Which expression shows a way to factor $36 + 27$?
The goal is to factor the expression \(36 + 27\) and choose the correct option from the given list. Factoring a sum involves identifying a common factor between the terms and rewriting the sum as a product of that common factor and the sum of the remaining values. Our objective is to find which of the provided options: \(9(4 + 2)\), \(3(11 + 8)\), \(9(4 + 3)\), or \(3(12 + 8)\) correctly represents the factored form.
First, we calculate the sum of the original expression: \[36 + 27 = 63.\] Next, we identify the greatest common factor (GCF) of 36 and 27.
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36.
The factors of 27 are: 1, 3, 9, 27.
The greatest common factor is 9. Dividing each term by 9 gives:
\[36 \div 9 = 4\]
\[27 \div 9 = 3\]
Thus, the expression can be rewritten as \[9 \times (4 + 3).\]
Now we evaluate each of the given options to see which matches the value 63:
Option c yields the value 63 and correctly represents the sum \(36 + 27\) after factoring out the greatest common factor of 9. Therefore, option c is the correct choice.
Factoring is a fundamental skill used in everyday life to simplify tasks and organize resources. For example, if you are organizing a small event and need to buy 36 sodas and 27 water bottles, you might want to arrange them into identical packs. By factoring out the greatest common factor, you realize you can create 9 identical bundles, each containing 4 sodas and 3 water bottles. This makes it much easier to distribute the items evenly among your guests.