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.

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.

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!

I’m not bad in math except when it comes to word problems any advice?

Hey, the GED’s real big on word problems, so you gotta get the hang of them. Why’d they gotta have word problems? Cuz they ain’t so much int’rested if you can figure out 3x + 4 = 12 as if you can figure out how much you’ll save each month if you buy generic soda instead of regular soda. See what I mean? One’s a plain math problem, the other’s a word problem. You’ve gotta first figure out what math you need to use it! See, my math teacher told me, math’s like a tool box. You got all these different math tools, and they help you do different things. You gotta know when to use what tool, to solve the problem you got in front of you. So, a math word problem is like a real-life problem that you might use math to solve. Okay, okay, whatcha really wanna know is, how to solve ‘em?

1) Read the Problem and Figure Out What It’s Asking

The first step is to figure out what the answer you’re lookin’ for is. How ’bout that question I asked before?

Greg buys 4 2-liter bottles of brand-name soda a week, at the price of $1.29 per bottle. One week each month, the soda goes on sale for $.79 per bottle. The store also has generic soda, which always costs $.99 per bottle. How much will Greg save in one year by buying the generic soda instead of brand-name soda?

There’s a word problem for ya’. So, read it through. What’s the main idea? What’s it asking? What is it you’re trying to find? In this place the answer is savings, in one year, of buying generic soda. It can help you out to rewrite what you’re trying to find in your own words:

Find the savings, in one year, of buying generic soda.

2) Look at What Information You’ve Got

Go through the problem and make notes of what information it gives you. This is what you’ve got to work with. I might go through the problem an’ pick out:

2-Liter Sodas Bought: 4 bottles a week
Costs: $1.29 each, $.79 once a month for 1 week
Generic Costs: $.99 each

Sometimes it helps to draw a picture or a chart. Anything that helps you get the info straight in your head.

3) Make a Plan

Now you gotta figure out what to do. How do you take the info it gives you, an’ get from there to the answer? This is where thinkin’ it through comes in. You need a plan. You got all the tools in your math toolbox: addition, subtraction, multiplication, division. Which ones make sense? What info do you need to use?

Well. Let’s look at it, one step at a time. We wanna know how much he’ll save in a year. So, how much does he spend in a year? Let’s start there. Then, we’ll figure out how much he’ll spend if he buys generic. Then, we want to know the difference of the two. That means, subtracting. So, that’s my plan:

1) Figure out how much Greg spends in a year.
2) Figure out how much Greg would spend buying generic.
3) Subtract to find out how much he’d save.

3) Do the Math!

Step 1: How much does he spend in a year? Greg buys 4 sodas a week. Most of the time, they’re $1.29 each. To figure out how much he spends most weeks, what do you do? Multiply, right? $1.29 times 4 sodas:

4 × 1.29 =5.16

Okay, that’s a regular week. What about when the soda’s on sale? That’s:

4 × .79 =3.16

Now, you need some more thinking. How many weeks in a year does he spend $3.16? Once a month, right? So that’s 12. For each of 12 weeks, he pays $3.16. Multiplication again:

3.16 × 12 =37.92

Now, that’s part of the year. The rest of the year, he pays 5.16. Now, to know how many weeks that is, you (1) need to know there’s 52 weeks in a year, and (2) need to subtract, because you want to know how many are left.

52 – 12 = 40

So, for 40 weeks, he spends $5.16:

40 × 5.16 =206.40

Great. Long road to get here. But what’s the total he spends in a year? When you want to know a total, you want to add…

206.40 + 37.92 = 244.32

Yikes! That’s a lot of dough. (Hey, most GED problems won’t have so many steps, but it’s good practice.)

Step 2: How much would he spend buying generic? This is easier, cuz it’s all one price. $.99 times 4 bottles times 52 weeks.

.99 × 4 × 52 = $205.92

Step 3: Subtract to find out how much he’d save:

$244.32 – 205.92 = $38.40

4) Does the Answer Make Sense?

Okay. Take a step back. Does what you did make sense? Does it seem like a reasonable answer to the question? The question is, how much will he save in a year if he buys generic soda, about .30 cents less (usually) than brand-name soda–but sometimes .20 cents more. So, on average, what’s he saving? .20 per soda? Maybe? 50 weeks, 4 sodas a week, so 200 sodas-ish a year, at 20 cents would be about 40 bucks.  The answer’s about 40 bucks. That sounds reasonable. I ain’t bein’ exact enough to estimate an answer, but I know my answer at least ain’t way off in the wild somewhere. I mean, if I got $384.00 by accident, I’d KNOW it was wrong.

