Question

Describe two different ways that you could find the product 8 x 997 using mental math. Find the product and explain why your methods work.

Answer 1

There are two ways to find the product 8 x 997 using mental math. The first method involves recognizing the number 997 as close to 1000 and breaking down the multiplication. The second method involves splitting one of the numbers and adding the results together.

Step-by-step explanation:

There are two ways to find the product 8 x 997 using mental math:

1. Recognize that 997 is close to 1000, which is 10 times larger than 100. So, you can multiply 8 by 10 to get 80 and then multiply 80 by 100 to get 8000. Finally, subtract 3 times 8, which is 24, from 8000 to get the final answer of 7976.
2. Split the number 8 into 5 and 3. Multiply 997 by 5 to get 4985. Then multiply 997 by 3 to get 2991. Finally, add the two results together to get the final answer of 7976.

Both methods work because they use basic multiplication and addition properties to break down the problem into simpler calculations.

Answer 2

One method is to round 997 up to 1000, multiply by 8, and then subtract 8 times 3. This would give you the solution of 7976.

Another method (Which I personally wouldn't use) is to recursively double 997. This is more difficult, although effective. After you double 997, double the resulting number, and then double the resulting number from that, you have the solution. This is because 2^3 is 8.