Multiplication Tables in 2 Minutes

You aren't allowed  to take multiplication tables into a GED exam. But what if there was a strategy that would allow you to write them out once the exam had started? In under 2 minutes, no less. Use the multiplication tables then for multiplying, dividing, putting fractions in lowest terms, finding roots and finding square numbers. In under 2 minutes? Impossible you say. See here for the strategy.

Type 5

% Solved!

Type #5

4)    Increasing or decreasing a number by a given %

I have:  1 number

 I have: A given % increase or decrease

I need to find: The new value, after the % change has been applied.

Example:    a) What is $640.00 decreased by 10%?

                   b) What is $200.00 increased by 20%?

Key to Solving:

These questions are not much different from a type 2 question. You just need to think of the % as a new value.

a)     What is $640.00 decreased by 10%?

Step 1 – a 10% decrease is equal to 90% of the original value

Step 2 –       90    X  640.00 = $576.00  

                   100

b)    What is $200.00 increased by 20%?

Step 1 – a 20% increase is equal to 120% of the original value

Step 2 –       120    X  200.00 = $240.00  

                   100

Tricks to look out for.

Watch out for fractional percents like 3  1 %

                                                                  2

a) What is $360.00 increased by 3  1 %  ?

                                                                  2

Step 1 – a 3  1 %  increase is equal to 103.5% of the original value

                     2

Step 2 –       103.5   X  $360.00 = $372.60  

                   100

b)      What is 12 increased by 1 %  ?

    4

Note – a  1 %  increase is equal to 100.25% of the original value. It is a

                4    

                       quarter of a percent, not a quarter.

ý  Wrong! 125   X  $12 = $15.00   

                   100

þ Right!   100.25   X  $12 = $12.03  

% Type 4 - Percent Change

% Solved!

Type #4

The percent change. D’oh!

This is the “donuts rose from 75¢ each to 90¢ each” type of question. You will be asked to find out what percent the price rose. This is a fairly common percentage question and one that is often used to explain how much prices or salaries have risen or fallen.

I have:                         1 number

I have:                         A 2^nd number

I need to find:            The percentage value for the difference between the 2 numbers.

Example:              a) Donuts rose from 75¢ each to 90¢ each. What  percentage did the price rise?

Key to Solving:

The price of doughnuts went up! D'oh!    D’O   Homer Simpson saves the day! The key to solving these questions is Difference ÷ The Original

Step 1 – Calculate the Difference.      90¢ - 75¢ = 15¢.

Step 2 – Divide 15¢ by the Original price, which is 75¢. Note – the 90¢ does not appear in the calculation below. It only played a part in calculating the difference.

Step 3 –       15¢    X  100% = 20%  

                   75¢.

Donuts rose by 20%. (Was it the extra baking powder?)

 Tricks to look out for.

 Remember to concentrate on which value is the Original price. It is not necessarily the smaller of the 2 prices.

a) A price decreased from $50.00 to $40.00. What is the percentage of change?

ý Wrong! 10  X  100%  = 25%

                   40               

þ Right!   10   X  100% = 20%. The price decreased by 20%

       50 

The original price was $50.00

Percent Type 3

% Solved!

Type #3

This is the “$700.00 is 20% of what number” type of question. This is a more uncommon percent question and not one that is used a lot.

I have: 1 number

I have: A percent value

I need to find: “A 2^nd number, which the 1st number is a given percent of.”

Example: a) $700.00 is 20% of what number?

Key to Solving:

Make a 4 element relation box. Percentages stick together, so always divide the percent value by 100. For the question above:

Step 1 – change the 20% to 20

100

Step 2 – We know that the $700.00 and the 20 are related, so they go across from each other. The “x” is the value we are looking for.

20 =  $700.00

100  X

Step 3 – Multiply UP and ACROSS from the bottom left number, then divide by the top left number.

100 X $700.00 ÷ 20 = $3500.00

$700.00 is 20% of $3500.00

Tricks to look out for.

$700.00 is 20% of what number?

a) Read the question carefully. Do not work out 20% of $700.00.

 Wrong! 20 ÷ 100 x $700.00 = $140.00 $700.00 is 20% of $140.00

 Right! 20 =  $700.00

100  X

100 X $700.00 ÷ 20 = $3500.00

$700.00 is 20% of $3500.00

% Type 2

% Solved!

