(28) What is the sum of the numerator and denominator for the fractional equivalent of 0.82323232 . . .?
A) 122 B) 343 C) 361 D) 1031 E) 1805

My kid is doing UIL Math in junior high and on one of the study tests this is one of the questions. The other 49 questions were pretty easy but this one stumped me as far as how I would tell my kid how to do this problem with no calculator and spend no more than 60 to 90 seconds on it.

The test and answer key is located here (https://www.uiltexas.org/files/academics/aplus/A+_Math_Sample_Answer_Sheet,_Test,_and_Key.pdf ) so I know the answer but I am wondering if there is something that I am missing as far as how you get the answer quickly without a calculator.

Think you just need to use process of elimination

Sounds like a job for physics clown

C

I would say A since it's the only one that added up to an even number.

When in doubt C it out

Using process of elimination;

C) 361

163/198

82/99=.828282
Nope

164/198=.82828282
Nope (Same as above)

163/198=.823232323
Yep

No idea how to do it without guessing.

I just said C can't you read

Dad said:

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how you get the answer quickly without a calculator.

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1. Sit by the Asian kid.
2. Copy off them.

THE_CHOSEN_ONE said:

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Think you just need to use process of elimination

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What's the bathroom got to do with this?

x/y = .82323232...
x=z-y

z-y=.82323232(y)

y=z/1.82323232

try the answers as z, which one gives a whole number as y?

122 > y=66.91
343 > y= 188.12
361 > y= 198.0000351

I'm going with 361, doubt you'll get closer to a whole integer with the other 2

TX AG 88 said:

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x/y = .82323232...
x=z-y

z-y=.82323232(y)

y=z/1.82323232

try the answers as z, which one gives a whole number as y?

122 > y=66.91
343 > y= 188.12
361 > y= 198.0000351

I'm going with 361, doubt you'll get closer to a whole integer with the other 2

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Yeah, something like this. Setup the algebra and punch in the numbers.

TX AG 88 said:

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x/y = .82323232...
x=z-y

z-y=.82323232(y)

y=z/1.82323232

try the answers as z, which one gives a whole number as y?

122 > y=66.91
343 > y= 188.12
361 > y= 198.0000351

I'm going with 361, doubt you'll get closer to a whole integer with the other 2

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I like this answer. I will probably tell my kid to skip one like this but this is better than what I had come up with. I turned the decimal into something close to 14/17 and then tried to guess and check which answer times 14/31 was close to a whole number. Your answer has less calculations that need to be done and is much better.

X=.823232323. . .
10x=8.232323
1000x=823.232323
1000x-10x=815
990x=815
X=815/990=163/198

Sum of digits = 361

What do I win?

Dad said:

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(28) What is the sum of the numerator and denominator for the fractional equivalent of 0.82323232 . . .?
A) 122 B) 343 C) 361 D) 1031 E) 1805

My kid is doing UIL Math in junior high and on one of the study tests this is one of the questions. The other 49 questions were pretty easy but this one stumped me as far as how I would tell my kid how to do this problem with no calculator and spend no more than 60 to 90 seconds on it.

The test and answer key is located here (https://www.uiltexas.org/files/academics/aplus/A+_Math_Sample_Answer_Sheet,_Test,_and_Key.pdf ) so I know the answer but I am wondering if there is something that I am missing as far as how you get the answer quickly without a calculator.

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Use one of the lifelines, I'd go with Phone a Friend.

Mathguy64 said:

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X=.823232323. . .
10x=8.232323
1000x=823.232323
1000x-10x=815
990x=815
X=815/990=163/198

Sum of digits = 361

What do I win?

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I don't know why this blew my mind but it did. I've taken all the usual maths for engineering but never would have approached it this way.

Is this just one of the general accepted ways of doing these types?

What is the sum of the numerator and denominator for the fractional equivalent of 0.82323232 . . .?

Does he know how to turn repeating decimals to fractions? If he doesn't, teach him. This problem should be able to be done in a short amount of time.

Top number (numerator) -> entire number- non-repeating part (823-8) or 815.

Bottom number (denominator)-> nine for each repeating digit and a zero for each non-repeating part (990)

Simply 815/990 with short division or other mental math and sum to give answer.
163/198
163+198=361

That's how you turn repeating decimals into fractions.

Mathguy64 said:

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That's how you turn repeating decimals into fractions.

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Ah. Missed that lesson entirely it seems. I swear I somehow skipped all the cool algebra tricks during my life journey.

Learned something new today. Thanks.

