Write the fact family for the numbers 32, 8, and 4.
The Correct Answer and Explanation is :
A fact family is a group of related math facts using the same set of numbers. For the numbers 32, 8, and 4, we can create a fact family using multiplication and division.
Fact Family for 32, 8, and 4
- Multiplication facts:
- ( 8 \times 4 = 32 )
- ( 4 \times 8 = 32 )
- Division facts:
- ( 32 \div 8 = 4 )
- ( 32 \div 4 = 8 )
Explanation
Fact families are a great way to reinforce understanding of the relationships between multiplication and division. They help illustrate the idea of inverse operations, meaning that one operation can “undo” another. In this case, multiplication and division are inverse operations.
For example, in our fact family, ( 8 \times 4 = 32 ) shows how combining groups (multiplication) results in a larger number. Conversely, ( 32 \div 8 = 4 ) takes that total and breaks it down into smaller groups (division). This approach shows that division can be used to find one of the factors if the product and one factor are known.
Understanding fact families aids in mental math and builds a foundation for algebra. When students or learners are familiar with fact families, they are able to see that if they know one fact, they inherently know the other three. This is especially useful when solving problems, as it helps to recall facts more easily and strengthens fluency in arithmetic.