I am really having a hard time understanding translating word expressions into equations, and wondering if you can help?

Example:
1. the sum of 16 times a number and the number less another number times 3

2. a number less the sum of another number and 13

Workin’ these problems is almost like translating another language. You gotta know exactly what each word translates to a mathematical expression. Here’s a list of how they break down:

+ = “the sum of x and y (you’d put the + where the “and” goes here: x + y)

− = “less” or “minus” (note that if it says something like “a less b” then it’s a − b but if it says “a less than b” it’s b − a)

× = “times” or “the product of a and b” (a times b = a × b)

÷ = “divided by” (a divided by b = a ÷ b)

a,b,c or x,y,z = These are variables, so if it say “a number” that’s one of these variables. You usually wanna start with the first one in a list. Then if it says “another number” you pick the next one. If it said “a third number” you’d pick the last one. I don’t think it’d ever go above three numbers. (a number = a, another number = b, a third number = c)

Where it can get tricky is like when you start gettin’ a bunch of problems all mashed together. So like, take the first one that Trish posted.
“the sum of 16 times a number and the number less another number times 3″

You wanna write this stuff down on paper:

So, I put red parenthesis around the different parts of the problem. Is says the sum of “this” and “this” so you want to make sure to separate the two. Then you can translate things directly:

(16 × a) + (a − b × 3)

Then you can simplify it down:

16a + (a − 3b)

16a + a − 3b

17a − 3b

In this problem, the parenthesis didn’t really do anything. But it’s important to keep things separated in case it does matter. You wanna get into the habit of looking for the way problems are broken apart. Like, if it said “the product of “…” and “…” then the parenthesis would be crucial ’cause you gotta make sure to do any addition inside the parenthesis before you do the multiplication. If you check out the next problem, parenthesis play a bigger part.

So, we got “A number less the sum of another number and 13.” Translating it directly, we get a − b + 13. But since it says “less the SUM” you gotta use the parenthesis to separate the first part, “a number” and the second part, “the sum of another number and 13.” So it gotta look like this:

a − (b + 13)

Now when we simplify it, we distribute the negative:

a − b − 13

As a side note, make sure to read the directions of a problem carefully. If they just want you to write the equation out as a mathematical expression, the answer’d be a − (b + 13). If they want you to simplify, it’d be a − b − 13. If they want you to solve for a number, like a, then the answer would be a = 13 + b. A lot of the time, simply missin’ things like that in the question can make a problem wrong, even though you actually knew what you was doin’.

Good luck, all.

For more information about the GED test and GED test preparation, visit the GED Academy at http://www.passGED.com.

I been hearing about this thing lately called dyscalculia. I ain’t never heard of that before, but I have heard ’bout dyslexia. So, I figured the two were linked. I looked it up, and it turns out they are. Discalculia’s kinda like dyslexia with numbers. Only it’s more than that. It effects people’s sense of time and space and all that. Check out this list of symptoms.

Anyway, it kinda helped me understand people a little better. Like, when I add up numbers, I just get it, you know? But if I think about it like dyslexia, that’s somethin’ I can understand. Sometimes I just don’t get words. It’s like they all a jumble, and I gotta slow down and really pay attention. But there’s people out there who can just scan a page real quick and tell you everything that be on it. Maybe those same people can’t get numbers like I can, right?

So, maybe some people got discalculia without knowing it. It’s not well known, like dyslexia. Maybe someone famous gotta have it first before the public notices it. For now, there’s a cool site called Dyscalculia Forum that’s got a lot of info and other people who’ve got dyscalculia. They help each other out and offer up solutions they’ve found that helps them remember numbers.

Mostly, it seems like if someone’s got problems in one area, they probably are pretty good at somethin’ else. So, if you’re having problems with numbers, you gotta think about somethin’ else you’re good at, like words, art, or music. For instance, there’s ten numbers total, right? Maybe you can assign a color to each number. Like this:

0123456789

So, 0 is black ’cause it’s nothin’ so it’s not a color too, right? Then I started with pink, red, orange, yellow, green, teal, blue, purple, violet. Someone who’s real artistic might be able to remember the order of colors easier than the order of numbers. And maybe they can remember mental multiplication easier with colors. So instead of 7×8=56, they might think, blue x purple = green-teal.

