To simplify the expression \( \frac{2}{7} \cdot 53 \cdot \frac{7}{2} \) to \( 53 \), the following properties were used:
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Commutative property of multiplication: This property allows us to rearrange the order of the factors. Here, \( \frac{2}{7} \) and \( \frac{7}{2} \) can be reordered.
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Multiplicative inverse: The multiplicative inverse refers to the property that states \( a \cdot \frac{1}{a} = 1 \) for any non-zero \( a \). In this case, \( \frac{2}{7} \) and \( \frac{7}{2} \) are multiplicative inverses since \( \frac{2}{7} \cdot \frac{7}{2} = 1 \).
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Multiplicative identity: The multiplicative identity states that multiplying any number by \( 1 \) will yield that number. After simplifying \( \frac{2}{7} \cdot \frac{7}{2} \) to \( 1 \), we have \( 53 \cdot 1 = 53 \).
The following properties were NOT used in this simplification:
- Associative property of multiplication (not needed in this specific problem).
- Commutative property of addition (not relevant as there is no addition).
- Associative property of addition (not relevant as there is no addition).
- Distributive property (not relevant in this particular simplification).
Therefore, the correct answers are:
- Commutative property of multiplication
- Multiplicative inverse
- Multiplicative identity
1 answer