (GCF=_____) 3) 35 + 28 (GCF=_____)

______________ _______________ ________________

4) 63 + 54 (GCF=_____) 5) 80 + 30 (GCF=_____) 6) 12 + 9 (GCF=_____)

______________ _______________ ________________

7) 54 + 36 (GCF=_____) 8) 49 + 84 (GCF=_____) 9) 24 + 18 (GCF=_____)

______________ _______________ ________________

10) 20 + 44 11) 4 + 12 12) 6 + 8

______________ _______________ ________________

13) 25x + 40x 14) 16a + 20a 15) 60b + 72b

______________ _______________ ________________

16) 42y + 63y 17) 48y2 + 80y 18) 9ab + 30a

______________ _______________ ________________

19) 14x + 32x2 20) 11a + 55a

______________ _______________

Name _______________________________________ Date ____________________Mrs. Labuski / Mrs. Portsmore Period ________ Unit 4 Lesson 6 GCF & Distributive

OC 3-5

Essential Question: How can using properties help you to represent mathematical relationships?

Objective: Students need to express a sum of two whole numbers as two factors with a common factor as a multiple of the sum of two whole numbers with no common factor by applying the Distributive Property.Example: 36 + 8 as 4(9 + 2).

Step 1: Find the GCF of the numbers in the sum. GCF of 36 and 8 is 4.

Step 2: Replace each number by a product of the GCF and its other factor.

36 + 8 = 4 9 + 4 2

Step 3: Replace the sum of the products by two factors with the GCF as a multiple of the sum of two whole numbers.

36 + 8 = 4 9 + 4 2 = 4(9 + 2)

Write each of the following sums as two factors of their GCF and a sum:

1) 24 + 16 2) 25 + 15 3) 35 + 28 4(6+4) 5(5+3) 7(5+4)

4) 63 + 54 5) 80 + 30 6) 12 + 9 9(7+6) 10(8+3) 3(4+3)

7) 54 + 36 8) 49 + 84 9) 24 + 18 18(3+2) 7(7+12) 6(4+3)

10) 20 + 44 11) 4 + 12 12) 6 + 8 4(5+11) 4(1+3) 2(3+4)

13) 25x + 40x 14) 16a + 20a 15) 60b + 72b 5x(5+8) 4a(4+5) 12b(5+6)

16) 42y + 63y 17) 48 y2 + 80y 18) 9ab + 30a 6y(7+9) 16y(3y+5) 3a(3+10)

19) 14x + 32x2 20) 11a + 55a 2x(7+16x) 11a(1+5)

Name _______________________________________ Date ____________________Mrs. Labuski / Mrs. Portsmore Period ________ Unit 4 Lesson 6 GCF&Distributive HW

OC 3-5

Write each of the following sums as two factors of their GCF and a sum:

1) 22 + 16 (GCF=_____) 2) 35 + 20 (GCF=_____) 3) 32 + 28 (GCF=_____)

______________ _______________ ________________

4) 63 + 45 (GCF=_____) 5) 70 + 40 (GCF=_____) 6) 18 + 42 (GCF=_____)

______________ _______________ ________________

7) 54 + 18 (GCF=_____) 8) 49 + 98 (GCF=_____) 9) 51 + 18 (GCF=_____)

______________ _______________ ________________

10) 24 + 40 11) 20 + 24 12) 49 + 63

______________ _______________ ________________

13) 25a + 30a 14) 18cd + 24c 15) 27x + 72x

______________ _______________ ________________

16) 42x2 + 63x 17) 4a + 8a2 18) 2.5 + 7.5

______________ _______________ ________________

19) 3.3 + 21 20) 4.5 + 9

________________ ________________

Name ____________________________________Date ____________________Mrs. Labuski / Mrs. Rooney Period ________ Application of Distributive Property HW

Write each of the following sums as two factors of their GCF and a sum:

1) 22 + 16 (GCF=__2___) 2) 35 + 20 (GCF=__5___) 3) 32 + 28 (GCF=__4___)

2(11+8) 5(7+4) 4(8+7)

4) 63 + 45 (GCF=__9___) 5) 70 + 40 (GCF=__10___) 6) 18 + 42 (GCF=__6___)

9(7+5) 10(7+4) 6(3+7)

7) 54 + 18 (GCF=_18____) 8) 49 + 98 (GCF=__7___) 9) 51 + 18 (GCF=__3___)

18(3+1) 49(1+2) 3(17+6)

10) 24 + 40 11) 20 + 24 12) 49 + 63

8(3+5) 4(5+6) 7(7+9)

13) 25a + 30a 14) 18cd + 24c 15) 27x + 72x

5a(5+6) 6c(3d+4) 9x(3+8)

16) 42x2 + 63x 17) 4a + 8a2 18) 2.5 + 7.5

21x(2x+3) 4(1+2a) 2.5(1+3)

19) 3.3 + 21 20) 4.5 + 9 3(1.1+7) 4.5(1+2)