Question: 44 Percent of W

Comment on 44 Percent of W

I did .44w and 4.444w. I then canceled out the w's. Why isn't that a valid approach?
greenlight-admin's picture

When you say "cancel out the w's" you are suggesting that we divide both quantities by w. There's a problem with this approach of dividing both quantities by a VARIABLE (w).

First, we don't know whether or not w = 0. If w were to equal 0, then dividing by w means we are dividing by zero, which is never a good thing.

Second, we don't know whether or not w is NEGATIVE. If w is NEGATIVE, then dividing by w means we are dividing by a NEGATIVE value, which we shouldn't do with QC questions.

For more on this, watch

Got it.

The necessary caveat we must always find in a question like this is that w>0.

If not, (D).

greenlight-admin's picture


Abdul Hannan's picture

hi Mr Hanneson,
I have a doubt in this question
at side A it is clearly mention "Percent" of, while on the B side its just mentioned "of". there is no mention of the word "percent" on the B side. how did you assumed that 4/9 is asked as a percent of W.
greenlight-admin's picture

Hi Abdul,

In quantity B, 4/9 is a fraction (not a percent).

However, there is a strong relationship between fractions and percents. In fact, in the following lesson, we examine how to convert fractions to percents:

For example, the FRACTION 1/2 is equal to 50 PERCENT. So, 1/2 of Q is equal to 50% of Q.
Likewise, the FRACTION 3/4 is equal to 75 PERCENT. So, 3/4 of Y is equal to 75% of Y.

In the video question above, the FRACTION 4/9 is equal to 44.444...PERCENT.
So, 4/9 of W is equal to 44.444...% of W.

Does that help?


Hi in the above problem, it is being said as 1/9=11.11 approx But actually 1/9=0.11 right?

Please correct me if I'm wrong.
greenlight-admin's picture

It depends whether we're working with DECIMALS or PERCENTS.
For example, 1/2 = 0.5 = 50%
So, the DECIMAL 0.5 is equal to the PERCENT 50%

In the DECIMAL conversion, 1/9 = 0.1111111111...
In the PERCENT conversion, 1/9 = 11.1111111111...%

If we want to approximate, we can say 1/9 ≈ 0.11 ≈ 11%

For more on fraction/decimal/percent conversions, watch

Does that help?


hii brent,
in the first quantity if we convert 44% of w we get 0.44 w also in quantity b if we do 4/9 of w we get 0.44w then wont it be option c?
greenlight-admin's picture

Be careful.
4/9 is APPROXIMATELY equal to 0.44
In the DECIMAL conversion, 1/9 = 0.1111111111..., where the 1's go on forever.

So, if we want to be precise (which is required for this question), we must recognize that 4/9 = 0.4444444444.....

Does that help?


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