The other advice I got is, practice! Here’s some places to get practice word problems. Hey, they won’t all be this complex. Start with the easier ones an’ work yo’ way up. An’ show me any of ‘em that give you problems. I’ll try walkin’ thru ‘em.

http://www.mathplayground.com/wordproblems.html

http://www.quia.com/pop/13193.html

http://www.quia.com/jq/19998.html

http://www.cdli.ca/CITE/math_problems.htm

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

Im about to take my math test,I am horrible in math.right now I am working on word probloms.How do I know if these word probloms are asking me to subtract,divide,multiply or add.please help.

Yeah! Tough, ain’t it? But the GED wants to know if you can do math on the fly, you know. That’s why they give you word problems. Like, you’re waitin’ in the line at the supermarket. Do you got enough money for what’s in your cart? How do you know? You’ve got to choose what math to do to figure it out… in this case, ADD together everything in your cart, and SUBTRACT from how much money you’ve got.

Try to think through the problem in concrete terms. Picture it. How do the diff’rent numbers relate to each other?

ADD if you need to find a total, figure out what more than one thing together is. For example, if you deposit $40, $160 and $30 in your bank, and you started out with $200, how much you got? You ADD because you’re trying to find out what it is all together.  $200 + $40 + $160 + $30 = $430. That’s more than I got!

SUBTRACT if you need to find the difference between two things or what you got left over, or how much bigger one thing is than another. For example, how much more will you save from buying the $150 TV instead of the $180 TV? Subtract, because you need to find out how much more one is than the other. $180 – $150 = $30 saved by buyin’ the cheaper TV.

MULTIPLY if you need to find out the total of something repeated over a number of years, over a number of miles. For example, if you’re going to drive 40 miles to the beach, and each mile costs $0.10 in gas, how much will the drive cost in gas? You need 10 cents for each mile… and that’s what MULTIPLICATION is for. All you gotta do is multiply 40 x $0.10 to get $4.00 in gas for the whole trip.

DIVIDE if you need to find out a part of something, or how something separates into even amount. So, if Karen paid $45 for 5 of the same scarf to give to people for Christmas, how much is one scarf? It’s 45 ÷ 5 = $9 for each scarf. DIVIDING divides a number into equal parts.

That’s the quick low-down. Here’s some resources for more info on word problems…

http://mathforum.org/dr.math/faq/faq.word.problems.html

http://academic.cuesta.edu/acasupp/as/706.htm

http://www.studygs.net/mathproblems.htm

And get some practice…

http://www.satmathpro.com/SMP_WordProblems.html

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

Satix is at a flea market. She wants to get the most knives at the lowest price. But she also wants to get at least one of each. The prices of the knives are: $ 4.30, $12.80, $11.50, $7.30, $ 7.50. If she has $50 to spend how much will her change be?

This is a tough word problem, so you gotta think it through. Hey, it’s great practice. Cuz if you can think through this, thinkin’ through some other word problems’ll be E-Z. This is what I call a number sense problem, cuz there ain’t no real advanced math, just makin’ sense of it, bein’ logical about it, and doin’ some basic math.

So, Satix wants one each of all the knives. You know she’s gonna buy one of each, so she’s going to buy at least:

$ 4.30 + $12.80 + $11.50 + $7.30 + $ 7.50 = $43.40

She’s spent $43.40, just on one of each knife. But she wants as many knives as possible. So, does she buy anything else? How much’s she got left?

$50.00 – $43.40 = $6.60

She’s got $6.60 left, so she can buy one more of the cheapest knives.

$6.60 – $4.30 = $2.30

That gives her $2.30 in change. Not enough to get another knife. So she be done. And you got the answer to the question…how much change she got left? $2.30. There ya go.

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

So, here’s somethin’ that happened. And I figure it makes a pretty good word problem, especially since it’s got to do with fractions. So, lemme explain somethin’ first. I don’t cook, generally. But my friend Liz, she cooks all the time. She says it’s better for you to eat at home, and cheaper, too, and I guess I can’t argue too much widdat. So, she says she gonna teach me how to cook, right? So, she’s showin’ me how to make pancakes.

Well, the recipe for pancakes says 1-1/2 cups flour, but I don’t got a lot of measuring cups and stuff in my kitchen, and after looking around, all I could come up with is a 1/3-cup measuring cup, which I don’t know how it got there, but there it was. So, here’s the question: how many 1/3 cups of flour do I need to put in to get 1-1/2 cups?

How’s that for a word problem?

Any ideas? How’d you set about it, d’y think?

