Answered: Nancy writes the following equations to…

PREALGEBRA

15th Edition

ISBN:9781938168994

Author:OpenStax

Publisher:OpenStax

Chapter9: Math Models And Geometry

Section9.2: Solve Money Applications

Problem 76E: Parent Volunteer Laurie was completing the treasurer’s report for her son’s Boy Scout troop at the...

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Related questions

Question

The sequence of equations below shows a way of using properties of addition to calculating a sum. State
specifically which properties of addition were used, and where.
27 + 89 + 13 = 27 + (89 + 13)
= 27 + (13 + 89)
= (27 + 13) + 89
= 40 + 89
= 129
(2) Write a sequence of equations that correspond to the given description for how to solve the problem.
Problem: 23 + 45
Solution: 23 plus 40 is 63, and then 5 more makes 68
(3) Write a sequence of equations that correspond to the given description for how to solve the problem.
Problem: 800 −297
Solution: 800 −300 = 500, but subtracting 300 subtracts 3 too many, so we must add 3 back, making
503.

(4) Nancy writes the following equations to solve 37 + 14:
30 + 10 = 40 + 7 = 47 + 4 = 51
(a) Explain why Nancy’s work is incorrect.
(b) Write correct equations that solve 37 + 14 and that incorporate Nancy’s solution strategy.

Expert Solution

Step 1

Here we will use commutative property and associative property of addition to find the sum.

Associative property-

$(a + b) + c = a + (b + c)$

Commutative property-

$(a + b) = (b + a)$

Given problem-

27 + 89 + 13 = 27 + (89 + 13) (Associative property is used, 27+(89+13)=(27+89)+13)
= 27 + (13 + 89) (Commutative property is used , 89+13=13+89)
= (27 + 13) + 89 (Associative property is used, 27+(13+89)=(27+13)+89)
= 40 + 89
= 129