Question

Byron wants to use the distributive property to rewrite the addition problem shown so that the numbers left in the parentheses have no common factor except 1.

(48 + 36)

Which is an equivalent expression that has numbers in the parentheses whose only common factor is 1?

A.
4(12 + 9)

B.
2(24 + 18)

C.
12(4 + 3)

D.
36(12 + 1)

Answer 1

Mr. Hon purchases a new car every 4 years. Ms. Jasper purchases a new car every 6 years. They both purchased new cars this year. When will they next both purchase new cars in the same year?

A.
in 2 years

B.
in 8 years

C.
in 12 years

D.
in 24 years

Answer 2

Which expression is NOT equivalent to 9x+4y+13-3x-y-10 ?

A. 3(2x+y+1)

B. 6x+3(1+y)

C. (9-3)x+(4-0)y+3

D. (13-10)+(9x-3x)+(4y-y)

Answer 3

B. 2(24 + 18)

Answer 4

The next time Mr. Hon purchases a new car will be in 4 years from now. The next time Ms. Jasper purchases a new car will be in 6 years from now. To find the next time they both purchase new cars in the same year, we need to find the least common multiple (LCM) of 4 and 6.

The prime factorization of 4 is 2^2.
The prime factorization of 6 is 2 * 3.

To find the LCM, we take the highest power of each prime factor that appears in either number. In this case, the LCM is 2^2 * 3 = 12.

Therefore, the next time they both purchase new cars in the same year will be in 12 years.

Answer: C. in 12 years

Answer 5

D. (13-10)+(9x-3x)+(4y-y)