To find the multiplicative inverse of [tex]\(\frac{21}{3}\)[/tex], follow the steps below:
1. Calculate the fraction [tex]\(\frac{21}{3}\)[/tex]:
- Perform the division: [tex]\(21 \div 3 = 7.0\)[/tex]. So, [tex]\(\frac{21}{3} = 7.0\)[/tex].
2. Determine the multiplicative inverse:
- The multiplicative inverse of a number [tex]\( x \)[/tex] is defined as a number [tex]\( y \)[/tex] such that [tex]\( x \times y = 1 \)[/tex].
- In this case, [tex]\( x = 7.0 \)[/tex].
- Therefore, the multiplicative inverse is [tex]\( y \)[/tex] such that [tex]\( 7.0 \times y = 1 \)[/tex].
- To find [tex]\( y \)[/tex], solve for [tex]\( y \)[/tex] by dividing 1 by 7.0:
[tex]\[
y = \frac{1}{7.0} = 0.14285714285714285
\][/tex]
So, the multiplicative inverse of [tex]\(\frac{21}{3}\)[/tex] is [tex]\( 0.14285714285714285 \)[/tex].
