To determine which option lists a correct set of fact family relationships for the numbers 3, 8, and 24, we need to verify if all the mathematical statements in each option are true.
Let's verify each option step-by-step:
### Option a:
1. [tex]\( 3 \times 8 = 24 \)[/tex]
- This is correct. [tex]\( 3 \times 8 \)[/tex] is indeed 24.
2. [tex]\( 8 \times 3 = 24 \)[/tex]
- This is correct as well. [tex]\( 8 \times 3 \)[/tex] is also 24.
3. [tex]\( 24 \div 3 = 8 \)[/tex]
- This is correct. Dividing 24 by 3 gives us 8.
4. [tex]\( 24 \div 8 = 3 \)[/tex]
- This is correct. Dividing 24 by 8 gives us 3.
Since all four statements in option a are true, this fact family is correct.
### Option b:
1. [tex]\( 3 + 8 = 11 \)[/tex]
- This is correct, but not part of a multiplication/division fact family for these numbers.
2. [tex]\( 8 \times 3 = 24 \)[/tex]
- This is correct. [tex]\( 8 \times 3 \)[/tex] is 24.
3. [tex]\( 8 \div 8 = 1 \)[/tex]
- This is correct. Dividing any number by itself gives 1.
4. [tex]\( 24 \div 8 = 3 \)[/tex]
- This is correct. Dividing 24 by 8 gives us 3.
Though three of the statements are correct, the first statement is addition and does not fit into the multiplication/division fact family. Therefore, option b is not entirely correct.
### Option c:
1. [tex]\( 3 \times 3 = 9 \)[/tex]
- This is correct, but does not relate 3, 8, and 24 together.
2. [tex]\( 8 \times 3 = 24 \)[/tex]
- This is correct. [tex]\( 8 \times 3 \)[/tex] is 24.
3. [tex]\( 24 + 3 = 27 \)[/tex]
- This is correct but, addition again is not part of the multiplication/division fact family.
4. [tex]\( 24 \div 8 = 3 \)[/tex]
- This is correct. Dividing 24 by 8 gives us 3.
Although three of these statements are true, the first and third statements include addition, which does not fit the criteria for a multiplication/division fact family. Therefore, option c is not entirely correct.
### Conclusion:
Based on the verification process, all four statements in option a are true and fit the multiplication/division fact family criteria for the numbers 3, 8, and 24.
Thus, the correct answer is:
- Option a. [tex]\( 3 \times 8 = 24 | 8 \times 3 = 24 | 24 \div 3 = 8 \mid 24 \div 8 = 3 \)[/tex]
