To find the number when [tex]\(\frac{2}{3}\)[/tex] of it is given as 6, we can follow these steps:
1. Let's denote the unknown number as [tex]\( x \)[/tex].
2. According to the problem, [tex]\(\frac{2}{3}\)[/tex] of [tex]\( x \)[/tex] is 6. We can write this as an equation:
[tex]\[
\frac{2}{3} x = 6
\][/tex]
3. To isolate [tex]\( x \)[/tex], we need to get rid of the fraction [tex]\(\frac{2}{3}\)[/tex]. We can do this by dividing both sides of the equation by [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
x = \frac{6}{\frac{2}{3}}
\][/tex]
4. Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of [tex]\(\frac{2}{3}\)[/tex] is [tex]\(\frac{3}{2}\)[/tex], so:
[tex]\[
x = 6 \times \frac{3}{2}
\][/tex]
5. Now, multiplying 6 by [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
6 \times \frac{3}{2} = 6 \times 1.5 = 9
\][/tex]
So, the number is [tex]\( 9 \)[/tex].
