Work the numbers, not the pictures

When asked for the measure of angle x...

How many people are tempted to...

  a)...              

                        o

...answer   120   ? (Because "x" looks to be twice as big as 60)

       or          

                b)...

...get out a protractor and measure. (And, of course, find that the answer is not one of the 5 choices given.)

                            o

The answer is 30  . The little box at the bottom left                                                                       o

indicates that the two black lines form a 90   angle. 90 - 60 = 30.

The picture is drawn purposely to mislead you. Work the numbers, not the picture.

Some important things to remember are...

All straight lines are 180 degrees.

All interior angles of a triangle add up to 180 degrees.

All interior angles of squares and rectangles add up to 360 degrees.

Mean, Median, Mode

Mean  - Add them All Up and Divide by How Many numbers you have. The answer for the picture above is 42.4. (1060 divided by 25)

"Mean" is what we think of when somebody says average score, average height, etc. The word "average" has replaced the word "mean" to some extent. There are 2 other "averages"... median and mode

When numbers are close together, the "mean average" can give an accurate picture. However, if you have 2,2,2,3 and 10,000, your average is over 2000. This isn't necessarily a true reflection of what is going on.

Median - Put them in Order of size and pick the Middle number. (Or the value between the two "middle" numbers.) It is crucial that you put the numbers in order from lowest to highest (or highest to lowest) in order to get the right answer. The example in the picture above is easy because the numbers are already in order. There is an odd number of numbers.Your middle number is 41, so the median is 41. 

If you added the number 99 to the end of the list, your median ends up as 42. You now have an even number of numbers, so there is no clear "middle" number. Your 2 "middle numbers" are 41 and 43. 42 sits in the middle, so becomes your median.

When numbers are spread apart, the "median" can give a more accurate picture. If you have 2,2,2,3 and 10,000, your median average is 2, which may be a truer reflection of what is going on.

Mode - The number that occurs the Most. In the picture above, there is no mode. In 2,2,2,3 and 10,000, your mode is 2.

DLMR Part 3 - Dividing Decimals

DLMR Part Three  - Work Smart, Not Hard!

Work Smart, Not Hard!

Review...

Remember DLMR. Here's some suggestions for DLMR...

Does Love Mean Rules?

Do Like Mother Recommends

Doughnuts Leave Me Retching

Do Like My Rap!

Ducks Like Marshy Rivers

Dogs Like My Rug

Doug Lost My Respect

Digital Listening Mobile Radio

Don't Like My Ride

Down Long Mountain Roads

Detours Leave Me Ranting

When multiplying or dividing numbers containing decimals by 10, 100, 1000, etc., there's no need for long division or multiplication. You need only MOVE the decimal place.

D.L.M.R tells us that when we divide by 10, 100, 

1000, etc., we move the decimal...........................................

left.

We move one place for every zero (0) in the 10, 100, 1000, 10,000, etc. 

So...     27.5  ÷ 100

In the example above, we are dividing by 100. There are 2 zeroes. We need to move the decimal 2 places to the..............................................

left.. 

The answer is .275 or 0.275 (the same thing, really.)

So... what about 27.5  ÷ 10,000? We need to move the decimal 4 places to the left and there's only 2 spaces (the "2" and the "7"). What to do?

Captain Zero to the rescue. 

Is he a bird? A plane? No - he's one big zero. You may know him. You may have seen him. He fires blanks. As many as you need. Tack them onto the left of the 27.5

00000027.5  ÷ 10,000         Put as many zeroes as you like. Captain Zero will never run out.

(Move the decimal place 4 spaces to the left. One for each zero in 10,000.) We move to the left when we divide.

The answer is...              .00275 or 0.00275. Or even 000000000.00275. They are all the same.

DLMR Part Deux - Captain Zero to the Rescue!

D.L.M.R. - Work Smart, Not Hard!

Work Smart, Not Hard!

Review...

Remember DLMR. Here's some suggestions for DLMR...

Does Love Mean Rules?

Do Like Mother Recommends

Doughnuts Leave Me Retching

Do Like My Rap!

Ducks Like Marshy Rivers

Dogs Like My Rug

Doug Lost My Respect

Digital Listening Mobile Radio

Don't Like My Ride

Down Long Mountain Roads

Detours Leave Me Ranting

When multiplying or dividing numbers containing decimals by 10, 100, 1000, etc., there's no need for long division or multiplication. You need only MOVE the decimal place.

D.L.M.R tells us that when we divide by 10, 100, 

1000, etc., we move the decimal

left 

and when we multiply, we move the decimal 

right

We move one place for every zero (0) in the 10, 100, 1000, 10,000, etc. 

So...2.70 x 100 was 270. How about 2.3 x 10,000?

In the example above, we are multiplying by 10,000. There are 4 zeroes. We need to move the decimal 4 places to the...............................................right. But there is only the one decimal place (the .3). What now?

Captain Zero to the rescue. 

Is he a bird? A plane? No - he's one big zero. You may know him. You may have seen him. He fires blanks. As many as you need. Tack them onto the right of the 2.3

2.3 0 0 0 x 10,000 = 23,000. (Move the decimal place 4 spaces to the right. One for each zero in 10,000.) We move to the right when we multiply.

More examples, covering some trickier problems, will follow in the next postings.

D.L.M.R. - Work Smart, Not Hard!

Work Smart, Not Hard!

Remember DLMR. Here's some suggestions for DLMR...

Does Love Mean Rules?

Do Like Mother Recommends

Doughnuts Leave Me Retching

Do Like My Rap!

Ducks Like Marshy Rivers

Dogs Like My Rug

Doug Lost My Respect

Digital Listening Mobile Radio

Don't Like My Ride

Down Long Mountain Roads

Detours Leave Me Ranting

When multiplying or dividing numbers containing decimals by 10, 100, 1000, etc., there's no need for long division or multiplication. You need only MOVE the decimal place.

How many times have you seen something like this ... ?

    2.72

X  100

   0 0 0

0 0 0 0

27200

____________________

This is working hard, not smart.

D.L.M.R tells us that when we divide by 10, 100, 

1000, etc., we move the decimal

left 

and when we multiply, we move the decimal 

right

We move one place for every zero (0) in the 10, 100, 1000, 10,000, etc. 

In the example above, we are multiplying by 100. There are 2 zeroes. We need to move the decimal 2 places to the...............................................right. 

The answer is 272.

More examples, covering some trickier problems, will follow in the next postings.

Wipe, Cancel, Divide and Stick. When "powers" aren't all that powerful - dividing monomials

24 x³

 -----

 4 x²                        Confusing? Scary?

Not really, when you can WIPE, CANCEL, DIVIDE and STICK.

Step One - WIPE out the powers.  Rewrite them as...

24 x x x

  --------

 4 x  x 

Step Two - CANCEL

24 x x x

  --------

 4 x  x 

Step Three - DIVIDE  -     24/4 = 6

Step Four - STICK  the "x" on the end...

...   6x

Step Five - Done

Beer saves the day - again. Improper Fractions

21   What do I do with this improper fraction?

 8

You need to change it into a mixed fraction. How do you do this? Well, think of beer. You have 21 bottles but can only carry 8 bottles at a time...

You will make 1 full trip, carrying 8 bottles.

You will make a 2nd full trip carrying another 8 bottles.

You have 5 bottles left.  They do not represent a "full" trip. Your 2 "full trips" become the whole number component of the mixed fraction. 

Your 5 bottles that are "left over" go on the top shelf of the fridge. (That is where all left overs go." Your denominator was 8, so let's keep it at 8. You now have...

2  5

     8    

For a video explanation, start 2 minutes into the video here