I don’t think in colors myself, and that’s a pretty wild example, but it shows how you might get started thinkin’ about different ways to understand numbers. Here’s some other ways to think about numbers differently:

• Read problems aloud and talk through the answers (sometimes hearing yourself problem solve is helpful).
• When learning a new concept, make sure you understand it well enough to teach it back before moving on.
• Try to visualize the Math problem. If the problem is about a house, draw the house, then add in the dimensions as the problem goes along.
• Practice estimating as a way to solve problems.
• Don’t be afraid to count on your fingers.
• Use scratch paper! You may remember things better by writing them down and working through the problem on paper and not in your head.
• Try using colored pencils for emphasis or to differentiate problems.
• Memorize Math facts to music or a beat (Mary had a little lamb, etc.).
• If you are doing a “non story problem” type of Math problem, make up a story for it. If you can relate the problem to real life, it may be easier to solve.

When it comes down to it, though, everyone’s different, so you gotta figure out a method that works for you. Check out these 8 different types of intelligences that Dr. Howard Gardner discovered. Maybe you can figure out which one fits with you and come up with your own strategy for understanding Math better.

1. Linguistic and verbal intelligence: good with words
2. Logical intelligence: good with math and logic
3. Spatial intelligence: good with pictures
4. Body/movement intelligence: good with activities
5. Musical intelligence: good with rhythm
6. Interpersonal intelligence: good with communication
7. Intrapersonal intelligence: good with analyzing things
8. Naturalist intelligence: good with understanding natural world

For more information about the GED test and GED test preparation, visit the GED Academy at  http://www.passGED.com.

A 12lb turkey at the grocery store costs $13.50 and feeds 8 people. A pint of potato salad costs $3.50 per pint, and one pint can feeds about 3 people. A large can of yams is on sale for $4, and that feeds 5 people. Finally, a pumpkin pie feeds about 6 people and costs $4.99. Paula is shopping for Thanksgiving and is planning on having 16 guests, including herself. How much will it cost to make sure there is enough of each item for everyone?

This is the kinda question that shows how Math can be practical for everyday use, right? I’ve never bought thanksgiving dinner myself, but sometimes you get some friends comin’ over for some pizza and beers, and you gotta know how much to buy for everyone (and how much you charge them at the door).

So first thing I gotta do here is write out all the information, to make sure I get what they’re askin’.

Paula’s got 16 people comin’ for dinner. First I gotta break down the problem and see how many people each type of food feeds. I’ll make a quick list.

12lb Turkey – $13.50 – Feeds 8

Potato Salad – $3.50 – Feeds 3

Yams – $4.00 – Feeds 5

Pumpkin – $4.99 – Feeds 6

Once I got all this information laid out, it’s pretty simple to figure things out:

The turkey feeds 8, and we know that 8 × 2 is 16, so that’s easy. She needs 2 turkeys. That’s $27.

A pint of potato salad feeds 3, so she’d need 6 pints to feed 16 since 3 × 6 = 18. 3 × 5 is only 15, and that wouldn’t be enough salad for everyone. So then I gotta times 6 × 3.50 to get $21

She’d need 4 cans of yams, so that’s $16, and 3 pumpkin pies. That’s $14.97. Usually I’d just round the pie up to $5, which makes it an easy $15, but since we gotta have the exact answer here, I can’t do that. So adding up all those answers, I got $78.97. Damn, that’s expensive. And it ain’t even including no drinks. See, that’s why I never have no Thanksgiving at my place. Gotta clean it all up too, no way. I just go out to a buffet and pay like ten bucks for all I can eat. That’s how you do it, yo.

Have a good Thanksgiving y’all.

For more information about the GED test and GED test preparation, visit the GED Academy at http://www.passGED.com

Super Subs Inc. is planning on hiring new employees for the summer. They want to make sure their new employees are available to work on the busiest day of the week. Below is a chart of their four different stores, and how many sub sandwiches they sold at each store the previous week. According to this chart, which day will the new hires most likely need to work?

1. Wednesday

2. Thursday

3. Friday

4. Saturday

5. Sunday

Super Subs Inc. may need to shut down a store due to the bad economy. According to the chart, which store would they most likely shut down?

1. Store A

2. Store B

3. Store C

4. Store D

5. None of the Stores

For more information about the GED test and GED test preparation, visit the GED Academy at http://www.passGED.com

What Percent OF the Original amount IS the Difference between the two amounts?

P × O = D

Percent decrease is pretty much the same thing. What percent of the original amount is the difference between the two amounts? Only difference in figuring it out is that the second amount is lower than the first, not higer. No sweat. The percent times the original amount still equals the difference. It’s just a decrease, not an increase. Get it?

Let’s look at it. Here’s a practice problem.

I filled up my car, so it had 15 gallons of gas in the tank. So, I drove out to my uncle’s house and back, and it took $18 in gas at $2 per gallon to fill up the tank. What was the percentage decrease in gas during the trip?

Did I get you with a tough one? More than jus’ one step here. Try to figure it out, then I’ll walk you through it…

Okay, here’s the deal. You need to do some steps to get the info you need to solve the problem… so what info do you need? Well, here’ s the formula we said….

P × O = D

Percent decrease (P) is what you’re tryin’ to find. Original value, you know that, it was 15 gallons, like the problem said.

P × 15 = D

But what’s the difference between the old amount of gas an’ the new one? Well, you gotta figure it out. It’s the amount of gas that got used, right? The info you have is that it took $18 at $2 per gallon to fill up the tank. How much gas can you get at $2 a gallon for 18 bucks? You know that, right? Divide 18 by 2, an’ you got 9 gallons. It took 9 gallons to fill up the tank, so the gas left at the end of the trip was 6 gallons. The difference between the 15 gallons started with an’ the 6 gallons ended with is 9 gallons. Get it?

P × 15 = 9

So, the percentage decrease is 9 divided by 15, or .6

P = 9 ÷ 15 = .6

Now, you gotta turn .6 into a percentage, an’ you jus’ move the decimal point over two to the right. So’s it’s 60%.

P = 9 ÷ 15 = .6 = 60%

The guy used 60% of his gas on the trip.

Knowin’ what a percent increase or decrease problem is askin’ is the big thing, and bein’ able to think through word problems. Let me know if you got any GED math that’s givin’ you a problem, an’ I’ll help you out.

For more information about the GED test and GED test preparation, visit the GED Academy at http://www.passGED.com.

I got a new hard drive, to back up my computer. The old hard drive I was usin’ was 250 GB. Now, the new one’s 640 GB. Sweet! So, what’s the percent increase in hard drive space from the old hard drive to the new one?

Give it a minute, try to work it out. What’dya think?

Here’s how I’d work through this one. First, you got to know what they mean when they say “what’s the percent increase?” It means, what PERCENT of the ORIGINAL AMOUNT is the DIFFERENCE BETWEEN (increase between) the two amounts. That’s puttin’ it in some context, right? First off, you got 3 important numbers. (1) PERCENT (P) = what you’re trying to find. (2) ORIGINAL (O) AMOUNT. (3) DIFFERENCE (D) BETWEEN old and new amounts.

Now, in math, “of” usually means “times.” And “is” usually means “equals.” So, I could put it like this.

P × O = D

What Percent OF the Original amount IS the Difference between the two amounts?

Well, you know the original amount. Dat’s my original hard drive size, 250 GB.

P × 250 = D

And to find the “difference” between two things, you gotta subtract. So the difference is the two amounts subtracted: 640 − 250 = 390

P × 250 = 390

To find P, the percent, you got to get P all by itself. So, to get rid of the “times 250,” you divide both sides by 250…

P × 250 ÷ 250 = 390 ÷ 250

P × 1 = 390 ÷ 250

P = 390 ÷ 250

P = 1.56

Now, P’s supposed to be a percent. To change a number to a percent, move the decimal place two to the right… the answer is:

156%

Let’s check it out… 100% bigger would mean it’s 250 GB bigger… one whole hard drive bigger. And it’s more than that. It’s more like 1-1/2 times bigger… that’s 150%. So the answer makes sense, right? Now, can you do the same thing with a percent decrease problem? What if it asked what the percent decrease was from 640 GB to 250 GB? Think about it, I’ll have a percent decrease problem in my next post….

Get that GED quick… you can do it!

For more information about the GED test and GED test preparation, visit The GED Academy at http://www.passGED.com.

Plus, remember ’bout Stephen Wolfram? Yup, mathematics guy, wrote some software to do advanced math real quick. Well, he’s starting a new online website, and here’s what it does… You type in your question, and it’s got a big encyclopedia of a bunch of info, right? So it figures out your question… and sends you the answer. Don’t think that math ain’t at the bottom of it. The website’s up later this month… called Wolfram Alpha. so check it out, the next cool thing, brought to y’all by MATH.

Math ain’t too hard. Jus’ take it step by step, once you get the basics down, you get there. How ’bout a practice question to get the juices goin’? Here it is…

Annie is an interior designer, and she’s got a budget of $345 to buy fabric for drapes. She needs 12 yards of fabric. The fabric that she really wants, Fabric A, costs $29 per yard. Her second choice, Fabric B, costs $27.50 per yard, and her third choice, Fabric C, costs $26 per yard. She wants to buy her top choice that she can afford and stay in budget. Which fabric should she buy?

1) Fabric A

2) Fabric B

3) Fabric C

4) All the fabrics are too expensive.

So… what’d'ya get? And how’d ya go about it? Here’s what I figure… I could multiply the cost of each fabric by 12 yards to find out how much each would cost, but that seems like too much work to me. So I wanna take the shortest short-cut I got. Here’s what I did… take the total budget, $345, and divide it by 12 yards of fabric. That gonna give me the budget PER YARD, then I can jus’ compare that with all the prices.  $345 divided by 12 is $28.75, so I got my max price per yard. Now, I can’t afford the $29 fabric, jus barely. Don’t know bout you, but I’d be all smooth-talkin’ the fabric store owner to try to get a discount. But dat ain’ t part of the question. So the answer’s 2, Answer B, the $27.50 fabric.

And, you notice, this GED question’s all ’bout a real-life job that’d really use this kinda math. So, keep it in mind… math’s real good for your future!

Algebra’s like a puzzle. Know those puzzles where you gotta move the pieces around to make a picture? It’s like that. To find what number “x” is, you gotta move the numbers around, so that “x” is by itself on one side. And there’s rules. Here’s the key: you have to do the same thing to both sides of the equation.

So, if x + 3 = 5 and you want x by itself, you’ve got to “zero out” the + 3. To make the + 3 cancel out, you’ve got to subtract 3. That means you’ll have 3 – 3 on the side with the x, and 3 – 3 is 0, and 0 is nothing. That’s what you want… nothing with the x.

But, if you want to subtract 3 from the left side, you gotta subtract 3 from the right, too, to keep ‘em equal.

x + 3 = 5
x + 3 – 3 = 5 – 3
x + 0 = 2
x = 2

Okay, that’s the easy part. Hard part is, if you got x’s on both sides.

2x = x + 5

What do I want to do? Subtract x from both sides, to get rid of the x on the right (x – x is the same as 3 – 3 or 23 – 23…. it’s zero).

2x = x + 5
2x – x = x – x + 5
2x – x = 0 + 5
2x – x = 5

Now, what’s 2x – x? The shorthand rule is, you subtract (or add) the numbers by the x’s, and leave the x alone. “x” without a number has an invisible “1″ next to it. So:
5x – 3x = 2x
22x + 5x = 7x
x + x = 2x
5x – x = 4x

That means, if 2x – x = 5, then x = 5.

Here’s why. 5x means 5 times x. And 5 times x means x + x + x + x + x. That’s what multiplication is, a shorthand way to add a number plus itself a bunch of time.
5 × 9 = 9 + 9 + 9 + 9 + 9
5x = x + x + x + x + x

So, 2x – x means x + x – x. Two of the x’s cancel out (x – x = 0). So, it’s x + 0, or just plain x.

2 x’s minus 1 x is… 1 x. Just like if you got 2 apples and take away 1 apple, you got one apple left.

So, here’s a problem:

5x + 14 = 3x + 22

I can subtract 14 from both sides to move all the numbers to the right…
5x = 3x + 8

Now, I can subtract 3x from both sides to move all the x’s to the left…
2x = 8

The last step, since x is multiplied by 2, is divide both sides by 2 to get the x by itself….

x = 4

There ya go!