Well, here’s how I did it. I know that 3 of the 1/3 measures will give me 1 cup. Then, I need 1/2 cup. Well, if three 1/3 cups give me a whole cup, then half of that will give me a half cup. Follow? That’s 1-1/2 of the 1/3 measures. So all together, three plus 1-1/2 is 4-1/2 of the 1/3 cup measures. So, I measure out 4 and eyeball a half of the 1/3 measure. That gives me 1-1/2 cups, but I got to get some measuring cups!! Did you figure it out?

Well, how about lookin’ at the math? What we’re really doin’ here is dividing…. how many times do 1/3 go into 1-1/2… how many 1/3rds are in 1-1/2 cups? So you could write it out:

1-1/2 ÷ 1/3 =

Now, first off, I’m going to change 1-1/2 to an improper fraction, so it’s all one fraction. 1-1/2 is the same as 3/2 (that’s 2/2 plus 1/2)… so we got:

3/2 ÷ 1/3 =

Now, to DIVIDE fractions, you gotta do a switcheroo. You turn over the second fraction, so 1/3 becomes 3/1, and you change division to multiplication…

3/2 × 3/1 =

Both those steps just make the problem easier. Now, to multiply two fractions, you multiply across the top (3 × 3 = 9) to get the top, and multiply across the bottom (2 × 1 = 2) to get the bottom:

3/2 × 3/1 = 9/2

How much is 9/2? 2 goes into 9 four times, with 1 left over:

3/2 × 3/1 = 9/2 = 4-1/2

Four and a half! Same as I got just by thinkin’ it through. How’s that for some math?

How’d you do? Be sure to send me any GED problems you havin’ trouble with!

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

Hey Curtis ,

Thanks for your prompt reply man . This is one of the problems I struggled with involving distance :

- A man started walking at 2 mph, while a woman 2 miles behind him began walking at the same time at a rate of 4 mph, and in the same direction. Just then, the man’s dog left him and ran toward the woman. Upon reaching her, it instantly turned around and ran back toward thr man. And so, the dog continued to run back and forth between them, at a constant rate of 5 mph, until the woman finally overtook the man. How far did the dog run?

**** Go enjoy figuring it out and let me know how to do it man !

Zaher

In the GED test, on the page with all the formulas, you got one for distance:

distance = rate x time

So, what’s it mean? Distance is how far you gonna go, rate is how fast you goin’, and time is, well, time. So, how far you go is how fast you go times how long you’re travelin’. In other words, if you get in your car and start drivin’ down the highway, the faster you go, and the longer time you drive, the farther you’ll get. Makes sense, right? If your speed (rate) goes up, the distance you travel goes up. If your time (how long you drive) goes up, the distance you travel goes up.

How does it get applied to the problem? This problem is tough, not because the math is tough, but because it’s tough to figure out how to use the math to solve it. You gotta take it one step at a time and figgure out what’s really goin on here.

Okay, we got a guy walkin’. Same idea as driving, how far = how fast x time. And, we got a woman walking, to. So that’s complicatin’ it up. We got to deal with 2 people walkin’ at once. And a dog, runnin’ back an fo’! Okay, problem with this problem is it’s hard to see. What’s the real question? How far’s the dog go? How do I figure that out?

Hey, this is harder than anythin’ on the GED. So, let’s stretch our minds. To get my mind around it, sketchin’ a picture sometimes helps. Scuse my bad drawin’.

So, the real point is, how far does the dog go? We want to know distance (how far), which is rate times time:

dog distance = rate x time

dog distance = 5 mph x time

Okay, to answer the question, we run into another question… how long does the dog run? He runs from the time they start walkin’ until the two people meet. Now, we gotta answer a second question to answer the first. How long does it take the woman to get to the guy?

We’re usin’ the same formula, an’ tryin’ to find the time it takes for the woman to catch up.

distance = rate x catchup time

The distance they start out is 2 miles:

2 miles = rate x catchup time

What’s the rate? The man is walking at 2 mph, and the woman is walking at 4 mph. She’s catching up to him, but how fast? For every 4 mph she walks, you’ve gotta subtract the 2 mph he’s walked in the same direction during that same time. So, she’s gaining 2 mph on him.

2 miles = (4 mph – 2 mph) x catchup time

2 miles = 2 mph x catchup time

Now, it’s just math. divide each side by 2, and you get:

1 hour = catchup time

How do you know the units are hours? It’s 1 hour, because we’re talkin’ miles and miles per hour. So, one question solved! Now we take the answer and go back to our original question:

dog distance = 5 mph x 1 hour

dog distance = 5 miles

Whew! Dat dog goin’ doggone fast!

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