Two students are using estimation to determine reasonable solutions to the expression 89.1 times 9.3. Katie uses the expression 90 times 10. Amaya uses the expression 89 times 9. Which is the best comparison of the estimates and the actual product?

Question

Both estimates will be less than the original product.
Both estimates will be greater than the original product.
Katie’s estimate will be less than the actual product, and Amaya’s estimate will be greater than the actual product.
Katie’s estimate will be greater than the actual product, and Amaya’s estimate will be less than the actual product.

Answer 1

To determine which estimates are closer to the actual product of 89.1 times 9.3, let's first calculate the actual product:

\[ 89.1 \times 9.3 = 830.37 \]

Next, let's evaluate the estimates provided by Katie and Amaya.

Katie's estimate: Katie estimates 89.1 times 9.3 as:

\[ 90 \times 10 = 900 \]

Amaya's estimate: Amaya estimates 89.1 times 9.3 as:

\[ 89 \times 9 = 801 \]

Now, we can compare the estimates to the actual product.

1. Katie's estimate (900) vs actual product (830.37):

   • 900 is greater than 830.37.

2. Amaya's estimate (801) vs actual product (830.37):

   • 801 is less than 830.37.

Based on this analysis:

• Katie's estimate is greater than the actual product.
• Amaya's estimate is less than the actual product.

Thus, the best comparison of the estimates and the actual product is:

Katie’s estimate will be greater than the actual product, and Amaya’s estimate will be less than the actual product.