R1 query

course Mth 158

If your solution to stated problem does not match the given solution, you should

self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution:

If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what

you do or do not understand about it. This response should be given, based on the work you did in completing the assignment,

before you look at the given solution.

001. `* 1

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Question: * R.1.26 \ was R.1.14 (was R.1.6) Of the numbers in the set {-sqrt(2), pi + sqrt(2), 1 / 2 + 10.3} which are

counting numbers, which are rational numbers, which are irrational numbers and which are real numbers?

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Your solution:

In this equation, there are NO counting numbers, because counting numbers are numbers that are used to count things such as

(1,2,3,4).

The rational numbers in this equation are ½, and 10.3. These numbers can be expressed as a quotient of a/b of two integers.

The Irrational numbers, which can be expressed as the ratio of two integers, . {-sqrt(2)}, pi+sqrt(2) are irrational numbers.

All of the numbers in this equation are real numbers.

Confidence rating #$&* 3

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Given Solution:

* * ** Counting numbers are the numbers 1, 2, 3, .... . None of the given numbers are counting numbers

Rational numbers are numbers which can be expressed as the ratio of two integers. 1/2+10.3 are rational numbers.

Irrational numbers are numbers which can be expressed as the ratio of two integers. {-sqrt(2)}, pi+sqrt(2) are irrational

numbers.. **

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Self-critique (if necessary):0

Self-critique rating #$&*0

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Question: * R.1.44 \ 32 (was R.1.24) Write in symbols: The product of 2 and x is the product of 4 and 6

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Your solution:

2*x=4*6

Confidence rating #$&* 3

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Given Solution:

* * ** The product of 2 and x is 2 * x and the product of 4 and 6 is 4 * 6. To say that these are identical is to say that

2*x=4*6. **

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Self-critique (if necessary):0

Self-critique rating #$&*0

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Question:

* R.1.62 \ 50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ]

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Your solution:

In accordance to the Order of Operations, the numbers in the parenthasis are to be evaluated first, therefore 3-4=-1.

2-5*4-[6*(3-4)]

2-5*4-[6*(-1)]

Then, the items in the brackets must be evaluated.

2-5*4-[-6]

Then, multiply from left to right.

2-20+6.

Then subtract and add from left to right to get,

-12.

Confidence rating #$&* 3

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Given Solution:

* * **Starting with

2-5*4-[6*(3-4)]. First you evaluate the innermost group to get

2-5*4-[6*-1] . Then multiply inside brackets to get

2-5*4+6. Then do the multiplication to get

2-20+6. Then add and subtract in order, obtaining

-12. **

* R.1.98 \ 80 (was R.1.72) Explain how you use the distributive property to remove the parentheses from the express

(x-2)(x-4).

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Your solution:

When using the distributive property, you can use FOIL to solve the equation using the distributive property.

First, multiply the First of each equation, then all the quantities on the Outside of each equation followed by the numbers

Inside, then Last.

(x^2)(-4*x)(-2*x)(8)

Then combine like terms.

(x^2)(-6*x)(8)

Confidence rating #$&*

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Given Solution:

* * ** COMMON ERROR: Using FOIL. FOIL is not the Distributive Law. FOIL works for binomial expressions. FOIL follows from the

distributive law but is of extremely limited usefulness and the instructor does not recommend relying on FOIL.

Starting with

(x-2)(x-4) ; one application of the Distributive Property gives you

x(x-4) - 2(x-4) . Applying the property to both of the other terms we get

x^2 - 4x - (2x -8). Simplifying:

x^2 - 4x - 2x + 8 or

x^2 - 6x + 8. *

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Self-critique (if necessary):0

`sc1

Self-critique rating #$&*0

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Question:

* R.1.102 \ 86 (was R.1.78) Explain why (4+3) / (2+5) is not equal to 4/2 + 3/5.

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Your solution:

These equations are not equal because in the first equation, order of operations indicates that the items in the parenthesis

are to be added first, which gives me

7/7=1

In the second equation, order of operations indicates that the times being divided be done first.

2+3/5 = 2 3/5

Confidence rating #$&* 3

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Given Solution:

* * ** Good answer but at an even more fundamental level it comes down to order of operations:

(4+3)/(2+5) means

7/7 which is equal to

By order of operations, in which multiplications and divisions precede additions and subtractions,

4/2+3/5 means

(4/2) + (3/5), which gives us

2+3/5 = 2 3/5

* Add comments on any surprises or insights you experienced as a result of this assignment.

Although I remember the material, I enjoy ironing out my habit of making simple errors and I am beginning to get in the swing

of taking my time instead of rushing.

&#Good responses. See my notes and let me know if you have questions. &#

#$&*