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how do I simplify 329/967 ratio

787 day(s) ago

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Answers (7)

jcatta21 		The ratio cannot be simplified because 967 is a prime number.

Posted 786 dy ago

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To simplify fractions like this you need to find the largest number that will divide evenly into both numbers.

usually you list all the PRIME FACTORS of each number and cancel out the ones they have in common,
then what is left is the fraction in lowest terms.

for very large numbers of 3 digits or more I start with the square root of each first
sq root of 329 is about 18.14
and the
sq root of 967 is about 31.1

being that both numbers in the ratio are odd, you only have to check the odd numbers
from 3 to 17 for 329
and
from 3 to 31 for 967
to see if any will divide evenly.

we can also rule out any odd numbers ending in 5 because 329 and 967 do not end in 5.

so for 329 we have these to try:
3, 7, 9, 11, 13, 17
only 7 will divie evenly to give 47

and for 967 we have these also to check,
and these odd numbers also: 19, 21, 23, 27, 29, 31
NONE of these will divide into 967 evenly so it is a PRIME number

the answer is that 329/967 is already in its lowest terms

NOW if the ratio was 329/987, THEN 47 will divede both to give just 7/21
and of course this is just 1/3

maybe the problem was ment to be this?

Posted 787 dy ago

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samzappala 		A ratio is the same as a fraction. 329/967 becomes 329:967. In order to simplify it, round it off to 330:970=33:97. To go further 1:3.
It depends on how much precision they're calling for.

Posted 787 dy ago

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jdrew39 		These two numbers have no common factor, so the fraction cannot be simplified.

Posted 787 dy ago

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MichaelT 		This ratio can't be simplified any more than it is. Sorry.

Posted 787 dy ago

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math_fanatic 		First, you need to determine if the numbers are divisible by the digits 2-9.

They're both odd numbers so neither are divisible by 2 which means they're also not divisible by 4 and 8.

If they're divisible by 3, then their digits will add to a number divisible by 3. 3+2+9 = 14 and 9+6+7=22
14 and 22 are not divisible by three so neither number is divisible by 3, 6, or 9.

Which leaves 5 and 7.

Only numbers that end in 0 or 5 are divisible by 5 so 5 is out. So is 10 since neither number ends in 0.

329/7 = 47 but 967 is not divisible by 7 and they both have to be divisible by 7 in order to simplify.

So you've ruled out all the digits 2-9. Now you have to move on to the prime numbers after 9. Use 329 as your test since it's the smallest number.

Divide 329 by 11.
The answer you get is 29. 909...

You know that if you divide by a higher prime number you're going to get a lower answer.
Because we've ruled out all the digits 2-9 and 11 you know that in order to have a common factor
with 967, the factor has to be a prime between 11 and 29.909.

Those primes are 13, 17, 19, 23
So 329 has to be either 13 * 17, 13*19, 13*23, 17*19, 17*23, or 19*23.
329 is not the product of any of these numbers so 329 and 967 can't have a common factor.
This ratio cannot be simplified.


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matherapist 		You will need to find a prime # that divides both numerator and denominator with no remainder in either. If you can't find one it is irreducible. If you can't find one, then the fraction is irreducible. You have to do this by trial and error.

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