What makes 14?
Understand the Problem
The question is asking for the numbers or factors that can combine in some way to equal 14. It's likely looking for a mathematical perspective on how to arrive at the number 14 through addition, multiplication, or other operations.
Answer
Additive pairs: (0, 14), (1, 13), (2, 12), (3, 11), (4, 10), (5, 9), (6, 8), (7, 7); Multiplicative pairs: (1, 14), (2, 7)
Answer for screen readers
The numbers that can combine to equal 14 through addition or multiplication are:
- Additive pairs: (0, 14), (1, 13), (2, 12), (3, 11), (4, 10), (5, 9), (6, 8), (7, 7)
- Multiplicative pairs: (1, 14), (2, 7)
Steps to Solve
- Identify Additive Factors of 14
To find numbers that add up to 14, we can check pairs of numbers:
- Starting with 0: (0 + 14 = 14)
- 1: (1 + 13 = 14)
- 2: (2 + 12 = 14)
- 3: (3 + 11 = 14)
- 4: (4 + 10 = 14)
- 5: (5 + 9 = 14)
- 6: (6 + 8 = 14)
- 7: (7 + 7 = 14)
The additive factors are thus (0, 14), (1, 13), (2, 12), (3, 11), (4, 10), (5, 9), (6, 8), (7, 7).
- Identify Multiplicative Factors of 14
Next, we check the pairs of numbers that multiply to give 14. The factors of 14 are:
- 1 and 14: (1 \times 14 = 14)
- 2 and 7: (2 \times 7 = 14)
Thus, the multiplicative factors are (1, 14) and (2, 7).
- List Possible Operations
To come up with combinations involving operations, let's list:
- Addition: Possible pairs as outlined before.
- Multiplication: (1 \times 14) and (2 \times 7)
- Subtraction and Division do not yield pairs that satisfy reaching 14 without going negative or resulting in fractions from integers only.
- Summary of Factors
The complete list of factors that can come together to yield 14 through addition or multiplication are:
- Additive pairs: (0, 14), (1, 13), (2, 12), (3, 11), (4, 10), (5, 9), (6, 8), (7, 7)
- Multiplicative pairs: (1, 14), (2, 7)
The numbers that can combine to equal 14 through addition or multiplication are:
- Additive pairs: (0, 14), (1, 13), (2, 12), (3, 11), (4, 10), (5, 9), (6, 8), (7, 7)
- Multiplicative pairs: (1, 14), (2, 7)
More Information
The number 14 can be formed from various combinations of integers, showcasing the different operations like addition and multiplication. These factors reflects the versatile nature of numbers in arithmetic.
Tips
- Ignoring negative numbers: Sometimes people forget to consider that negative factors can also add up to a positive number, but here it's not needed since we use only positive integers.
- Overlooking pairs: It's easy to miss combinations that also involve zero or pairs that are not immediately obvious.
