In the Dog House, Part Deux - Captain Zero to the Rescue (Yet Again)

A quick review...

Look familiar? 
Pat scored 54 out of 200 on a test. What percent is this?

The key to solving these types of questions comes in the words " out of ".

The " out of " number needs to be thrown " out of " the house.  200 is not allowed in the house.

54 is inside...

and 200 is out of the house, in the dog house...

So now we have...

200 divided into 54. 

This is a job for Captain Zero. (More powerful than a speeding doughnut, able to leap tall O's in a single bound...)

Put as many zeroes as you like. Captain Zero never runs out. Make sure you put a decimal point immediately to the right of the 54, and one directly above.

Now you have a standard long division question.

Looking at the roof line, you will see that 27 is to the right of the decimal. Whatever is to the right of your decimal becomes your %. So...

.27 = 27%

.03 = 3%, etc.

Pat scored 54 out of 200 on a test. What percent is this? 27%

In the dog house

Look familiar? 

1) Pat scored 54 out of 200 on a test. What percent is this?

or...

2) 36 out of 300 people ride bikes to work. What percent is this?

The key to solving these types of questions comes in the words " out of ".

The " out of " number needs to be thrown " out of " the house. 200 has forgotten the wedding anniversary (yet again!) and has to go and sleep in the dog house. 200 is not allowed in the house.

54 is inside...

and 200 is out of the house, in the dog house...

So now we have...

 200 divided into 54. 

This is a job for Captain Zero and will be covered in the next blog post. 

Note: Do not get into the habit of assuming you are dividing the "bigger number" into the smaller one. You might get a question such as...

Pat scored 154 out of 150 on a test. Bonus marks were scored! What percent is this? 

If Pat scored more than 150, then the answer has to be more than 100%. In this case, 150 is your " out of " number.

          

Inequalities < > (#@!^@@@$$$!!!!!)

Look familiar?

"Which inequality is represented by this picture?"



Well, you've always got 4 options. Something (usually represented as "x") is either...


1) Greater than a given number
2) Greater than, or equal to, a given number
3) Less than a given number
4) Less than, or equal to, a given number



Examples...

1) Greater than a given number

Answer      x > -1 (x is greater than minus 1)

2) Greater than, or equal to, a given number

Answer      x > -1 (x is greater than, or equal to, minus 1)

Notice a difference? If the circle above the number line is OPEN, your < or > sign has NO line under it. 

If it is a closed circle, your < or > sign has a line under it. 

This line signifies "or is equal to."

3) Less than a given number

Answer      x < -1 (x is less than minus 1)

4) Less than, or equal to, a given number

Answer      x < -1 (x is less than, or equal to minus 1)

Ah, yes, the good old Circular Lawn or Swimming Pool Question

You may get a question that not many people, outside of a math test, would worry about. Or think about.

The old circular lawn or swimming pool question.

As the incredibly professional-looking graphic above looks more like a pool than a lawn, let's go with this type of question...

A circular pool has a sunbathing deck in the middle. The distance from the centre to the inner edge of the water is 4m. The distance from the centre to the outer edge is 6m. What area does the water cover?

(Hint: It isn't 2 metres.) 

What is missing?

Imagine the pool deck is a like the centre of a pie that has been eaten.The water is the pie that hasn't been eaten. So, work out the area of the whole pie and subtract the area of the piece that was eaten. What is left is your answer.

The area of a circle is...

pi X radius squared

So...

pi x 6 squared         subtract        pi x 4 squared

62.83 square metres.

Note: You won't get the right answer by working out pi x 2 squared (2 being the difference between 6 and 4.)

Perhaps the easiest way to remember this is  

pi x big radius squared  

subtract 

pi x small radius squared 

I Part (With My Money)

Calculating simple interest? Think of parting with your money. (Parting, in this case, is not always such sweet sorrow.)

The formula for calculating simple interest is...........

i = prt         (I part). 

I is the interest.

R stands for "rate". 

T stands for time period.

i = p X r X t

P stands for principal. This is a fancy term for the chunk of money you are talking about. (You borrow $2000.00 or you invest $3000.00. This is your principal. So...

If you are investing that $3000.00 over 2 years at 1% interest rate, you work it out like this... (Don't forget to convert your 1% to decimal form (0.01)

i = prt

i = 3000.00 x (0.01) x 2

i = $60.00

When you invest, you part with your money for 2 years and you are rewarded with $60.00.

