Kiss those Math Headaches GOODBYE!

Posts tagged ‘Common Core’

Common Core Math Workshop Saturday in Santa Fe


Anyone out there feeling frustrated or confused about the new Common Core math?

I’m hosting a free workshop at 4:00 – 5:30 this Saturday, May 2, at the LaFarge Library in Santa Fe.

Please show up and bring any and all questions you have about Common Core math so that I can help you help your children.

New Math Frustration.

The focus is how to understand the basics of Common Core math so that you can help your child understand the concepts being taught in school.

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How to Convert Percents to Decimals — Flawlessly


My last post showed how you convert decimals to percents.

Now I’ll dare to do the obvious with a post on how to convert percents to decimals.

Since converting percents to decimals is the opposite of converting decimals to percents, it makes sense — does it not? — that we’d use the opposite procedure. And that is the case.

Coffee, Pi and More

Not only that, but we do the opposite procedure in the opposite order, too. How’s that for going totally opposite?

Since the final step in converting decimals to percents is tacking on a percent symbol (%), the very first step in converting percents to decimals is taking off that symbol.

And since the first step in converting decimals to percents is nudging the decimal point two places to the right, the last step in converting percents to decimals is pushing the decimal point two places to the left.

Let’s take a look at the process with this example.

Problem:  convert 73.2% to a decimal.

Step 1:  Take off the percent symbol. 73.2% changes to just 73.2

Step 2:  Move the decimal point two places to the left. 73.2 changes to .732 That’s all there is to it. This tells us that 73.2% is the same as .732, or 7 hundred thirty-two thousandths.

If you don’t recall the steps that you’re turning around, here’s a quick way to remember the process of converting percents to decimals. As I said in my last post, we can make use of alphabetical order, setting up the words for decimal and percent, in order, like this:

D-Decimal                              P-Percent

Then we draw an arrow showing that we’re converting from percent form to decimal form. The arrow shows the direction of the conversion: percent to decimal.

D-Decimal    <————–    P-Percent

This arrow points to the left, and that tells us that we move the decimal point to the left when we convert a percent to a decimal.

Let’s look at the process again, this time focusing now on how we use the arrow’s direction to help us.

Problem:  Convert  4.782% to a decimal.

Step 1:  Rip off the percent symbol. 4.782% changes to 4.782

Step 2:  Give the decimal point two shoves in the arrow’s direction. Since a percent to decimal conversion makes the arrow point left, we shove the decimal point two spaces to the left.  4.782 changes to .04782

This tells us that .04782 is the same as 4.782%

Note: if there are no digits showing to the left, we’re free to add 0s on the left side of the leftmost digit to create a place where the decimal point lands, after being shoved to the left.

In the last example, we had to tack a 0 on the left of 4.782 — making it 04.782, to get a digit (0) to the left of which we placed the final decimal point. Be confident that you can write as many 0 digits as you need to the left of a number’s leftmost digit. For example, it is just fine (though admittedly strange) to write 4.3 as 0004.3. You’d do this weird maneuver if you need that many zeros to the left of the 4. This occurs in converting numbers to scientific notation, for example.

So, now that you know the process, try your hand at converting the following percents to decimals: (Answers at the bottom of this post.)

a)  38%                                                                                                                           b)  19.3%                                                                                                                         c)   4.2%                                                                                                                         d)  175%                                                                                                                         e)  398.6%
f)  2,400%

Answers to the problems in the last post, converting decimals to percents:

a)  8590%                                                                                                                     b)  416.2%                                                                                                                     c)  20873.5%
d)  4.7%
e)  207,465%
f)  28.3%
g)  .569%

Answers to problems in this post:

a)  38%        =  .38
b)  19.3%     =  .193
c)   4.2%      =  .042
d)  175%      =  1.75
e)  398.6%   =  3.986
f)  2,400%    =  24.0, or just 24

How to Find the GCF for Three or More Numbers


To find the GCF for three or more numbers,  follow these steps:

1)  Determine which of the given numbers is smallest, then find the smallest difference between any pair of numbers.

2)  See what is smaller:  the smallest number, or the smallest difference. Whichever one  is smallest, that number is the GPGCF (Greatest Possible GCF). That means that this is the biggest number that the GCF could possibly be. Or, more formally we would say:  The GCF, if it exists, must be less than or equal to the GPGCF.

3)  Check if the GPGCF itself goes into all of the given numbers. If so, then it is the GCF. If not, list the factors of the GPGCF from  largest to the smallest and test them until you find the largest one that does divide evenly into the given numbers. The first factor (i.e., the largest factor) that divides evenly into the given numbers is, by definition, the GCF.

EXAMPLE:

Problem:  Find the GCF for 18, 30,  54.

1)  Note that the smallest number is 18, and  the smallest difference between the pairs is 12 [54 – 30 = 24;  54 – 18 = 36;  30 – 18 = 12] .

2)  Of those four quantities (the smallest number and the three differences), 12 is the least. This means that the
GPGCF = 12.

3) Check if 12 divides evenly into the three given numbers: 18, 30 and 54. In fact, 12 doesn’t divide evenly into ANY of these  numbers. Next we check the factors of 12, in order from largest to smallest. Those factors are: 6, 4, 3 and 2. The first of those that divides evenly into all three numbers is 6. [18 ÷ 6 = 3;  30 ÷ 6 = 5;  54 ÷ 6 = 9]. So the GCF = 6. And we are done.
MORE CHALLENGING PROBLEM:

Find the GCF for 24, 148, 200.

1)  Note that the smallest number is 24, and that the smallest difference between the pairs is 52 [200 – 148 = 52;  200 – 24 = 176;  148 – 24 = 124] .

2)  Of those four quantities (the smallest number and the three differences), 24 is the least. This means that for this problem, the GPGCF = 24.

3) Check if 24 divides evenly into the three given numbers: 24, 148 and 200. While 24 does divide evenly into 24, it does not divide evenly into 148 or 200. So next we check the factors of 24, in order from largest to smallest. Those factors are: 12, 8, 6, 4, 3 and 2. The first of those that divides evenly into the three given numbers is 4. [24 ÷ 4 = 6;  148 ÷ 4 = 37;  200 ÷ 4 = 50]. So the GCF = 4. And, once again, we are done.

The process may seem a bit long, but once you get used to it and start doing it in your mind, not on paper, you should find that it actually is quite fast. And you’ll find yourself figuring out the GCF for three or more numbers all in your mind — with no need for pencil and paper — while everyone around you will be making prime factor trees or using calculators. And surely that is a good feeling.

Josh Rappaport is the author of five books on math, including the Parents Choice-award winning Algebra Survival Guide. If you like how Josh explains these problems, you’ll certainly  like the Algebra Survival Guide and companion Workbook, both of which are available on Amazon.com  Just click the links in the sidebar for more information!