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Choose the property that justifies the following statement. \( \frac{5}{6} \cdot 1=\frac{5}{6} \)

Ask by Hamilton Griffin. in the United States
Jan 27,2025

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Answer

The statement is justified by the **Multiplicative Identity Property**, which states that any number multiplied by 1 remains unchanged.

Solution

The statement: \[ \frac{5}{6} \cdot 1 = \frac{5}{6} \] is justified by the **Multiplicative Identity Property**. ### **Multiplicative Identity Property** This property states that any number multiplied by **1** remains unchanged. In other words, for any real number \( a \): \[ a \cdot 1 = a \] **Application in the Given Statement:** Here, \( a = \frac{5}{6} \). Applying the Multiplicative Identity Property: \[ \frac{5}{6} \cdot 1 = \frac{5}{6} \] This confirms that multiplying \(\frac{5}{6}\) by 1 leaves it unchanged, which aligns perfectly with the Multiplicative Identity Property. **Visual Representation:** \[ \frac{5}{6} \cdot 1 = \frac{5}{6} \quad \text{(Multiplicative Identity Property)} \]

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The property illustrated in this statement is known as the Multiplicative Identity Property. This property states that any number multiplied by 1 remains unchanged, meaning you can think of 1 as the "invisible friend" of numbers; it keeps things the same while allowing for other operations. To bring this idea to life, think about how you might bring a friend to a party. If you invite 1 friend along, the party's vibe doesn’t change—just like our fraction stays the same when multiplied by 1. So no matter how fancy your fraction is, 1 stands as the faithful companion that won’t change the party atmosphere!

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