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

1 answer

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. \(5 \times \frac{1}{2} \text{ is equal to } \frac{1}{2} \times 5\).