Type #2

The good old “What is 32% of 60” type of question. This is a common percent question and one that we use regularly.

I have:   A  percent value

I have:    1 number

     I need to find:   A 2^nd number, which is a certain percent of the 1st number.

Examples:             a) What is 75% of 640?

b) Prices rose by 25% last year. If a TV cost $600.00 last year, what does it cost this year? (What is 25% of $600.00 added to the price?)

c) She got a 15% discount on the books. If the books cost $400.00 originally, what is the discounted price? (What is 15% of $400.00 subtracted from the price?)

Key to Solving:

All three questions above are “percentage of” questions. For question 1 above:

Step 1 – change the 75% to 75

                                             100

Step 2 – Cross out the word “of” with an “X”. This becomes your multiplication sign.  

75   X

100

Step 3 – Divide 75 by 100, then multiply by 640.

75   X  640 = 480

100

Tricks to look out for.

a) Prices rose by 25% last year. If a TV cost $600.00 last year, what does that TV cost this year?

ý  Wrong! 25 ÷ 100 x $600.00 = $150.00       The TV costs 150 dollars.

þ Right!   25 ÷ 100 x $600.00  = $150.00      $600.00  PLUS  $150.00 = $750.00.

You need to add the 25% value (in this case, $150.00) because the price ROSE or went up.

b) She got a 15% discount on the books. If the books cost $400.00 originally, what is the discounted price?

ý Wrong!  15 ÷ 100 x $400.00 = $60.00   The books cost $60.00.

þ Right!   15 ÷ 100 x $400.00 = $60.00      $400.00 MINUS $60.00 = $340.00   The books cost $340.00. You need to subtract the 15% value (in this case $60.00) because the prices were discounted.

% Solved Type 1

% Solved!

Type #1

·        “rate”

·        “test score”

·        “one number as a percent of another number”.

These questions compare 2 given numbers and you are looking for the percent. ( x 100 )

I have:                  1 number.

     I have:                  A  2^nd  number.

  I need to find:            “The percent that one number "is" of the other number.”

Examples:            a)   24 out of every 60 people drive to work. What percent is this?

               

b)   He got 52 out of 67 on his test. What percent is this?

    

c)   What percentage is 42 out of 68?

Key to Solving:

Step 1: Divide one number by the other number.

Note: The word “of” is the key here. The number associated with the word “of” is what you are “dividing by”.

Step 2: Multiply this answer by 100.

Answers

a)   24 ÷ 60 x 100 = 40%

b)   52 ÷ 67 x 100 = 77.6%

c)   42 ÷ 68 x 100 =  61.8%

 Tricks to look out for.

a) What percentage is 68 out of 42?  

ý  Wrong! 42 ÷ 68 x 100 = 61.8%

þ Right!   68 ÷ 42 x 100 = 161.9%.   

·        Don’t assume you divide the smaller number by the larger number! 68 is larger than 42, so your answer must be more than 100%.

·        The word “of” is associated with 42, so you need to divide by 42, not 68.

b) A vet treats 32 dogs and 25 cats. What percentage of animals treated were cats?

ý Wrong!  25 ÷ 32 x 100 = 78%

þ Right!   25 ÷ 57 x 100 =  43.9%    

Where did the 57 come from?

There are 57 animals in total (“of animals”). Thinking about it, 25 cats is slightly less than 32 dogs, so nearly a 50/50 percent split. 43.9% represents lightly less than half the total, which makes sense. 78% does not make sense in this case.

% Solved!

Some GED students find percent calculations difficult because there are many different types of percent questions. For example...

1)   What is 25 out of 62 expressed as a percent?
2)   What is 25% of 62
3)   62 is 25% of what number?
4)   The price increased from $25.00 to $62.00. Calculate the percent change.
5)   The new price is $62.00, which represents a 25% decrease from the old price. What was the old price.

The part/whole = percent/100 method is usually employed as a teaching tool, which can be confusing for some students. In the next few blog postings, I will be examining ways to "decode" the question using key words and content found in the questions themselves.

Multiplication Tables

You cannot take your multiplication tables into the GED exam with you. But what if you could write them out on a spare piece of paper in under 2 minutes. See the Math Doctor on Youtube for the solution. He has the prescription.