Can 606/1000 be reduced further than 303/500?
A little known secret about your scientific calculator:
if you have a button labeled a b/c
enter 606
hit that button
enter 1000
press =
Voila!!
To determine if 606/1000 can be reduced further than 303/500, we need to find the greatest common divisor (GCD) of the numerator (606 and 303) and the denominator (1000 and 500) for both fractions.
First, let's find the GCD of 606 and 303:
- The factors of 606 are 1, 2, 3, 6, 101, 202, 303, and 606.
- The factors of 303 are 1, 3, 101, and 303.
- The common factors of 606 and 303 are 1, 3, and 101.
- Therefore, the GCD of 606 and 303 is 3.
Next, let's find the GCD of 1000 and 500:
- The factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.
- The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, and 500.
- The common factors of 1000 and 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, and 500.
- Therefore, the GCD of 1000 and 500 is 500.
Now, let's simplify both fractions:
- Simplifying 303/500: We divide the numerator and denominator by their GCD, which is 3. After dividing, we get 101/166.
- Simplifying 606/1000: We divide the numerator and denominator by their GCD, which is 500. After dividing, we get 121/200.
Comparing the simplified fractions, we see that 101/166 is already simplified to its lowest terms, but 121/200 can still be reduced further.
Therefore, the answer is no, 606/1000 cannot be reduced further than 303/500.