Percents

*******************PERCENTS********************
To change from:
1) a fraction 3/5 to a decimal ...
just divide 3/5 is .6
2) a decimal .6 back to a fraction ...
just read the decimal --- .6 is 6 tenths or is 6/10
3) a decimal .6 to a percent ...
just multiply by 100 --- .6 times 100 or 60%
4) a percent to a decimal ...
just divide by 100 ---- 7.45% becomes .0745
5) a Fraction to a Percent or Versa Visa
---we will not do this directly ---
change to a Decimal first and then proceed as before...
*******************PERCENTS********************

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***Change the given item into the form of the ANSWER***

***Change the given item into the form of the ANSWER***


***Change the given item into the form of the ANSWER***


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HINT: "WHOLE" usually appears after the word "OF".
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FIND the REQUIRED ITEM!****

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Working with Negative Numbers

Suppose each time a football team started on offense

they were at MID-FIELD. (Also assume that the

field is marked like a number line!)

Determine the position of the ball

after these sequences of plays:

Gain 10, Lose 5

The ball would rest on the 5 YARD LINE.

In math this would be represented by the

ADDITION PROBLEM:

(10) + (-5)  = 5

Thus, it seems that we are subtracting 10 minus 5.

And since the Gain is LARGER the ball is in the

POSITIVE DIRECTION

Try this set of plays starting at MID-FIELD:

Lose 30, Gain 20

ADDITION PROBLEM:

(-30) + (20) = -10
Again we subtract the numbers and the answer
has the sign of the LARGER  "-" (in size)

RULE:
When adding TWO numbers with
OPPOSITE SIGNS, subtract and
use the SIGN of the "LARGER"
(IN SIZE)

A review of PEMDAS might be in order before
attempting the following problems:

   

Simplify Arithmetic Expressions

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Why SUBTRACTION becomes ADDING opposites

At least once in an Algebra Class the students shouldsee the
"WHY"
 in 7 - (-3) becoming 7 + (+3)
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Graphing Inequalities

Many mathematical techniques lend themselves to shortcuts.
Sometimes these shortcuts are great and other times
they seem to be "too tricky" to make sense when the
same type problem needs attention later.
One particular case is graphing an Open Sentence
that is an INEQUALITY.
For example:
Graph the Solution Set for   "5 <  x"
During my teaching days I found that some of
my students were taught to always have the
"X" on the left so that the >  or < will point in the
direction of the shaded solution. This requires
the student to sometimes "SWITCH" the direction
that the inequality sign points. (This switching only
occurs when "X" is on the RIGHT SIDE!)
so "5 < x" becomes "x > 5"
the graph is  ...

The idea of 1) moving the x to the LEFT,
2) switching the direction of  "<"  to ">"
and then 3) pointing the arrow of the graph in the
direction of ">" does produce a correct graph.
My suggestion is to encourage the students
to read the inequality starting with "X".
"5 < x"
would be read "X is GREATER than 5."
Since we are graphing "X's", this method
of translation will lead to the correct
direction of the ARROW in the graph.



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