Questions: Find both the opposite, or additive inverse, and the reciprocal, or the multiplicative inverse, of the following number. -11/15 Type the opposite of -11/15. (Type your answer as an integer or fraction.)

$Find both the opposite, or additive inverse, and the reciprocal, or the multiplicative inverse, of the following number. -11/15 Type the opposite of -11/15. (Type your answer as an integer or fraction.)$

Transcript text: Find both the opposite, or additive inverse, and the reciprocal, or the multiplicative inverse, of the following number. \[ -\frac{11}{15} \] Type the opposite of $-\frac{11}{15}$. $\square$ (Type your answer as an integer or fraction.)

Solution

Solution Steps

To find the opposite (additive inverse) of a number, you change its sign. For the reciprocal (multiplicative inverse), you swap the numerator and the denominator of the fraction.

Step 1: Find the Opposite (Additive Inverse)

To find the opposite of the number $ -\frac{11}{15} $, we change its sign: \[ \text{Opposite} = -\left(-\frac{11}{15}\right) = \frac{11}{15} \]

Step 2: Find the Reciprocal (Multiplicative Inverse)

To find the reciprocal of the number $ -\frac{11}{15} $, we swap the numerator and the denominator: \[ \text{Reciprocal} = \frac{1}{-\frac{11}{15}} = -\frac{15}{11} \]

Final Answer

The opposite of $ -\frac{11}{15} $ is $ \frac{11}{15} $ and the reciprocal is $ -\frac{15}{11} $. Thus, the answers are: \[ \boxed{\text{Opposite} = \frac{11}{15}, \text{Reciprocal} = -\frac{15}{11}} \]

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