Question

7. Pedro and Ava each find the sum 3 x 105 + 2 x 105 + 4x 10³. Pedro uses the order

of operations, and Ava uses the distributive property.
Pedro's work:
3x105 + 2× 105 + 4×105 = 3 × 100,000 + 2× 100,000 + 4×100,000
= 300,000 + 200,000 + 400,000
= 900,000
Ava's work:
3 x 105 +2 x 105 +4 x 105 = (3+2+4) × 10³
=9x105
a. Who is correct? Explain.
b. Compare the two methods.

Answer 1

a. Pedro is correct.

Explanation: Pedro correctly applied the order of operations, which states that multiplication should be performed before addition. He multiplied each number by 105 separately and then added the results together. This is the correct way to calculate the sum of these numbers.

On the other hand, Ava used the distributive property incorrectly. The distributive property applies when you have a common factor that you want to distribute to each term inside parentheses. In Ava's work, there are no parentheses, so the distributive property does not need to be used. Adding the numbers together and then multiplying by 105 is an incorrect application of the distributive property.

b. Pedro's method is the correct and standard way to calculate the sum of the given numbers. It follows the order of operations, which ensures that calculations are performed in the correct order.

Ava's method, using the distributive property, is incorrect in this case. The distributive property is a useful property in mathematics, but it should be applied correctly. In this problem, there is no need to use the distributive property as there are no parentheses or common factors to distribute.