Final answer:
The fact family for 7×2 = 14 includes other multiplication and division facts that use the same numbers. After evaluating the options, only 5×7 = 35 belongs to the same fact family, because it includes the number 7 and a shared product 7 in their division counterparts.
Step-by-step explanation:
A fact family is a set of related multiplication and division facts that involve the same numbers. Since the student provided the multiplication fact 7×2 = 14, we're looking for other multiplication (and also division) facts that contain the numbers 7, 2, and 14. Let's evaluate each option:
- 3×5 = 15 does not belong to the fact family because 3, 5, and 15 are not used in the original fact.
- 4×6 = 24 also does not belong to the fact family, as it uses the numbers 4, 6, and 24.
- 8×3 = 24 is not part of the fact family for the same reason; it involves the numbers 8, 3, and 24.
- 5×7 = 35 does belong to the same fact family as 7×2 = 14 because it includes the number 7 which is also in the original fact. Furthermore, if we find the division facts for both 7×2 = 14 and 5×7 = 35, which are 14÷2 = 7 and 35÷5 = 7, respectively, they share a common product, which is 7.
Hence, the only option that belongs to the same fact family as 7×2 = 14 is 5×7 = 35.
In conclusion, fact families are helpful for students to perform in their head and understand that math offers multiple paths to the same answer. A fact family for 7×2 = 14 would include 2×7 = 14, 14÷2 = 7, and 14÷7 = 2, in addition to the option d) 5×7 = 35.