Question

Applying the Commutative Property

How are 5 x 1/2 and 1/5 related?
5 x ___ = 10
2 x 5 = ____
5 x 1/2 is _____ to 1/2 x 5

Answer 1

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.

1. 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 \(\frac{5}{2}\).

2. 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 \(2 \times 5 = 10\).

3. 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:

1. \(5 \times \frac{1}{2}\) and \(\frac{1}{2} \times 5\) are equal.
2. \(5 \times 2 = 10\)
3. \(2 \times 5 = 10\)
4. \(5 \times \frac{1}{2} \text{ is equal to } \frac{1}{2} \times 5\).