Let's examine each of the given equations to determine which one accurately relates to Hector's 10 cups of flour:
1. [tex]\( 10 + \frac{2}{5} = 25 \)[/tex]
- In this equation, we have 10 plus two-fifths.
- [tex]\( 10 + \frac{2}{5} \)[/tex] can be calculated as [tex]\( 10 + 0.4 \)[/tex].
- This sum equals [tex]\( 10.4 \)[/tex], not 25, so this equation does not make sense.
2. [tex]\( 10 \times \frac{2}{5} = 4 \)[/tex]
- In this equation, we have 10 multiplied by two-fifths.
- [tex]\( 10 \times \frac{2}{5} \)[/tex] can be calculated as [tex]\( 10 \times 0.4 \)[/tex], which equals 4.
- This equation is correct because it makes logical sense.
3. [tex]\( \frac{2}{5} + 10 = \frac{1}{25} \)[/tex]
- Here, we have two-fifths plus 10.
- [tex]\( \frac{2}{5} + 10 \)[/tex] can be calculated as [tex]\( 0.4 + 10 \)[/tex], which equals [tex]\( 10.4 \)[/tex].
- This is not equal to [tex]\( \frac{1}{25} \)[/tex] (which is 0.04), so this equation is incorrect.
4. [tex]\( \frac{5}{2} + 10 = \frac{1}{4} \)[/tex]
- Here, we have five-halves plus 10.
- [tex]\( \frac{5}{2} + 10 \)[/tex] can be calculated as [tex]\( 2.5 + 10 \)[/tex], which equals [tex]\( 12.5 \)[/tex].
- This is not equal to [tex]\( \frac{1}{4} \)[/tex] (which is 0.25), so this equation is incorrect.
Thus, the correct equation that shows how to determine the cups of flour in Hector's situation is:
[tex]\[ 10 \times \frac{2}{5} = 4 \][/tex]
Therefore, the correct choice is the second one.
