Simplify Arithmetic Expressions
Friday, January 23, 2015
Wednesday, February 12, 2014
Jeopardy had this category on a COLLEGE TOURNAMENT in 2014
Jeopardy had this category on a COLLEGE TOURNAMENT in 2014
Tuesday, January 21, 2014
Tuesday, January 8, 2013
Monday, July 23, 2012
Equivalent Fractions
2/3 is equivalent to 8/12
This can be shown by multiplying by 2/3 by 4/4
6/15 is equivalent to 2/5
Here we Divide 6/15 by 3/3
The two procedures of Multiplying or Dividing
by the same number TOP and BOTTOM
is useful to REDUCE FRACTIONS
or for ADDING and SUBTRACTING of fractions.
2/9 + 1/9 = 3/9
but 3/9 needs reducing so DIVIDE by 3/3
Thus, 3/9 is equivalent to 1/3
2/3 + 1/4
now we need to Multiply 2/3 by 4/4
and 1/4 is Multiplied by 3/3
Now the orginal problem becomes
8/12 + 3/12 which EQUALS 11/12
***************************************
For our next time:
Finish the LONG DIVISION PROBLEMS
and also:
Page 85 #3,4,5
Page 89 #4
Page 92 #1 thru 6
Page 93 #1 thru 6
and the POST TEST pages 101 and 102
***************************************
This can be shown by multiplying by 2/3 by 4/4
6/15 is equivalent to 2/5
Here we Divide 6/15 by 3/3
The two procedures of Multiplying or Dividing
by the same number TOP and BOTTOM
is useful to REDUCE FRACTIONS
or for ADDING and SUBTRACTING of fractions.
2/9 + 1/9 = 3/9
but 3/9 needs reducing so DIVIDE by 3/3
Thus, 3/9 is equivalent to 1/3
2/3 + 1/4
now we need to Multiply 2/3 by 4/4
and 1/4 is Multiplied by 3/3
Now the orginal problem becomes
8/12 + 3/12 which EQUALS 11/12
***************************************
For our next time:
Finish the LONG DIVISION PROBLEMS
and also:
Page 85 #3,4,5
Page 89 #4
Page 92 #1 thru 6
Page 93 #1 thru 6
and the POST TEST pages 101 and 102
***************************************
Sunday, July 8, 2012
Why use Fractions?
A Fractions is used to discuss PART OF A WHOLE!
Suppose someone offered you some pizza.
Your answer will determine how much you get.
"Do you want pizza?"
YES, BUT HOW MUCH?
1) "ONE" - you will get a WHOLE pizza.
2) "one-half" = "1/2" will get you a half of pizza.
(ONE PIZZA CUT INTO TWO EQUAL PARTS -
YOU WILL GET ONE OF THESE PIECES)
3) "two-thirds" = "2/3" might need a picture to represent.
First ONE PIZZA will be cut into 3 EQUAL PARTS
and then you will get 2 OF THESE EQUAL PARTS.
Bythe way, if the pizza is cut into
12 equal parts and you eat 8 parts
that is the same as 2/3.
Thus, the conclusion about a fraction:
The DENOMINATOR (Bottom)
represents the number of equal
parts in which that item (PIZZA) is to be cut.
The NUMERATOR (Top) represents the number of these parts that you want to have (to consider, to focus on, to use, to ...).
4) What would 5/8 get you?
The denominator says to cut it (the "ONE WHOLES" pizza) into 8 EQUAL PARTS
and then you get the number of these EQUAL PARTS - that is in the numerator, 5.
Suppose someone offered you some pizza.
Your answer will determine how much you get.
"Do you want pizza?"
YES, BUT HOW MUCH?
1) "ONE" - you will get a WHOLE pizza.
2) "one-half" = "1/2" will get you a half of pizza.
(ONE PIZZA CUT INTO TWO EQUAL PARTS -
YOU WILL GET ONE OF THESE PIECES)
3) "two-thirds" = "2/3" might need a picture to represent.
First ONE PIZZA will be cut into 3 EQUAL PARTS
and then you will get 2 OF THESE EQUAL PARTS.
Bythe way, if the pizza is cut into
12 equal parts and you eat 8 parts
that is the same as 2/3.
Thus, the conclusion about a fraction:
The DENOMINATOR (Bottom)
represents the number of equal
parts in which that item (PIZZA) is to be cut.
The NUMERATOR (Top) represents the number of these parts that you want to have (to consider, to focus on, to use, to ...).
4) What would 5/8 get you?
The denominator says to cut it (the "ONE WHOLES" pizza) into 8 EQUAL PARTS
and then you get the number of these EQUAL PARTS - that is in the numerator, 5.
Friday, June 29, 2012
Math Word Problems - Hints:
1) READ the ENTIRE problem.
2) Read it again (This time with a pencil in hand!)
and JOT DOWN any numbers that appear in the problem.
- Be sure to include a memo showing what the NUMBER REPRESENTS.
- Numbers are sometimes found as words (four, seven,...)
3) Eliminate any numbers that are IRRELEVANT to
the question that your are going to be solving.
4) Decide what OPERATION (S) you need to use:
Add, Subt., Mult., Divide, ...etc.
5) ANSWER THE WORD PROBLEM WITH WORDS!
(At an early age you may find that all you need to do is
to put your answer into a solution sentence provided for you.)
*******************
EXAMPLE:
Old McDonald had a farm with three fenced in areas.
In the first area he kept 20 chickens and 15 cows.
In the second area he kept 25 chickens and 30 sheep.
In the three areas combined he keeps 100 chickens.
How many chickens did he keep in the third fenced area?
*****SOLUTION*****
3 fenced areas
20 chickens in area I
15 cows in area I
25 chickens in area II
30 sheep in area II
100 chickens total
Add 20 plus 25 and then subt. this sum from 100
100 - (20 + 25) = 55
Old McDonald kept 55 chickens in the third area.
2) Read it again (This time with a pencil in hand!)
and JOT DOWN any numbers that appear in the problem.
- Be sure to include a memo showing what the NUMBER REPRESENTS.
- Numbers are sometimes found as words (four, seven,...)
3) Eliminate any numbers that are IRRELEVANT to
the question that your are going to be solving.
4) Decide what OPERATION (S) you need to use:
Add, Subt., Mult., Divide, ...etc.
5) ANSWER THE WORD PROBLEM WITH WORDS!
(At an early age you may find that all you need to do is
to put your answer into a solution sentence provided for you.)
*******************
EXAMPLE:
Old McDonald had a farm with three fenced in areas.
In the first area he kept 20 chickens and 15 cows.
In the second area he kept 25 chickens and 30 sheep.
In the three areas combined he keeps 100 chickens.
How many chickens did he keep in the third fenced area?
*****SOLUTION*****
3 fenced areas
20 chickens in area I
15 cows in area I
25 chickens in area II
30 sheep in area II
100 chickens total
Add 20 plus 25 and then subt. this sum from 100
100 - (20 + 25) = 55
Old McDonald kept 55 chickens in the third area.
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