If you are borrowing that $3000.00 over 2 years at 1% interest rate, you pay the bank $60.00 for lending you the money in the first place. You part with that $60.00 when you pay it to the bank.

3 Consecutive Numbers...

Look familiar? The sum of three consecutive numbers is 36. What are the numbers?

Method 1) 

Guess. It is unlikely to be 1, 2 and 3...

...or 34, 35, and 36. 

Best strategy is to start with half of 36, which is 18. 

So try adding 16, 17 and 18. This gives us 51. Too big. 

Try adding 14, 15 and 16. This adds up to 45. 

Getting closer...

Eventually you will arrive at 11, 12 and 13. 

Method 2)

Algebra saves the day...

The first number is "x". The second number must be "x + 1" because it is 1 more than the first number. The third number is "x + 2". Put these together and you can make an algebraic formula...

x + x + 1 + x+2 = 36

3x + 3 = 36

3x -3 = 36 -3

3x = 33

x = 11

Your three numbers are 11, 12 and 13.

IER - Solve For...

                 E
     I =       __
                 R

Look familiar? Solve for E? Solve for R? The answer is simple, if you think of a triangle...
                                  
                                      E

IR

(X)

Now, just cover up the letter you are asked to "solve for..." with your thumb and...presto...

1)     E = I x R

2)     R = E/I   (E divided by I)

3)     I =  E/R  (E divided by R)

Note: What throws a lot of people is that there is no numerical answer to this question. The answer isn't 4 or 2.6 or whatever. These questions look a lot harder than they really are.

Mirror Mirror - Polynomials

(x + 6)(x - 6)

The easy, quick answer is ...

      2
x   - 36

(x + 7)(x - 7)

The easy, quick answer is ...

       2

x   - 49

(x + 8)(x - 8)

The easy, quick answer is ...

      2

x   - 64

See a pattern? I call these "mirror" questions because the values inside the brackets are mirror images of each other. One sign is "positive" and the other is "negative." 

The quick and easy way to answer these questions is to put a square (2) behind the "x", 
                                                                   2

                                                           x  

put down a "negative sign ( - )"         2

                                                  x      -

and then multiply (or square) the two numbers in the brackets.    
                                            2

                     x      -    64

Done. Move on to the next question.

Note: You need to have mirror images. If you have (x + 8)(x + 8), you have a whole 'nuther question, which can't be solved using this short cut.

Look "Ma", no hands!

     3
2  ----
     7


Changing a mixed number to an improper fraction?


Step One - Like every job, start at the bottom. (I think Rodney Dangerfield said that proctology is the only profession where you start at the bottom and stay there.) Start with the 7.


Step Two - Work Clockwise 


Step 3 - Remember to listen to Ma! M = Multiply, A = Add


Step 4 - Multiply 7 by 2 to get 14.


Step 5 - Add 14 to the 3. You now have 17.


Step 6 - Your denominator stays 7.


Your new improper fraction is...


  17
------
   7

I Can't Do Algebra! That "x" is a box.

"Algebra" scares people. When alphabets start invading our math pages, we panic. However...

we all did algebra in Grade 2. It just wasn't called algebra.


Grade One math looked like this..



The teacher told us to add the 2 numbers together and put the answer in the box.We did as we were told, because in Grade One, we generally did as we were told.


Grade Two, Day One math looked like this...

Pretty much the same as Grade One's work. 

The teacher told us to add the 2 numbers together and put the answer in the box.We did as we were told, because in Grade Two, we generally did as we were told. (How long would this last?)

Grade Two, Day Two math looked like this...

Everyone will say they wrote 3 in the top box and 1 in the bottom box. However, you probably wrote 7 in both boxes. Why? Because...  

The teacher told us to add the 2 numbers together and put the answer in the box.We did as we were told, because in Grade Two, we generally did as we were told. (How long would this last?) Our brains might have been telling us that our answers were illogical and wrong but we didn't want to go against the teacher. Over time we learned to put 3 and 1 in the boxes. So, if we could do that in Grade Two, then why can't we do...

The "y" and "x" are just boxes. 

If  2 + y = 5, then y = 3. 

If 3 + x = 4, then x = 1.

There - not so scary after all.

Scientific Notation

Scientific Notation - 

Looks difficult but is an easy mark on the GED exam.

See this link for an explanation.