Born to Run

Which one is the radius...

and which one is the diameter?

I remember the radius as the one that starts in the 

middle...

...and then RUNS to the outside.

The diameter crosses the entire diagram.

That's it. Work smart, not hard.

Mixed Fraction Subtraction - Let's Go Shopping

Mixed Fraction Subtraction - kinda rolls off the tongue, doesn't it?

OK - how about...?


     4
5  ---
     7

subtract

     5
4  ---
     7


We know the 4 and 5/7 is smaller than the 5 and 4/7.

But how to subtract 5/7 from 4/7?

Some might suggest converting both fractions to improper fractions...

...and coming up with 39/7 - 33/7 

...and arriving at 6/7.

However, if you are not particularly strong at multiplication, you might try this method...

Let's go shopping...

     4
5  ---
     7

First off - let's just make the 5 one LESS.

Why?

1) Because we can.
2) You always come away with LESS money when you go shopping. (Yes, yes, yadda, yadda, you might end up shopping for lottery tickets and win. Heard that one. Heard 'em all.)

So now our fraction is modified a bit from

     4
5  ---
     7


To...

     4
4  ---
     7


But not for long. Now let's buy a top.

Hmm, stylish. Who said I had no taste?






OK. Now remember...our top (denominator) was 4.

Better now add some pants to this stylish ensemble.

Let's add the
bottom (pants) to the
top. Can this ensemble get any more stylish? I doubt it. 


4  add  7 = 11










Remember...
     4
5  ---
     7


changed to...

     4
4  ---
     7

and we are now going to add the pants (bottom) onto the top

4  add  7 = 11


    11
4  ---
     7

Now we can finish the question.

    11
4  ---
     7

subtract

     5
4  ---
     7


Let's get rid of those whole numbers...
4 - 4 = 0

Now...

11/7 - 5/7 = 6/7


6/7 is our answer. Work SMART, not HARD!

Is it Prime (Or is it Memorex)?

A prime number is a natural number greater than 1, that has no positive divisors (factors) other than 1 and itself.

If you think of this definition in pictures of rectangles...

2 - ᥆᥆
3- ᥆᥆᥆
4 - ᥆᥆᥆᥆ or  ᥆᥆
                       ᥆᥆
5 - ᥆᥆᥆᥆᥆
6 - ᥆᥆᥆᥆᥆᥆  or ᥆᥆᥆
                             ᥆᥆᥆

Any number that can ONLY be represented by a straight line is prime.

Straight line is prime.

Integer Football Game

I came across this cool way to explain integers. Integer football. See for yourself at...

Integer Football

Pass The GED - Tips and Tricks

Many times it is the little things that stand between passing and failing. 

Here's a video to help everyone pass the GED exam by dealing with those little things.

Find the video here.

Don't Call it Algebra (And Nobody Will Know!)

The word Algebra can be intimidating to GED students.

Many people have this conception of Algebra...

I always tell my students that they did algebra back in Grade 2 but they just didn't know it.

Grade 1 -    1 + 1 = ▭

We followed the directions and added the 2 numbers together and wrote "2" in the box.

1 + 1 = 2

Grade 2  Day 1

1 + 1 = ▭

We followed the directions and added the 2 numbers together and wrote "2" in the box.

Grade 2  Day 2

1 + ▭ = 4

We followed the directions and added the 2 numbers together and wrote "5" in the box.

1 + 5 = 4

It looked wrong, and we knew it was wrong, but we followed the directions that said we had to add the two numbers together and put the answer in the box.

After a leap in our thinking, we were able to say that...

1 + "something" = 4

That "something" is 3. 

1 + 3 = 4

1 + ▭ = 4        The ▭ = 3

So how about 1 + x = 4?

"x" is just a ▭                  x = 3

I tell my students that they did Algebra in Grade 2 so they can certainly do it now in GED study.

Dividing Fractions #%$^&*() Don't choke!!!!!!!!!!!!!!!!!

Dividing fractions? Don't choke!!!!!!!!!!!!!!!!!

Isn't one of the fractions supposed to be flipped around or something? I can never remember which one...

Here's the easy way to remember the process...

(Note - you are under no obligation to use this simple and easy to remember explanation. You can use any unnecessarily long and convoluted method you wish to help explain it.)

