To solve the problem, let's follow these steps:
1. Let's denote the unknown number as [tex]\( x \)[/tex].
2. According to the problem, two-thirds of the number is 40. We can write this as an equation:
[tex]\[
\frac{2}{3} \times x = 40
\][/tex]
3. To solve for [tex]\( x \)[/tex], we'll isolate [tex]\( x \)[/tex]. We can do this by dividing both sides of the equation by [tex]\(\frac{2}{3}\)[/tex]. However, dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of [tex]\(\frac{2}{3}\)[/tex] is [tex]\(\frac{3}{2}\)[/tex]. So, we multiply both sides of the equation by [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
x = 40 \times \frac{3}{2}
\][/tex]
4. Now we perform the multiplication:
[tex]\[
x = 40 \times \frac{3}{2} = 40 \times 1.5 = 60
\][/tex]
5. Therefore, the number [tex]\( x \)[/tex] is [tex]\(\boxed{60}\)[/tex].
