- Evaluate each prime factorization expression:
- \(2 \times 2 \times 3 = \boxed{12}\) (item b)
- \(2 \times 7 = \boxed{14}\) (item a)
- \(2 \times 2 \times 2 = \boxed{8}\) (item d)
- \(2 \times 3 \times 3 = \boxed{18}\) (item c)
- Match the expressions to the corresponding values: 1-b, 2-a, 3-d, 4-c.
Explanation
- Problem Analysis and Data Review
We are given a list of prime factorization expressions in the left column and a corresponding list of numerical values in the right column. Our task is to calculate the product of each expression in the left column and match it to its correct value in the right column:
- \(2 \times 2 \times 3\)
- \(2 \times 7\)
- \(2 \times 2 \times 2\)
- \(2 \times 3 \times 3\)
The list of target values is:
- Calculations and Matching
We evaluate each expression by performing the indicated multiplication:
- For expression 1: \(2 \times 2 \times 3 = 4 \times 3 = 12\). This matches with item (b).
- For expression 2: \(2 \times 7 = 14\). This matches with item (a).
- For expression 3: \(2 \times 2 \times 2 = 4 \times 2 = 8\). This matches with item (d).
- For expression 4: \(2 \times 3 \times 3 = 2 \times 9 = 18\). This matches with item (c).
- Conclusion and Final Answer
Based on the calculations, we have established the following correct pairings:
- 1 maps to b (12)
- 2 maps to a (14)
- 3 maps to d (8)
- 4 maps to c (18)
The final answer is: 1-b, 2-a, 3-d, 4-c.
Examples
In real-world applications, prime factorization is essential for simplifying fractions, finding common denominators, or understanding the structure of numbers in cryptography. For instance, if you are dividing supplies into equal sets, knowing the factors of the total number of items helps you determine all the possible ways to group them efficiently. By mastering these basic factors, you gain a foundational tool used in fields ranging from computer science to daily budgeting and planning.