onathan says that when you add 723723 to 223223 , you must add the whole numbers together first ( 7+2=97+2=9 ). