Final answer:
To solve 3/9-3/7, find a common denominator (63), subtract the fractions to get -6/63, and simplify by dividing by the GCD (3) resulting in an answer of -2/21, which is a reasonable small negative fraction.
Step-by-step explanation:
To perform the operation 3/9 - 3/7, we first look for a common denominator. The numbers 9 and 7 have no common factors (other than 1), so the common denominator is simply 9 times 7, which is 63. We then rewrite each fraction with the common denominator:
(3/9) becomes (3×7)/(9×7) = 21/63
(3/7) becomes (3×9)/(7×9) = 27/63
Now we can subtract the two fractions:
21/63 - 27/63 = (21 - 27)/63 = -6/63
To simplify the result, we find the greatest common divisor (GCD) of 6 and 63, which is 3. We then divide both the numerator and the denominator by this GCD:
-6/63 ÷ 3/3 = -2/21
The simplified answer is -2/21. To check if this is reasonable, we note that since 3/9 is equal to 1/3 and 3/7 is slightly less than 1/2, the difference should be a small negative fraction, which confirms the reasonableness of our answer.