Express 99 2/3% as a fraction? No calculator

Question

My 9-year-old daughter is stuck on this question and normally I can help her, but I am also stuck on this! I have looked everywhere to find out how to do this but to no avail so any help/guidance is appreciated:

The possible answers are:

$1 \frac{29}{300}$

$\frac{269}{300}$

$9 \frac{29}{30}$

$\frac{299}{300}$

$1 \frac{299}{300}$

Whenever I try this I am doing $\frac{99.66} \times 100$ is $\frac{9966}{10000}$ and then simplify down, but I am not getting the answer. I get $\frac{4983}{5000}$? Then I can't simplify more — unless I am doing this totally wrong?

---

Hello All - just an update - I managed to teach this to her right now, and she cracked it pretty much the first time! Thanks sooooooo much for the answers and here is some of the working she did:

Answer 1

So you want to find $$\frac{99+\frac{2}{3}}{100}.$$

The numerator is equal to $$\frac{3(99)}{3}+\frac{2}{3} = \frac{297}{3}+\frac{2}{3} = \frac{299}{3}.$$

Dividing by $100$ you get $$\frac{\frac{299}{3}}{100} = \frac{299}{3(100)}=\frac{299}{300}.$$

The reason you are getting the wrong answer is because you are rounding. The fraction $\frac{2}{3}$ is not equal to $0.66$ but rather is equal to $0.6666\cdots$ (often written $0.\overline{6}$).

Answer 2

$99 \frac{2}{3} \% = 99 \frac{2}{3} \cdot \frac{1}{100} = \frac{299}{3} \cdot \frac{1}{100} = \frac{299}{300}$.

Answer 3

99 and $2/3$ percent is $\frac{\displaystyle 99 + \frac{2}{3}}{100}=\frac{\displaystyle\frac{3\times 99 + 2}{3}}{100}$. Does this help?

Answer 4

Multiply both numerator and denominator by $3$ to get $$\frac{3 \times (99 \frac{2}{3})}{3 \times 100} = \frac{3 \times 99 + 3 \times \frac{2}{3}}{300}$$

Which is $$\frac{297 + 2}{300} = \frac{299}{300} $$

Answer 5

Separately, $$99\%=\frac{99}{100},$$ and $$\frac{2}{3}\%=\frac{\frac{2}{3}}{100}=\frac{2}{300}$$

Adding together we get $$99\frac{2}{3}\%=99\%+\frac{2}{3}\%=\frac{99}{100}+\frac{2}{300}.$$ Using algebra of fractions you then get $$\frac{99\times 300+2\times 100}{100\times 300}=\frac{99\times 3+2}{300}=\frac{299}{300}.$$

Remark As a teaching "aside", I like to think about what "percent" means. Break it down. "Percent" is a juxtaposition of the two words "per" and "cent". "Per" just means "for each" and "cent" literally means "100" (e.g. there are a 100 cents in a dollar!). So "percent" just means something per 100, i.e $1.2345\%$ is just $1.2345$ per $100$, or in other words $\frac{1.2345}{100}$. Similarly $10\%$ is just $10$ per $100$, or in other words $\frac{10}{100}$. And related to the above $\frac{2}{3}\%$ is just $\frac{2}{3}$ per $100$, or in other words $\frac{\frac{2}{3}}{100}$. And to finish $99\frac{2}{3}\%$ is just $99\frac{2}{3}$ per $100$, or in other words $\frac{99\frac{2}{3}}{100}$. Therefore, if you know your fractions, then percentages are a breeze !!

Answer 6

You can almost eyeball this, which is a useful technique for dealing with multiple choice quizzes against the clock.

If 100% = 1, then you're looking for a fraction slightly less than one. That lets you rule out all but two of the answers. How much less? A third of a percent. One percent is 1/100. Divide that by three to get 1/300. That points you at 299/300 being the answer.

Answer 7

Already it has been shown how to arrive at the correct answer using fractions. One may also consider using the process of elimination. $99 \frac{2}{3}\%$ is clearly less than $1$. So, by inspection, we can rule out choices 1,3, and 5. We are left with two possibilities, $\frac{269}{300}$ and $\frac{299}{300}$. Now, $\frac{269}{300} \approx \frac{270}{300}=.90$ or 90%. Since $269 <270$, $\frac{269}{300} < \frac{270}{300} = 90\%$. Thus, the answer cannot be $\frac{269}{300}$. This leaves one possibility, $\frac{299}{300}$.

While this method may not be immediately available to a 9 yo, it is easy to see that three possibilities are easily ruled out. This sort of thinking (process of elimination) can go a long way with multiple choice tests in the future and with math in general. (Think proof by contradiction.)

Answer 8

Here's how I did it in my head:

$99\%$ is $\frac{99}{100}$. This leaves $\frac{2}{3}\%$ unaccounted for. So we need to go $\frac{2}{3}$rds of the $1\%$ distance from $\frac{99}{100}$ to $\frac{100}{100}$. Clearly, we need more than one step to do this; we need three. So, we need to go $\frac{2}{3}$rds of the distance from $\frac{297}{300}$ to $\frac{300}{300}$, which is $\frac{2}{300}$. So the final answer is $\frac{297}{300}+\frac{2}{300}=\frac{299}{300}$.

Answer 9

$99\frac{2}{3}\%$ is $\frac{1}{3}\%$ away from $100\%$ or $1$. $\frac{1}{3}\%$ is literally $\frac{1}{300}$. The answer is therefore $\frac{299}{300}$.

Answer 10

Why are you even trying to do this as a math problem? Because it is a multiple choice question, figure out which answers are wrong.

1. The First, third and fifth are all incorrect because they are over 1.00 and of course 99 2/3% is less than 1.00
2. The second answer is 1.00 - 31/300 or 1/10 less than 1.00, or .90~something, and therefore wrong also
3. The fourth answer is 1.00 - 1/300, or most likely 99 2/3% if you can't actually do the math

My wife is a fifth grade teacher, and what they are actually teaching is that if you are stuck on the mathematical equations, use inference and elimination to deduce the correct answer and work backward. That simple.

Answer 11

A third of a percent is missing, i.e. one three-hundredth. Two hundred and ninety nine three-hundredths remain.

Answer 12

There are multiple roads that lead to Rome:

First, take out the $\%$. We find $\frac{299}{3}$

$99 \frac{2}{3} = 99 + \frac{2}{3} = \frac{1}{3} \cdot ( 297 + 2) = \frac{1}{3} \cdot 299 = \frac{299}{3}$

or

$99 \frac{2}{3} = 99 + \frac{2}{3} = 3 \cdot \frac{99}{3} + \frac{2}{3} = \frac{297}{3} + \frac{2}{3} = \frac{299}{3}$

Lastly, add the $\%$ back: $\frac{299}{3} \cdot \frac{1}{100} = \frac{299}{300}$

Answer 13

Is it too hard to mentally calculate the numerator?

$99*3 + 2 = 300 - 3 + 2 = 299$

Answer 14

$99 \frac{2}{3} = 99 + \frac{2}{3} = 99 + (1 - \frac{1}{3}) = 100 - \frac{1}{3} = \frac{300}{3} - \frac{1}{3} = \frac{299}{3}$

So $99 \frac{2}{3}\% = \frac{299}{3}\% = \frac{299}{300}$