To find the multiplicative inverse of a fraction, we need to understand that the multiplicative inverse of a fraction [tex]\( \frac{a}{b} \)[/tex] is [tex]\( \frac{b}{a} \)[/tex]. This means that if we multiply [tex]\(\frac{a}{b}\)[/tex] by its multiplicative inverse [tex]\(\frac{b}{a}\)[/tex], the result will be 1:
[tex]\[
\frac{a}{b} \times \frac{b}{a} = 1
\][/tex]
For the fraction [tex]\(\frac{-3}{7}\)[/tex], we can follow these steps to determine its multiplicative inverse.
1. The original fraction is [tex]\(\frac{-3}{7}\)[/tex].
2. To find the multiplicative inverse, we switch the numerator and the denominator. So, the inverse will be [tex]\(\frac{7}{-3}\)[/tex].
3. Simplifying [tex]\(\frac{7}{-3}\)[/tex] gives us [tex]\(-\frac{7}{3}\)[/tex].
4. Converting this to a decimal gives approximately [tex]\(-2.3333333333333335\)[/tex].
Therefore, the multiplicative inverse of [tex]\(\frac{-3}{7}\)[/tex] is [tex]\(- \frac{7}{3}\)[/tex] or approximately [tex]\(-2.3333333333333335\)[/tex].