So what is 6/31  divided by 2/3?

Here's dad and son. Dad is 6 feet tall and aged 31. Dad is first in age so he's the first fraction.

Son is 2 feet tall and aged 3 months. Son is second.

Son starts to choke...

Dad, being dad, starts to swear. (He never swore much before the had children.) Swearing is bad (apparently), so we cross this out. Son gets turned upside down and becomes 3/2. Choking stopped!


So now we have 6/31  X   3/2

Solve as you would a normal fraction multiplication question. Remember....

Leave the first fraction alone. The guy is trying to save his son's life, here, people, so leave him alone to get on with the job. Please disperse. Back away from the man. Go about your business.

Turn the 2nd fraction upside down.

Put an X between your two fractions.

Solve as you would a normal fraction multiplication question.



Work smart, not hard.

Exponent Secrets

See this link           http://www.mathsisfun.com/activity/secret-safe-exponentially.html  for a great explanation of exponents.

! #@$%&#@#

Ever wonder what that...

or...

                                                                                                                                                                                  

           

               

                                                           X

...key is for on your calculator? Well...

That's your gold plated 

short cut to solving those "arrangement"-type questions. 

You know (and love) the ones - "You have one red, one green, one blue and one yellow circle. How many ways can you arrange these 4 circles?"

So you might set out to make a grid or chart, starting with red. 

1) ০০০০

2) ০০০০

3) ০০০০

etc., etc., until your crayons and patience are worn out.

Or you could just enter 4 on your calculator and then press the factorial (x!) key (you might have to press shift first, depending on your calculator.) Bang. Done. Work smart, not hard.

"3 out of 4" Questions - Rate and Proportion

This is a modification from an earlier post. I realised there might be a few Heavy Metal fans out there...fans of the band MUAADON.

"3 out of 4" Questions - Rate and Proportion

Look or sound familiar? 



"A 10 metre flag pole casts a shadow of 6 metres. A 12 metre pole would cast a shadow that is ______ metres in length."

"A motorcyclist rides 125 miles in 3 hours. At this rate, how much distance will be covered in 5 hours?"

A factory produces 3000 widgets every 45 minutes. How many widgets will be produced in 7 hours?


These questions, I like to call, are "3 out of 4" questions. You are given 3 numbers and you need to find the 4th. How to solve? Make yourself a 4-way relationship box. 


Let's look at question 1 again. 

"A 10 metre flag pole casts a shadow of 6 metres. A 12 metre pole would cast a shadow that is ______ metres in length."

Your two "measurements" are height (H) and shadow length (SL).

H           SL
10            6
12            ?

Remember MUAADON - Multiply Up And Across, Divide by the Other Number.

12 x 6 = 72
72/10 = 7.2

You could have set your box up another way.

H      10    12
SL     6      ?

6 x 12 = 72
72/10 = 7.2

Same answer...


Tricks to watch out for!

In question 3, the two "measurements" are time and widgets. However, the first "time" is in minutes and the second one is in hours. You need to either convert the 45 minutes to .75 hours, or convert the 7 hours to 420 minutes. Then set up your box, remember MUAADON, and get yourself the right answer. Rock on!

Math Doctor Video - New Version

See Math Doctor Link for the new Math Doctor Video - write out a 10 by 10 multiplication in under 1.5 minutes.

Come Undun

From  de.wikihow.com

Mean Median Mode Range - from www.showme.com

Circumference

Formula for Circumference?

Well - if you eat a pie a day, you will get a big circumference. (Distance around your middle.)

 

C = ∏   x  D    (diameter)

Find the diameter (or double the radius if the radius is given), multiply by pi and you will get the circumference.












Work Smart, Not Hard!

Do you know "Y" you were intercepted Part Deux

OK - so maybe the last post was a bit easy.

Perhaps there might be a harder question on the GED test?

A quick review... Which line has the equation

 

 y = x + 6

 

 

First of all, image you have been driving along and are suddenly "intercepted" by the police.

"Do you know "y" you were intercepted?" is probably the question you will be asked.

 

The key to this question is the "y" intercept, or the location at which the line crosses (intercepts) the "y" or vertical axis. (For some reason, nobody really cares about the poor old "x" axis. As with all "ex's", they are best left forgotten.)

