To find the reciprocal of a fraction, you swap the numerator and the denominator.
The given fraction is [tex]\(\frac{3}{9}\)[/tex].
Step-by-step, first identify the numerator and the denominator:
1. The numerator of the given fraction [tex]\( \frac{3}{9} \)[/tex] is [tex]\(3\)[/tex].
2. The denominator of the given fraction [tex]\( \frac{3}{9} \)[/tex] is [tex]\(9\)[/tex].
To find the reciprocal, we swap the numerator and the denominator:
- The new numerator (originally the denominator) is [tex]\(9\)[/tex].
- The new denominator (originally the numerator) is [tex]\(3\)[/tex].
Therefore, the reciprocal of [tex]\( \frac{3}{9} \)[/tex] is [tex]\( \frac{9}{3} \)[/tex].
So, the expression [tex]\( 2 \div \frac{3}{9} \)[/tex] becomes:
[tex]\[
2 \times \frac{9}{3}
\][/tex]
The reciprocal of [tex]\( \frac{3}{9} \)[/tex] is [tex]\( \frac{9}{3} \)[/tex].
