GED Math: Percent and Ratio Word Problems

Hey, yo. Here’s a comment Jen sent over:

Hi Curtis,

I need some help with percent and ratio word problems. Unfortunately your previous explanations regarding word problems have been too complicated. Perhaps you could give more information on the basics, the formulas? I know I am not completely understanding these formulas. My knowledge in math is only the basic concepts, and I do not understand algebra yet.

While percents seem simple enough; I become lost when I try to solve word problems with them. I have been using the triangle method to work with percent problems. [The method shown in the GED book.]

1- Multiply when the problem gives you the whole and the percent.

2- Divide when the problem gives you the part and the percent.

3- Divide when the problem gives you the whole and the part.

However, I am still finding word problems with percents and ratios very confusing, so I know I am definitely not understanding the formula. Ratios especially – the whole idea of cross multiplying sounds good, but when I do this I become lost as I attempt to finish the problem. I hope you can help me begin to make sense of these areas.

Thanks, Jen

Hey, Jen. The problem with percent and ratio word problems is, you gotta really think through what information they give you an’ how it relates to the problem they want you to solve. What are you actually tryin’ to find? How can you get it? It’s knowing when to use the different rules and formula’s that’s confusin’.

Like the triangle rules you said you use:

1- Multiply when the problem gives you the whole and the percent.

2- Divide when the problem gives you the part and the percent.

3- Divide when the problem gives you the whole and the part.

To use ‘em, you gotta know what ‘percent’ ‘whole’ an’ ‘part’ they mean. Here’s an example.

40 of the students in a class of 200 got B’s on their test. 10 got A’s, 2 got F’s, and 20 got D’s. What percentage of students got C’s?

What’s the whole, part, and percent?

The whole is the whole class: 200.

The percent is the percent of students got C’s. That’s what you’re looking for.

The “part” is the number of students that got C’s.

See, a “percent” is the fraction (or ratio) of the part to the whole. That’s all… it’s just a fraction, with the top divided by the bottom. So, 1/2 = 50% (1 divided by 2 = .5 = 50%) and 3/4 = 75% (3 divided by 4 = .75 = 75%). The part divided by the whole = the percent.

Part ÷ Whole = Percent

So, in a sense, a percent is the same thing as a fraction. 1/8 of a pizza is the part (1 piece) over the whole (8 pieces make a whole pizza). That same slice of pizza is 12.5% of the pizza, because 1 divided by 8 = .125 (12.5%).

All three of the “rules” come from the equation: Part ÷ Whole = Percent, just written in different ways.

1- Multiply when the problem gives you the whole and the percent. (Part = Percent x Whole)

2- Divide when the problem gives you the part and the percent. (Whole = Part ÷ Percent)

3- Divide when the problem gives you the whole and the part. (Percent = Part ÷ Whole)

All these formulas say the same thing… it’s just moving the three pieces of the formula around. So really, all you need to do is figure out what the question’s askin’, and find the other two numbers to plug into the formula.

Back to the word problem. It’s asking for a percent:

Percent = Part ÷ Whole

The “whole” is the whole class, 200 students.

Percent = Part ÷ 200

The “part” is trickier, cuz the word problem is really in 2 parts. The “part” is the number of students that got c’s. So, you need to subtract all the other students who got other grades from 200.

200 – 40 – 10 – 2 – 20 = 128

That’s the number to plug into the formula:

Percent = 128 (number of students with C’s) ÷ 200 (number of students in the class)

128 ÷ 200 = .64 = 64%

64% of students got C’s.

Okay, let’s try a ratio. A ratio is also sort of like a fraction, but it’s not necessarily the ratio of “part” to “whole.” A fraction is a ratio of “part” to “whole,” but a ratio is a ratio of anything to anything. In a speed problem, it can be a ratio of “miles” to “hours.” It’s anything that has a regular relationship. Okay, let’s try a ratio problem, and we’ll try an’ walk thru cross-multiplying.

A man works 8 hours per day in a factory, and he makes $20 per hour. In a 5-day workweek, how much does the man make?

Now, you might figure this out without even using a ratio. But it is a ratio… any time you see “per,” you can use a ratio. You need to figure out what’s equivalent to what. We’ve got some ratios:

8 hours : 1 day

That’s the same as 8 hours per day.

20 dollars : 1 hour

That’s the same as $20 per hour.

Now, if I want to find out how many dollars per day, I need to figure out the ratio of dollars to 8 hours. A ratio like this (something per something else) gives two things that are equivalent. 8 hours = 1 day, so a ratio of dollars per 8 hours will give us dollars per day.

20 dollars : 1 hour

x dollars : 8 hours

Now, I’ve got two ratios, with the same units, and they’ll be equal to each other. That gives me an equation:

20/1 = x/8

Now’s the time to cross multiply. Basically, cross multiplication is some simple algebra. It’s just a shorthand way to remember how to solve this kind of problem. To move numbers from one side of the equation to the other, you do the opposite operation. If one side is divided by a number (like 1), you can move that number to the other side of the equation by multiplying both sides by 1.

(20/1) x 1 = (x/8) x 1

The two ones on the left cancel each other out, and on the right you end up with x times 1 (or just x) over 8:

20 = x/8

Now, do the same thing with the 8:

20 x 8 = (x/8) x 8

The two 8′s cancel each other out, and 20 x 8 = 160:

160 = x

He makes $160 in a day.

160 dollars : 1 day

Now, how much does he make in 5 days?

y dollars : 5 days

It’s the exact same sort of problem. You can make an equation:

160/1 = y/5

Using the shorthand version of the math we did before, this is the same as 160 x 5 = 1 x y (cross multiplying)

160 x 5 = 1 x y

800 = y

That’s the answer: he makes $800 in a five-day workweek.

So, what you need to find out from a ratio problem is what ratio equals what other ratio. Then, you can cross-multiply to solve.

Hope this helps! If a practice problem is giving you problems, send it to me an’ I’ll walk thru it.

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