Finding percentage from fractions ??

[glimonez]

Hello everyone,

I hope I named the topic correctly. I have this word problem and I think I know how to solve it but I am not getting it.

Here it is:

At a concert 1/4 of the audience is composed of adults and the rest are youth. Two-fifths of the youth are female. What part of the youth are female?

Answer: 3/10

My attempt at the problem is that the youth are 3/4 of the audience, 4 divided by 3 is .75.
Two-fifths of the youth are female, 5 divided by 2 is .40.
I'm not sure what this method is, but it's the only way I know how to attempt.

.40 ??
–––––– = ––––––
.75 100

.40 x 100 = 40, 40 divided by .75 = 53.33333??? Then I get completely lost. Please help. I really want to UNDERSTAND how this should work.

Thank you so much for reading,

 

[tkhunny]

One sep at a time. It often helps to defien a fake audience.

"At a concert 1/4 of the audience is composed of adults and the rest are youth"

1/4 Adults
1 - 1/4 = 3/4 Youth You have that.

"Two-fifths of the youth are female.

2/5 Female
1 - 2/5 = 3/5 Male

"What part of the youth are female?"
This has a few problems. Is this REALLY this question? The answer is 2/5 = 0.40 = 40%. It is given in the problem statement.

"What part of the audience is female?"
We can't answer this, because we don't know how the adults divide up.

"What part of the audience is youth and female."
Here's a question we can answer.
Youth are 3/4.
If you now talk about ONLY the youth, that 3/4 is 100% of the youth. Ponder on this idea. 3/4 of the audience is 100% of the youth.
Female is 2/5 of the youth.
2/5 of the youth is the same number as 2/5 of 3/4 of the audience. (2/5) of (3/4) is (2/5)*(3/4) = 3/10 = 0.30 = 30%

Notice how easy it is if we pick an audience.

Let's do 100 people.

100 * (1/4) = 25

Of The Audience
25 are adults
75 are youth

Of the 75 youth

75 * (2/5) = 30 -- And we're done. 30/100 = 0.30 = 30%

 

[soroban]

Hello, glimonez!

It's a really silly problem . . . I must assume there is a typo.
. . and you are reading it incorrectly.

At a concert 1/4 of the audience is composed of adults and the rest are youths.

Two-fifths of the youths are female. [1]

What part of the youths are female? [2]

Answer: 3/10 . ??

First of all, note that it does not ask for a percent.


Look at statements [1] and [2] . . . and you'll see how silly it is.

. . \(\displaystyle \boxed{\text{Two-fifths}}\text{ of the youths are female.}\)
. . \(\displaystyle \boxed{\text{What part}}\text{ of the youths are female?}\)

Well, duh! . . . Could it be two-fifths?


I assume that the original question asked:
. . What part of the audience is female?


\(\displaystyle \text{If }\tfrac{1}{4}\text{ of the audience are adults, then }\tfrac{3}{4}\text{ of the audience are youths.}\)

\(\displaystyle \text{Then }\tfrac{2}{5}\text{ of the youths are female.: }\;\left(\tfrac{2}{5}\right)\left(\tfrac{3}{4}\right) \:=\:\tfrac{3}{10}\)

. . \(\displaystyle \text{Therefore: }\tfrac{3}{10}\text{ of the }audience\text{ is female.}\)

 

[lookagain]

At a concert 1/4 of the audience is composed of adults and the rest are youth. Two-fifths of the youth are female.
What part of the youth \(\displaystyle [no,\ the \ audience]\) are female?

Answer: 3/10

My attempt at the problem is that the youth are 3/4 of the audience, \(\displaystyle > \ > \ >\) 4 divided by 3 is .75. \(\displaystyle < \ < \ <\)

Two-fifths of the youth are female, \(\displaystyle > \ > \ >\)5 divided by 2 is .40.\(\displaystyle < \ < \ <\)

gliimonez,

along with soroban's post, let me point out about what I highlighted with the arrows above:

4 divided by 3 is 4/3, not 3/4 (which equals 0.75). And 5 divided by 2 is 5/2 = 2.5, not 0.40

 

[JHowell]

What's already written is exactly right.

I'll just add that in story problems, there are sometimes words that will help you figure out what to do before you start building an equation.

Any time I see "of", I immediately think multiplication.

For example, "One third of a dozen donuts" tells me I'm going to take 1/3, and multiply it by a dozen (or 12).

In this case, "1/4 of the audience is adults" tells me I'm going to multiply.

Since it's only one audience, the equation is:
1/4 x 1 audience = adults

BUT WATCH OUT! We don't want adults!

If 1/4 audience = adults, then the rest (3/4) must be youths!
3/4 audience = youths

"Two-fifths of the youth are female". Uh oh, there's our pesky of again!

So, 2/5 x youths = female

We already solved for youths!
2/5 x (3/4 audience) = female

When we multiply, we get 6/20 audience = female
Reducing gives us 3/10 audience = female


This problem is hard enough without jumping to and from percentages. If the problem is given in fractions, try to solve it in fractions. Notice that I also kept my labels (audience, youths, female, etc) in each step so it's easier for me to find a misstep. If I had just tackled the problem with numbers, I might have multiplied the 1/4, not noticing I was looking at adults and not youths!



Other handy word clues:
"More" will include addition
"Difference" will include subtraction
"Per" will include division. (Such as "I have 15 toys, and 3 kids. How many toys per kid?"... 15/3

 

[Deleted member 4993]

Very nice explanation -

welcome to the forum.

 

[lookagain]

At a concert 1/4 of the audience is composed of adults and the rest are youth.

Two-fifths of the youth are female.

What part of the youth are female?

\(\displaystyle \text{(alleged)}\)Answer: 3/10

What's already written is exactly right.

No, for 3/10 to be the answer, the question would have to have been the equivalent to:

"What fraction of the total number of people in the audience is equal to the number of female youths?"

Or it might be:

"What is the fraction that corresponds to the (number of female youths) out of (the total number of people in the audience)?"

\(\displaystyle But,\) the meaning of the given question is different from the meaning of either of the two questions given
immediately above.


Revised/amended update:

Let's again use the convenient number of 100 people as the total number of people in the audience.

100 people in the audience

1/4 of the number of people in the audience are adults

Then 3/4 of the number of the people in the audience are youths


(3/4)(100) = 75

75 youths


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2/5 of that result (75 youths) are females


75 youths

(2/5)(75) = 30

Then there are 30 female youths.

"What part of the youth are female?" \(\displaystyle is \ equivalent \ to\) "What fraction of the number of youths \(\displaystyle (denominator)\)
are \(\displaystyle (equals)\)the number of female youths\(\displaystyle (numerator)\)?"


\(\displaystyle Then \ this \ fraction \ is \ \frac{30}{75} \ = \ \frac{2}{5}, \ (which \ equals \ 0.4).\)