Question

Patti is using mental math to evaluate the expression (70 + 12.8 + 30) +6.1. she recognizes that the expression will be easier to simplify if she can combine 70 and 30 before she works with the other numbers. How do the properties of operations allow Patti to take that approach?

Answer 1

Answer:

Given that Patti is using mental mathematics to evaluate the expression (70+12.8+30)+6.1 and recognises that it will be easier to simplify if she can combined 70 and 30 in the beginning. We are to explain the way in which the properties of operation allow Patti to take that approach.

We will be using the following associative property of real numbers:

(a+b+c)+d=(a+c)+(b+d).(a+b+c)+d=(a+c)+(b+d).

Therefore, the simplification is as follows:

(70+12.8+30)+6.1\\=(70+30)+(12.8+6.1)\\\\=100+18.9\\\\=118.9.\

(70+12.8+30)+6.1

=(70+30)+(12.8+6.1)

=100+18.9

=118.9.

Hence explained.