Mr. Novak asked his students to use distributive property and the GCF at the same time to express 18+45 in a different way.

Question

Jude and Rachel came up with the expressions below.

Jude: 9(2 + 5) 

Rachel: 3(6 + 15)

Which student followed Mr. Novak's directions correctly. Explain your answer.

 

Answer 1

Hello Nathaniel.

 

The distributive property can be written as follows:

 

A * (B + C) = A*B + A*C.

 

If you look at Jude and Rachel's examples, they both used the distributive property correctly. However, Mr. Novak gives an additional instruction to use the GCF, or Greatest Common Factor. What is the GCF of 18 and 45?

 

3 and 9 are both common factors of 18 and 45 (3*6=18, 3*15=45, 9*2=18, and 9*5=45),

but 9 is the GCF. So who was correct?

Answer 2

Jude followed the directions correctly because 9 is the GCF of 18 and 45.

18=2*3*3

45=3*3*5

GCF=3*3=9