This document provides examples for expressing the sum of two numbers as two factors with a common factor. It gives the steps to find the greatest common factor (GCF) of the two numbers, rewrite each number as a product of the GCF and another factor, and then use the distributive property to rewrite the sum as two factors with the GCF and the sum inside parentheses. There are 20 practice problems for students to rewrite sums of numbers, variables, and expressions using this process.

1. 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 (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
______________ _______________

2. 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)

3. 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
________________ ________________

4. 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)