To rewrite the number 78 using the distributive property, we need to express it in the form of \( a \times b + a \times c = a(b + c) \). Let's evaluate the options provided:
A: \( 78 = 24 + 54 = (6 \times 4) + (6 \times 9) = 6(4 + 9) \)
Here, \( 24 + 54 = 78 \), and \( (6 \times 4) + (6 \times 9) = 6(4 + 9) \). This option is correct because it follows the distributive property correctly.
B: \( 78 = 22 + 56 = (2 \times 11) + (2 \times 28) = 2(11 + 28) \)
Here, \( 22 + 56 = 78 \), but \( (2 \times 11) + (2 \times 28) \) equals \( 2(11 + 28) \) incorrectly because \( 11 + 28 = 39\) which, when multiplied by 2, gives 78, but the terms factored out do not properly correspond to the original addition.
C: \( 78 = 18 + 60 = (6 \times 3) + (6 \times 10)= 6(3 + 10) \)
Here, \( 18 + 60 = 78 \), and \( (6 \times 3) + (6 \times 10) = 6(3 + 10) \) is correct as well.
After analyzing all options:
- A is correct and follows the distributive property accurately.
- B is incorrect because it doesn't maintain the equivalence under distribution.
- C is also correct and follows the distributive property accurately.
Therefore, options A and C correctly rewrite the number 78 using the distributive property.