Let's address the problem step-by-step:
We start with the fraction [tex]\(\frac{16}{40}\)[/tex] and we want to find a number that divides both the numerator and the denominator of this fraction to yield [tex]\(\frac{2}{5}\)[/tex].
### Step-by-Step Solution
1. Identify the original fraction:
The given fraction is [tex]\(\frac{16}{40}\)[/tex].
2. Identify the resulting fraction after division:
The resulting fraction is [tex]\(\frac{2}{5}\)[/tex].
3. Determine the relationship between the numerators:
- The original numerator is 16.
- The resulting numerator is 2.
The number that you would divide 16 by to get 2 is found as follows:
[tex]\[
\frac{16}{x} = 2 \implies 16 = 2x \implies x = \frac{16}{2} = 8
\][/tex]
4. Determine the relationship between the denominators:
- The original denominator is 40.
- The resulting denominator is 5.
The number that you would divide 40 by to get 5 is found as follows:
[tex]\[
\frac{40}{x} = 5 \implies 40 = 5x \implies x = \frac{40}{5} = 8
\][/tex]
5. Compare the results:
Both computations yield the number 8.
Hence, the number that correctly divides both the numerator and the denominator of the original fraction [tex]\(\frac{16}{40}\)[/tex] to give the resulting fraction [tex]\(\frac{2}{5}\)[/tex] is [tex]\(\boxed{8}\)[/tex].
