Question

fill in the boxes to add the expressions.
$(2n + 2.95) + (4.33n + 2.11)$
$=(2n + \underline{\quad\quad}) + (2.95 + \underline{\quad\quad})$

$(2n + 2.95) + (4.33n + 2.11)$
$=(2n + \square) + (2.95 + \square)$
$=\square$
(simplify your answer. use integers or decimals for any numbers in the expression)

Explanation:

Step1: Apply the commutative property of addition to group like terms. For the expression \((2n + 2.95)+(4.33n + 2.11)\), we can rewrite it as \((2n + 4.33n)+(2.95 + 2.11)\) by rearranging the terms. So the first two boxes (for the like - term grouping of \(n\) terms and constant terms) are filled with \(4.33n\) and \(2.11\) respectively.

Step2: Now, simplify the grouped terms. First, simplify \(2n+4.33n\). Combining like terms (using the rule \(an + bn=(a + b)n\)), we have \(2n+4.33n=(2 + 4.33)n=6.33n\). Then, simplify \(2.95+2.11 = 5.06\). So the expression becomes \(6.33n+5.06\).

Answer:

First part (grouping): \((2n+\boldsymbol{4.33n})+(2.95+\boldsymbol{2.11})\)
Second part (simplifying): \(\boldsymbol{6.33n + 5.06}\)