Allen is showing his work in simplifying-8.3 + 9.2 - 4.4 + 3.7. Identify and explain any errors in his work or in his reasoning. Write feed back to Allen explaining the mistakes he made and how to correct his work

Step-by-step explanation:

The question lacks Allen's workings. Find it below.

Step Work Reasoning

−8.3 + 9.2 − 4.4 + 3.7 Original problem

1 −8.3 + 9.2 + 4.4 + 3.7 Additive inverse

2 −8.3 + 4.4 + 9.2 + 3.7 Commutative property

3 −8.3 + (4.4 + 9.2 + 3.7) Associative property

4 −8.3 + 17.3 Simplify

5 9 Simplify

Given the equation −8.3 + 9.2 − 4.4 + 3.7, to solve this we are going to be using different properties.

Given three values A, B and C, the following are true:

A-B = A+(-B) Additive inverse

(A+B)+C = A+(B+C) Commutative property

Applying this laws to correct Allen's calculation

Original problem

−8.3 + 9.2 − 4.4 + 3.7

Applying the additive inverse property

−8.3 + 9.2 +(− 4.4) + 3.7 {since product of plus and minus sign still gives a minus sign)

Rearranging the equation based on signs according to the associative property we will have:

−8.3 +(-4.4) + 9.2 + 3.7

Using the commutative property to separate the positive variables from negative variables will give:

{−8.3 +(-4.4)} + {9.2 + 3.7}

Since {−8.3 +(-4.4)} + {9.2 + 3.7} = {9.2 + 3.7} + {−8.3 +(-4.4)}

Simplify the expressions in parenthesis:

= {−8.3 +(-4.4)} + {9.2 + 3.7}

= (-8.3-4.4)+(9.2+3.7)

= (-12.7)+(12.9)

= 0.2

From the above calculation, it can be seen that Allen made an error while using the additive inverse property in his first step. He should not have removed the minus sign. The negative sign was removed from step 1 which makes the remaining steps of his calculation to be wrong. Instead of replacing -4.4 directly with +4.4 he should have used the additive inverse property by replacing -4.4 with +(-4.4).