 

y = x + 6 

 

The free floating number here is the 6. The only line that crosses/intercepts the "y"axis at 6 is line 5. Job done. You are finished.

 

                                 

 

OK, but what about...

 

 

 

 

 

 

Looks like 2 lines intercepting the "y" axis at 6. (Lines 5 and 7) So how now, brown cow?

 

Well, the next clue is the slope of the line. The free floating number corresponds with the intercept while the value associated with the "X" determines the slope. In this case, the slope is positive 1.

 

How can that be? (In algebra, values of positive 1 are dropped, being "understood" to be positive 1.) The formula for this line could have been written as y = 1x + 6

 

So we now need to find which line has a slope of positive 1.

 

By convention, lines that "rise" from the lower left to the upper right are considered to have a positive slope, Lines that "fall" from the upper left to the lower right have negative slopes. That rules out line 7.

 

 

Work SMART, not HARD!

Slope - Wake Up First!

Have you been asked to calculate the slope of a line?

Think of jogging. If you want to go for a run up a slope in the morning, you must rise first before you run.

So...    to calculate the slope of a line...
use the formula...             slope = rise
                                                        run
Rise is the vertical distance between two points on a slope. Run is the horizontal distance between two points on a slope.

In this case, the rise is 2 and the run is 6.

slope = rise
             run   so...

2            1
6      =   3

Convention says that lines that "fall" as they move to the right have negative slopes and lines that "rise" as they move to the right have positive slopes. I guess it depends on your point of view - are you going up or down the hill?

Acute? Obtuse? Reflex? Which is Which?

Acute? Obtuse? Reflex? 

Which is Which?

Angles less than 90 degrees are...   Acute

Angles between 90 and 180 are...   Obtuse

Angles between 180 and 360 are...

Reflex

How to remember?

Alphabet! AOR. Fortunately, the angles are in alphabetical order.

A - Acute - up to 90

O - Obtuse - between 90 and 180

R - Reflex - between 180 and 360

Key Math Words - "English" words versus "Math" words

 

12 and 5...  What is the difference between these two numbers?

Well, you might say that 12 has two digits and 5 has only one. You might say that the digits in 12 are gold and the 5 is blue.

In the mathematical world, difference means subtraction. The difference, in this case, is 7.

Some key subtraction terms are...

reduce

minus

diminish

decrease

dropped      and...

fell

Some key addition terms are...

sum

total

raise

combine    and...

additional

Some key multiplication terms are...

product

per

Some key division terms are...

quotient

split   and...

shared

Knowing these terms can help with word questions, when you are trying to figure out which operation to perform.

TMI? No... Not Enough Information (NEI) or Extraneous Information (EI)?

At a recent sporting event, 25 athletes won one gold medal each. 25 others won a silver medal. 25 won bronze. 40 athletes did not win any medals. How many medals were awarded?

Answers

a) 115
b) Not enough information
c) 75

The answer is "c"

Note: 

You might be tempted to answer... a) (115) because that is 25 x 3 + 40. You see the numbers in the question and you combine them. 

You might be tempted to answer... b) "Not enough information" because the question involves medals awarded to some athletes and then suddenly some athletes aren't getting any medals.

********If you answer "Not enough information" more than twice on a fifty question exam, you should check the questions again. 

Solving Equations - Think "Hockey Trades"

Look familiar?  

x + 31 = 64            

Solve for "x"




Think of these problems as hockey trades. Good old #31...

...likes playing for team "x". (They are in first place in the league.) We know that "x" is happy because there is a plus/positive sign to the left of his number. Think of the equation as...

x /+ 31/ = 64   

However, hockey being hockey, sometimes players get traded. Good old /+ 31/ is being sent down the lines (=) to the last place team. Do you think he will be happy when he gets there. No... (note the incredible graphics here at the RUGS Blog) He's now not happy and, therefore, is now negative /-31/. The equation will now look like this...

x = 64  /- 31/

64 - (minus, take away, etc.) 31 = 33

Therefore x = 33





You can also have some grumpy, negative players on the last place team who are suddenly traded to the top team. 



x /- 15/ = 64            

Solve for "x"


When grumpy (negative) #15 gets sent down the lines (=) to the new team, he becomes very happy (positive).

x = 64  /+ 15/

x = 79