Question
Write the name of property used under multiplication in \( \frac{-19}{29} \times \frac{29}{-19}=1 \)
Ask by Love Lawson. in India
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The property used is the multiplicative inverse property.
Solution
1. We start with the multiplication:
\[
\frac{-19}{29} \times \frac{29}{-19} = 1
\]
2. Notice that the second fraction is the reciprocal (multiplicative inverse) of the first. The multiplicative inverse property states that for any nonzero number \( a \):
\[
a \times \frac{1}{a} = 1
\]
3. Therefore, the property used in the multiplication is the **multiplicative inverse property**.
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Simplify this solution Mind Expander
The property used in this multiplication is the concept of reciprocals. When you multiply a number by its reciprocal, the result is always 1. In this case, \( \frac{-19}{29} \) and \( \frac{29}{-19} \) are reciprocals of each other, hence their product yields 1. Another key concept demonstrated here is the property of signs in multiplication. The multiplication of two negative numbers yields a positive result. Since both fractions are negative, their product is positive, leading us again to arrive at 1 as the result.
