Question

Tasha believes that she can rewrite the difference 96−84 as a product of the GCF of the two numbers and another difference. Is she correct? Complete the explanation.She is/isn't correct. The GCF of 96 and 84 is ____ So 96−84 can be written as ____ x 8 - ____ x ____, which is ____ x (8 - ____) or ____ x ____ = ____

a) She isn't correct. The GCF of 96 and 84 is 12. So 96−84 can be written as 12×8−12×7, which is 12×(8−7) or 12×1=12.
b) She is correct. The GCF of 96 and 84 is 4. So 96−84 can be written as 4×8−4×7, which is 4×(8−7) or 4×1=4.
c) She isn't correct. The GCF of 96 and 84 is 6. So 96−84 can be written as 6×8−6×7, which is 6×(8−7) or 6×1=6.
d) She is correct. The GCF of 96 and 84 is 2. So 96−84 can be written as 2×8−2×7, which is 2×(8−7) or 2×1=2.

Answer 1

Tasha is correct; the difference 96-84 can be rewritten using the GCF by first finding that the GCF of 96 and 84 is 12, leading to the rewritten form 12 x (8-7), which equals 12.

Step-by-step explanation:

Tasha is correct in her belief that she can rewrite the difference 96−84 as a product of the GCF (Greatest Common Factor) of the two numbers and another difference. The GCF of 96 and 84 is 12. So 96−84 can be rewritten as the following:

96 = 12 × 8
84 = 12 × 7

Therefore, 96−84 becomes:

12 × 8 - 12 × 7

Which simplifies to:

12 × (8 - 7) or 12 × 1 = 12

The rewritten difference shows that Tasha's method of using the GCF and another difference is indeed correct.