No tits = no answer

Mathguy64 said:

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That's how you turn repeating decimals into fractions.

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lol, knew that method once. forgot it.

Mathguy is correct of course, but the algorithm I shared will be quicker for contests.

ag88man said:

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What is the sum of the numerator and denominator for the fractional equivalent of 0.82323232 . . .?

Does he know how to turn repeating decimals to fractions? If he doesn't, teach him. This problem should be able to be done in a short amount of time.

Top number (numerator) -> entire number- non-repeating part (823-8) or 815.

Bottom number (denominator)-> nine for each repeating digit and a zero for each non-repeating part (990)

Simply 815/990 with short division or other mental math and sum to give answer.
163/198
163+198=361

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Learned something new.

Mathguy64 said:

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X=.823232323. . .
10x=8.232323
1000x=823.232323
1000x-10x=815
990x=815
X=815/990=163/198

Sum of digits = 361

What do I win?

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No username checks out yet? GB is slipping.

ag88man said:

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What is the sum of the numerator and denominator for the fractional equivalent of 0.82323232 . . .?

Does he know how to turn repeating decimals to fractions? If he doesn't, teach him. This problem should be able to be done in a short amount of time.

Top number (numerator) -> entire number- non-repeating part (823-8) or 815.

Bottom number (denominator)-> nine for each repeating digit and a zero for each non-repeating part (990)

Simply 815/990 with short division or other mental math and sum to give answer.
163/198
163+198=361

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I don't follow how the bold part comes to 990 from the 0.823232323 based on nine for each repeating digit and a zero for each non-repeating part

Holy ****, how in the **** would you even begin to figure that out? **** me that's terrible.

Win At Life said:

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ag88man said:

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What is the sum of the numerator and denominator for the fractional equivalent of 0.82323232 . . .?

Does he know how to turn repeating decimals to fractions? If he doesn't, teach him. This problem should be able to be done in a short amount of time.

Top number (numerator) -> entire number- non-repeating part (823-8) or 815.

Bottom number (denominator)-> nine for each repeating digit and a zero for each non-repeating part (990)

Simply 815/990 with short division or other mental math and sum to give answer.
163/198
163+198=361

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I don't follow how the bold part comes to 990 from the 0.823232323 based on nine for each repeating digit and a zero for each non-repeating part

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I'm assuming it was a 9 for each repeating digit. As in the 2 and 3 repeat, so two 9's followed by the same with non repeating but with a 0 instead. So would .8623232323 be 9900?

PneumAg said:

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Holy ****, how in the **** would you even begin to figure that out? **** me that's terrible.

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Math, man. Chalk me as one of those who despised it as a kid and now as an adult I can truly see how beautiful it is. I blame my ****ty childhood public school coach/teachers for not being good at their jobs and cultivating good mathematics.

I'm assuming it was a 9 for each repeating digit. As in the 2 and 3 repeat, so two 9's followed by the same with non repeating but with a 0 instead. So would .8623232323 be 9900?

This is correct.

.8623232323…
Top-> (8623-86)
Bottom-> (9900)

ag88man said:

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I'm assuming it was a 9 for each repeating digit. As in the 2 and 3 repeat, so two 9's followed by the same with non repeating but with a 0 instead. So would .8623232323 be 9900?

This is correct.

.8623232323…
Top-> (8623-86)
Bottom-> (9900)

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Nice. Thanks. Won't be the first time I learned some new math at 2am

Wow, I have never seen that repeating decimal to fraction before (either way). In what grade level would that have been taught so I can properly direct my anger at the responsible teacher.

ag88man said:

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What is the sum of the numerator and denominator for the fractional equivalent of 0.82323232 . . .?

Does he know how to turn repeating decimals to fractions? If he doesn't, teach him. This problem should be able to be done in a short amount of time.

Top number (numerator) -> entire number- non-repeating part (823-8) or 815.

Bottom number (denominator)-> nine for each repeating digit and a zero for each non-repeating part (990)

Simply 815/990 with short division or other mental math and sum to give answer.
163/198
163+198=361

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redline248 said:

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Wow, I have never seen that repeating decimal to fraction before (either way). In what grade level would that have been taught so I can properly direct my anger at the responsible teacher.

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I took graduate level math classes as part of my Masters of Science in Engineering program at Virginia Tech and I didn't know this.

redline248 said:

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Wow, I have never seen that repeating decimal to fraction before (either way). In what grade level would that have been taught so I can properly direct my anger at the responsible teacher.

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In the 70's or 80's - Algebra 1
Today? Probably never.