Question

select all of the verbal expressions that represent \\(\frac{1}{2}(4) + 3(7)\\).\
\\(\square\\) a) half of four increased by the product of three and seven\
\\(\square\\) b) twice four plus three times seven\
\\(\square\\) c) the sum of four times one - half and three times seven\
\\(\square\\) d) the quotient of three and seven added to half of four\
\\(\square\\) e) the product of one half and four plus the product of three and seven

Explanation:

Step1: Analyze the first term

The first term $\frac{1}{2}(4)$ can be verbalized as "half of four", "four times one-half", or "the product of one half and four".

Step2: Analyze the second term

The second term $3(7)$ is "the product of three and seven" or "three times seven".

Step3: Analyze the operation

The $+$ sign means "increased by", "the sum of...and...", or "plus".

Step4: Match each option

• Option A: Matches the verbalization of $\frac{1}{2}(4) + 3(7)$.
• Option B: "twice four" is $2(4)$, not $\frac{1}{2}(4)$, so it is incorrect.
• Option C: Matches the verbalization of $\frac{1}{2}(4) + 3(7)$ (since $\frac{1}{2}(4)=4\times\frac{1}{2}$).
• Option D: "the quotient of three and seven" is $\frac{3}{7}$, not $3(7)$, so it is incorrect.
• Option E: Matches the verbalization of $\frac{1}{2}(4) + 3(7)$.

Answer:

A) half of four increased by the product of three and seven
C) the sum of four times one-half and three times seven
E) the product of one half and four plus the product of three and seven