**Problem 5: Balancing Method in Mental Math**Macy uses a technique called "Balancing" for mental addition. She simplifies sums by equalizing the numbers. For instance, to compute 39 + 41 mentally, she calculates 40 + 40 instead. Since 40 + 40 = 80, the original sum is also 80.**Tasks:**(a) Apply Macy's "Balancing" method to adjust these addition problems: - 69 + 71 - 58 + 62 - 46 + 54(b) Explain to Max how Macy uses the "Balancing" method with the problem 27 + 33.(c) Explore why Macy's method is effective.(d) Max attempts to use this method for multiplication on 39 x 41, estimating it as 40 x 40. Determine which product (39 x 41 or 40 x 40) is larger and by how much without calculating the exact products.

The balancing method can be done by simply making the sum easy just by adding some to one number and…

Macy has a method that she calls "Balancing" to help her compute certain sums in her head. For example, if she is trying to compute 39+41 in her head, she will instead compute 40+40. She then knows that since 40+40 = 80, it must also be true that 39+ 41 = 80. (a) If Macy were to use her "Balancing" method on each of the following addition problems, to what would she change each of them? 69+ 71? 58 + 62? 46 + 54? (b) Max doesn't quite understand what Macy is doing in her "Balancing" method. Use the problem 27+ 33 to explain to Max what Macy is doing. (c) Why does Macy's method work? (d) Max thinks this trick is pretty cool, so he tries to use it for multiplication. He needs to compute 39 x 41, so he thinks it will be equal to 40 x 40. Unfortunately this is not correct. Without actually computing either of the products, determine which one is larger and by how much. 54

Macy has a method that she calls "Balancing" to help her compute certain sums in her head. For example, if she is trying to compute 39+41 in her head, she will instead compute 40+40. She then knows that since 40+40 = 80, it must also be true that 39+ 41 = 80. (a) If Macy were to use her "Balancing" method on each of the following addition problems, to what would she change each of them? 69+ 71? 58 + 62? 46 + 54? (b) Max doesn't quite understand what Macy is doing in her "Balancing" method. Use the problem 27+ 33 to explain to Max what Macy is doing. (c) Why does Macy's method work? (d) Max thinks this trick is pretty cool, so he tries to use it for multiplication. He needs to compute 39 x 41, so he thinks it will be equal to 40 x 40. Unfortunately this is not correct. Without actually computing either of the products, determine which one is larger and by how much. 54

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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