Question
Connecting Ideas
What do these expressions mean?
1/2 x 5 = 5 x 1/2
1/2 1/2 1/2 1/2 1/2 = ____ or ____
___ of 5
What do these expressions mean?
1/2 x 5 = 5 x 1/2
1/2 1/2 1/2 1/2 1/2 = ____ or ____
___ of 5
Answers
GPT-4o mini
Let's break down the expressions you provided:
1. **1/2 x 5 = 5 x 1/2**: This equality demonstrates the commutative property of multiplication, which states that changing the order of the factors does not change the product. In this case, whether you take half of 5 (1/2 x 5) or double 1/2 five times (5 x 1/2), the result is the same, which is 2.5.
2. **1/2 1/2 1/2 1/2 1/2 = ____ or ____**: This expression suggests multiplying 1/2 by itself five times. Mathematically, this can be expressed as (1/2)^5. The result is 1/32. Another way to interpret this is as dividing 1 by 2 five times in succession, which will also yield the same result: 1/32.
3. **___ of 5**: This could be interpreted in a couple of ways. Given the context of the previous values, one way to complete this phrase could be "1/2 of 5", which is 2.5. Alternatively, if referencing the result from the second expression, it might mean "1/32 of 5", which is 5/32 or 0.15625.
So, summarizing these interpretations:
- 1/2 x 5 = 5 x 1/2 = 2.5
- 1/2 1/2 1/2 1/2 1/2 = 1/32
- For "___ of 5," possible answers could be:
- "1/2 of 5 = 2.5"
- "1/32 of 5 = 5/32"
1. **1/2 x 5 = 5 x 1/2**: This equality demonstrates the commutative property of multiplication, which states that changing the order of the factors does not change the product. In this case, whether you take half of 5 (1/2 x 5) or double 1/2 five times (5 x 1/2), the result is the same, which is 2.5.
2. **1/2 1/2 1/2 1/2 1/2 = ____ or ____**: This expression suggests multiplying 1/2 by itself five times. Mathematically, this can be expressed as (1/2)^5. The result is 1/32. Another way to interpret this is as dividing 1 by 2 five times in succession, which will also yield the same result: 1/32.
3. **___ of 5**: This could be interpreted in a couple of ways. Given the context of the previous values, one way to complete this phrase could be "1/2 of 5", which is 2.5. Alternatively, if referencing the result from the second expression, it might mean "1/32 of 5", which is 5/32 or 0.15625.
So, summarizing these interpretations:
- 1/2 x 5 = 5 x 1/2 = 2.5
- 1/2 1/2 1/2 1/2 1/2 = 1/32
- For "___ of 5," possible answers could be:
- "1/2 of 5 = 2.5"
- "1/32 of 5 = 5/32"