Question

select all of the expressions that could be used to evaluate (3 1/2)(14)
□ a) (3 - 1/2)(14)
□ b) 3(14)+1/2(14)
□ c) 3 1/2(10)+3 1/2(4)
□ d) (3 1/2)(20 - 4)
□ e) 3 1/2(8 + 6)

Explanation:

Step1: Rewrite $3\frac{1}{2}$ as improper fraction

$3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2}$

Step2: Analyze option A

$(3-\frac{1}{2})(14)=( \frac{6 - 1}{2})(14)=\frac{5}{2}\times14
eq\frac{7}{2}\times14$

Step3: Analyze option B

$3(14)+\frac{1}{2}(14)=(3 + \frac{1}{2})(14)=3\frac{1}{2}(14)$

Step4: Analyze option C

$3\frac{1}{2}(10)+3\frac{1}{2}(4)=3\frac{1}{2}(10 + 4)=3\frac{1}{2}(14)$

Step5: Analyze option D

$(3\frac{1}{2})(20 - 4)=(3\frac{1}{2})(16)
eq(3\frac{1}{2})(14)$

Step6: Analyze option E

$3\frac{1}{2}(8 + 6)=3\frac{1}{2}(14)$

Answer:

B. $3(14)+\frac{1}{2}(14)$, C. $3\frac{1}{2}(10)+3\frac{1}{2}(4)$, E. $3\frac{1}{2}(8 + 6)$