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6. How would you group the numbers to find $7 \times 2 \times 4$? Why?

You can group the numbers in different ways to simplify the multiplication. One possible way is to group $7 \times 2$ first: $(7 \times 2) \times 4 = 14 \times 4 = 56.$ Another way to group the numbers is $2 \times 4$ first: $7 \times (2 \times 4) = 7 \times 8 = 56.$ Both ways give the same result because of the associative property of multiplication, which states that the grouping of factors does not affect the product.

7. Ashon and Flora chose different ways to multiply $4 \times 5 \times 3$.

• Ashon’s method: Ashon grouped the numbers like this: $4 \times (5 \times 3)$. He found $5 \times 3 = 15$, then multiplied $4 \times 15 = 60$.

• Flora's possible method: Flora could have grouped the numbers differently, such as $(4 \times 5) \times 3$. First, she would find: $4 \times 5 = 20,$ then multiply: $20 \times 3 = 60.$ So, both Ashon and Flora would end up with the same result, $60$, but using different grouping of the numbers. This again demonstrates the associative property of multiplication.

8. Show two different ways to group $8 \times 2 \times 3$, then find the product.

• First method: Group $8 \times 2$ first: $(8 \times 2) \times 3 = 16 \times 3 = 48.$
• Second method: Group $2 \times 3$ first: $8 \times (2 \times 3) = 8 \times 6 = 48.$ Again, both methods give the same result, $48$, due to the associative property.

Would you like more details on any of these questions? Here are 5 related questions to expand your understanding:

1. What is the commutative property of multiplication, and how does it differ from the associative property?
2. How would you solve $6 \times 3 \times 5$ using different groupings?
3. Can the associative property be applied to division? Why or why not?
4. Why does the order of multiplication not affect the result, but grouping does?
5. If you had four numbers, like $2 \times 3 \times 4 \times 5$, how would you group them to simplify the calculation?

Tip: Always look for easier pairs of numbers to multiply first when using the associative property. For example, multiplying numbers that produce round numbers, like $5 \times 2$, can simplify the process.