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jim1174
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when I am adding, subtracting, multiplying and dividing fractions and I get an answer is there a way I can check to make sure my answer is in lowest terms ?
The short answer is: the fraction is in lowest terms if there are no factors other than 1 that appear in both the numerator and denominator.jim1174 said:when I am adding, subtracting, multiplying and dividing fractions and I get an answer is there a way I can check to make sure my answer is in lowest terms ?
If the numbers are really small, by inspection. However in general no, except by brute force. Example: 91/143.jim1174 said:when I am adding, subtracting, multiplying and dividing fractions and I get an answer is there a way I can check to make sure my answer is in lowest terms ?
HallsofIvy said:Or simply factor the numerator and denominator to prime factors. In mathman's "91/143" example, 91 is not divisible by 2, 3, or 5 but 91= 7(13) and 13 is also prime. 143 is not divisible by 2, 3, 5, or 7 but 143= 11(13). Since 91 and 143 have prime factor 13 in common, the fraction 91/143= (7(13))/(11(13)) is not "reduced to lowest terms" we can reduce further by cancelling the "13" in both numerator and denominator to get 7/11 which is "reduced to lowest terms.
To apply willem2's suggestion, n91 divides into 143 once with remainder 143- 91= 52. 52 divides into 91 once with remainder 91- 52= 39. 39 divides into 52 once with remainder 52- 39= 13. And 13 divides into 39 exactly three times with no remainder: 39= 3(13). That immediately tells us that the two numbers, 143 and 91 have common factor 13.
To see that this is true, since 39= 3(13), 52- 39= 52- 3(13)= 13 so 53= 4(13). Then 91- 52= 91- 4(13)= 3(13) so 91= 7(13). And then 143- 91= 143- 7(13)= 4(13) so 143= 11(13).
When a fraction is in its lowest terms, it means that the numerator and denominator have no common factors other than 1. In other words, the fraction cannot be simplified any further.
To simplify a fraction to its lowest terms, you need to find the greatest common factor (GCF) of the numerator and denominator and divide them both by it. This will result in a fraction with no common factors other than 1.
No, a fraction cannot be in its lowest terms if both the numerator and denominator are even. This is because they both have a common factor of 2, which means the fraction can be simplified further.
Yes, a fraction is in its lowest terms if both the numerator and denominator are prime numbers. Prime numbers have no common factors other than 1, so the fraction cannot be simplified any further.
You can check if a fraction is in its lowest terms by finding the GCF of the numerator and denominator. If the GCF is 1, then the fraction is in its lowest terms. If the GCF is greater than 1, then the fraction can be simplified further.