Math problem- how do I figure this out?

Mon, May 20 2019, 10:02 pm

SisterSix wrote:

This is by far the easiest and most intuitive way to find the answer. I have no idea why it got a hug.

Although my answer would have been that half of 2% is 1%, so just divide 200 in half (result is 100) and add two zeroes

It's an elegant solution, but the OP said she didn't understand it. Not everyone has an intuitive understanding of math. That's why I chose a step-by-step method. I hope it helped.

studying_torah

Mon, May 20 2019, 10:06 pm

I did not understand all of the ways to solve, but I did get some so thank you!
I tried to solve for x previously but got confused & Google kept giving me 2% of 200 which is why I posted.
I appreciate those who took the time to break it down step by step!
😊

amother

Rose

Mon, May 20 2019, 10:22 pm

Math teacher here. Love all the different approaches. Math is so lovely. Smile

If I were to choose one way to explain this as clearly as possible to a non-math person, I would say:

The percent sign means "per cent," in other words, "out of 100." This can be written as a fraction: a number over 100. So.....

2% means 2/100. That can be simplified by dividing the top and bottom numbers by 2. So 2% is 1/50.

So...... we are told that 200 is 1/50 of some number. That number is going to be a lot bigger than 200, so if you get a nice big number, that's logical!

I might then give an example with an easy fraction or two to show the principle I'm about to use:

Let's say 200 was half of some number. Then what would that bigger number be? Right, 400. What would you multiply by to get that number? Ah, 2. Great. What if 200 was 1/3 of some number, then how would you figure out the number? Right, multiply by 3.

So.....

If 200 is 1/50 of some number, we need to multiply by 50.

200 x 50 = 10,000

(Then if the person still did not understand, I would back up and figure out at what point they stopped understanding, if they didn't already tell me they had lost me. Smile

And then I'd be ready with ten other ways to explain it!!)

amother

Rose

Mon, May 20 2019, 10:32 pm

For someone who is comfortable with basic math but isn't sure how to set things up to figure out a percentage problem, I would use the word-for-word translation method someone showed above - to turn an English sentence into an equation.

200 is 2% of what number?

Translates to:

200 = 2/100 * x

Then continue by solving the equation.

This method is great because it prevents mistakes even for people who are good with math.

Mommyg8

Mon, May 20 2019, 11:32 pm

amother [ Rose ] wrote:

I posted something similar but didn't take the time to write it out. This method is from my amazing math high school teacher, I really want to write her name but not sure if she would appreciate it Wink

.

She taught us how to translate the English sentence into Math-ese.

200

IS - =

2% - .02

OF - TIMES *

What number? - X or the unknown.

Then you solve the algebraic equation by dividing both sides by .02.

You end up with - 200 divided by .02 on one side,

.02 * X divided by .02 on the other side, which turns into 1 * X, and of course 1 X anything is that number.

So - 200 divided by .02 = 10,000 and the other side is X.

10,000 is X or the unknown, the quantity you were solving for.

It's easier on a blackboard Wink

amother

Tangerine

Mon, May 20 2019, 11:47 pm

Mommyg8 wrote:

I learned it the same way, but for some reason, it totally didn't work for 99% of my class.

Last edited by amother on Mon, Jul 08 2019, 11:57 am; edited 1 time in total

Mommyg8

Mon, May 20 2019, 11:50 pm

smileforamile wrote:

I learned it the same way, but for some reason, it totally didn't work for 99% of my class.

My math teacher got our class to do very, very well on the Regents. Maybe I'm just not explaining it well. Ok, I'm not a math teacher.

amother

Rose

Tue, May 21 2019, 1:03 am

studying_torah wrote:

Ok so sorry for being dumb but how is 200 divided by .02 equal to 10,000? Doesn't divide mean break up into smaller amounts/groups?
So how does breaking 200 turn into 10, 000?
What am I missing?

Dividing by a number greater than 1 does end up with a smaller number. But dividing by a number less than 1 (which can be expressed as a fraction, a decimal, or a percentage) ends up with a number that is bigger than the one you started with!

It helps if you think of division as asking the question: "How many times does ____ go into ____?"

So for example, when you see 8÷4, you would ask, "How many times does 4 go into 8?" The answer is 2, which is smaller than 8, as you would expect.

And when you see 6 divided by 1/2, you would ask, "How many times does 1/2 go into 6?" Or you could say, "How many 1/2s are there in 6 wholes?" Try drawing six circles, then make a line through each one to cut them in half, and count the halves. There are 12 halves. A shortcut to get that answer, once you have visualized it with a picture, is to multiply 6 by 2 (the bottom number of the fraction).

So when you have 200 divided by .02, which is 1/50, you're asking "How many times does 1/50 go into 200?" And there are going to be a lot of those little 1/50 slices. There are 50 of them in every whole. (Imagine a circle sliced into 50 little slices.) So there are 50 x 200 of them in 200 wholes, which is 10,000 little slices. Smile

groisamomma

Tue, May 21 2019, 2:25 pm

I love this thread (can you tell I teach math?).

You can totally tell which person is using intuitive math skills and which are following the step-by-step instructions they learned in their days (back in the olden days when we took Regents I used to do the same thing! Algebraic equation, set up a proportion, of=times, etc.).

Carry on, ladies. I think I'll show this thread to my class the next time I teach percents.

amother

Tangerine

Tue, May 21 2019, 2:33 pm

Mommyg8 wrote:

My math teacher got our class to do very, very well on the Regents. Maybe I'm just not explaining it well. Ok, I'm not a math teacher.

I am a math teacher, as you know. I did understand it the way the teacher taught it, and actually got 100 on that test. Most of my class got in the 70s. Nothing on your teaching skills or your teacher's. I'm sure she was good.

This wasn't Regents-level material, though; it was a 7th grade test.

Last edited by amother on Mon, Jul 08 2019, 11:51 am; edited 1 time in total

amother

Tangerine

Tue, May 21 2019, 2:36 pm

groisamomma wrote:

The intuitive math skills are much more important than the equations, IMO. Honestly, you and I both know well that no one needs anything beyond basic proportional reasoning to get through life.

So I teach geometric constructions and the Pythagorean Theorem and pretend that they apply to my students' lives. Yes, maybe they are used to shape the world around us, but is anyone other than a programmer, an architect, or an engineer going to need to know trigonometry? Nope.

Last edited by amother on Mon, Jul 08 2019, 11:55 am; edited 1 time in total

studying_torah

Tue, May 21 2019, 3:01 pm

Thank u rose, your answer was so helpful to me!
Dr mom this is a real situation that I was stuck trying to figure out. I got a rewards check for a store and I was trying to see how to determine what was spent over the year.
The amounts were hypothetical.

Mommyg8

Tue, May 21 2019, 3:44 pm

groisamomma wrote:

Now I'm insulted. I happen to have an intuitive grasp of math - the right answer often pops into my head when I look at a math problem - but I was trying to figure out how to break it down for a non math person.

I had excellent math professors in college and this is mostly how they taught.

Smileforamile, this teacher got HALF the class to get a 100 on the Math A regent, when I spoke to a friend in a different school she told me half of her class failed the same regent. Maybe I'm not repeating it right.

studying_torah

Tue, May 21 2019, 3:55 pm

Mommy g8 please don't be insulted, your posts were helpful too! I think everyone has a bit of a different way to solve these things & I'm grateful for ppl who took the time to explain in various ways.
It's really interesting too how many ways ppl can come to the same answer.