Two cyclists start biking from a trail’s start 3 hours apart. The second cyclist travels at 10 miles per hur ans start 3 hours after the first cyclist who is traveing at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking

Okay. bicyclists. start 3 hours apart. You want to know when they meet, so you want to know when the distance is the same.

distance = rate × time

So, bicyclist 1, let’s call him “A” … “A” = 6 mph × time
An’ bicyclist 2, let’s call him “B” … “B” = 10 mph × (time – 3)

The minus 3 is cuz he’s travelin’ 3 hours less than the other one. Now, because “A” = “B” (they’ve gone the same distance when they meet), you’ve got an equation your can solve:

6 × time = 10 × (time – 3) …
that’s the same as: 6t = 10(t – 3)

Now, it’s jus’ algebra, right? you multiply the 10 by both the “t” and the 3…

6t = 10t – 30

Now, subtract 10t from both sides to get the “t”s all together… remember, cuz it’s minus 30, your 30’s gonna be negative:

6t – 10t = -30
-4t = -30

Now, divide by -4 to get t all by itself… a negative divided by a negative is a positive, which is good, otherwise they’d be time travelin’ into the past! Keep it real, man!

t = -30/-4 = 7.5 hours

Now, in what I wrote, “t” is the time of the first cyclist. t – 3, or 4.5 hours is the time from when the second cyclist starts to when he catches up. I ain’t too sure, the way the question’s worded, which time it wants. Read the original again an’ see if you can figure it out… is it from when the first guy starts or from when the second guy starts?

Now, the time seems pretty reasonable, but…. let’s check. First cyclist goes for 7.5 hours at 6 mph, that’s 45 miles. Second cyclist goes for 4.5 hours at 10 mph, that’s 45 miles, too. There’s your answer. It’s 7.5 hours from when the first guy started, and 4.5 hours from when the second guy started. There ya go.

For more information about the GED test and GED test preparation, visit the GED Academy at http://www.passGED.com.

See, it’s a scientific calculator with all kindsa cool functions that you don’t need on the test. It’s important to know how to use it so you don’t hit the wrong order of buttons and get the wrong answer. And the better you gonna get with the calculator, the faster you can do the math.

Hey, these things only cost bout 10 or 15 bucks. So, go get yo’self one, first off, to practice at home. Here’s a link to buy it on Amazon: Casio fx-260 Solar Calculator

Case ya don’t got one, here’s what it looks like:

So, here’s the most important stuff:

Press “on” to turn it on. Yeah, I know, basic, right? It’ll say “DEG” in the top of the screen. Don’t worry what it means, if it says “DEG,” you’re in the right mode to do regular math. But if it says somethin’ else, press “mode” and “4″ to get it to say “DEG”. Now you set!

Jus’ always press “ON” or “AC” to start a new problem, so you know your memory’s clear. Havin’ the last number from the last problem in memory’s gonna mess you up.

To do basic math, jus’ put in the math problem like it’s written “5 + 8 × 16″ or “29 × (4 + 200)”, or whatever, and press the equal key at the end to get the answer.  Remember: you got to press the equal key to get the answer!!!

It knows the order of operations, that is, like, what to do first in the problem. So, it’ll do (1) things in parenthesis, then (2) multiplication an’ division, then (3) addition and subtraction. So, if you’re fixin’ up 9your own equation to punch in, remember–that’s the order it’s done in. You type in parenthesis along with all the rest of your problem. Them’s the [(--- and ---)] keys, for the open and close parenthesis.

Now for the things that are different than just typin’ in the problem:

To get a square root, type in whatever you want the square root of, then “shift” (top left) then the key with x² on it, then equal to get the answer. To get a number squared, just type in the number and then press the x²key and equal.

To make a number negative, press the “+/-” key AFTER the number. So, to type in -9, type “9″ “+/-”

That’s the basics! Now, here’s some links to learn more:

http://www.ilc.org/cfmx/GED/GED_sample_m2.cfm?Menu_ID_Sel=35200&Lang_Sel=1
http://www.ket.org/GED2002/Mathcalc/Mathcalc1.htm

For more information on the GED test and GED test preparation visit the GED Academy at http://www.passGED.com.