The Commutative Property states that the order in which you add or multiply numbers does not affect the result. Let's analyze how the expressions involving \(5\) and \(\frac{1}{2}\) are related and complete your statements.
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The relationship between \(5 \times \frac{1}{2}\) and \(\frac{1}{5}\): These two expressions are not directly equal, but we can say that they are related in the sense that \(5 \times \frac{1}{2} = \frac{5}{2}\) and \(\frac{1}{2} \times 5\) also equals \(\frac{5}{2}\).
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To fill in the blanks:
- \(5 \times ___ = 10\) can be filled with \(2\), because \(5 \times 2 = 10\).
- \(2 \times 5 = ___\) can be filled with \(10\) since \(2 \times 5 = 10\).
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For the statement \(5 \times \frac{1}{2} \text{ is } ____ \text{ to } \frac{1}{2} \times 5\):
- You can say \(5 \times \frac{1}{2} \text{ is } \text{ equal to } \frac{1}{2} \times 5\) or simply "is the same as."
So, putting it all together:
- \(5 \times \frac{1}{2}\) and \(\frac{1}{2} \times 5\) are equal.
- \(5 \times 2 = 10\)
- \(2 \times 5 = 10\)
- \(5 \times \frac{1}{2} \text{ is equal to } \frac{1}{2} \times 5\).