Question

Add 3 to the product of 12 and the sum of 14 and 19.
A. 12 × 14 × 19 + 3
B. 3 + ( 12 × 14 ) + 19
C. 3 + 12 × ( 14 + 19 )
D. 3 + ( 12 × 14 + 19 )

Answer 1

Answer:

C. $\displaystyle 3 + 12 \times (14 + 19)$

Explanation:

Let us focus on "product of... and the sum of..." first. Whenever you have procedures arranged in an order similar to this, always remember that the second keyword tells you to put a mathematical operation inside grouping symbols, while the first keyword tells you to keep an operation isolated on the outside. In this exercise, the product of 12 tells you that you will be distributing it amongst another individual or set inside grouping symbols, which in this case is a "set inside grouping symbols" because the sum of 14 and 19 tells you that in order to complete the producted expression, the additive expression must be placed inside grouping symbols. Now, all we have left is 3, which can be added on either side of the entire expression because according to the order of operations, in this case, multiplication is performed before addition.

Well, I hope you will get a more decent understanding of the topic, and as always, I am joyous to assist anyone at any time.

Answer 2

$\huge\textsf{Hey there!}$

$\huge\textbf{Random run down meaning of}\\\huge\textbf{\boxed{some} key terms in pre-algebra or}\\\huge\textbf{algebra in general: \boxed{\downarrow}}$

$\large\textsf{\boxed{Product} means \underline{\underline{multiply/multiplication}}}\\\\\large\textsf{\boxed{Sum} means \underline{\underline{add/addition}}}\\\\\large\textsf{\boxed{Quotient} means \underline{\underline{divide/division}}}\\\\\large\textsf{\boxed{Difference} means \underline{\underline{subtract/subtraction}}}\\\\\large\textsf{\boxed{Of} meaning as \underline{\underline{multiplication}} (sometimes)}$

$\huge\textbf{Now, let's \boxed{answer} your given question:}$

$\huge\textbf{The \boxed{question \ reads}:}$

$\large\textsf{\boxed{ADD} \underline{3} to the \boxed{PRODUCT} of \underline{12} \& the \boxed{SUM} of \underline{14 and 19}}$

$\huge\textbf{A small checklist for better }\\\huge\textbf{understanding your equation:}$

$\large\textsf{We know that have to \underline{multiply} 12 since it is the product of the}\\\large\textsf{equation }\large\checkmark$

$\large\textsf{We also know that we are \underline{adding} 3 because it simply tells us to }\large\checkmark$

$\large\textsf{Lastly, we also know that we're \underline{adding} 14 \& 19 because it is the sum}\\\large\textsf{part of the equation but it most likely be in parentheses because it is}\\\large\textsf{a different kind of \underline{addition} equation, if that makes sense to you }\large\checkmark$

$\huge\textbf{Now, we have that information out}\\\huge\textbf{of the way, we can solve for it because,}\\\huge\textbf{our checklist made it a little bit easier}\\\huge\textbf{to solve.}$

$\huge\textbf{So, your equation SHOULD look like:}$

$\large\textsf{3 + 12}\times\large\textsf{(14 + 19)}$

$\huge\textbf{If you're having trouble locating it}\\\huge\textbf{in the answer choices, it should simply}\\\huge\textbf{be:}$

$\huge\boxed{\frak{Option\ C. 3 + 12 \times (14 + 19)}}\huge\checkmark$

$\huge\textsf{Good luck on your assignment \& enjoy your day!}$

~$\frak{Amphitrite1040:)}$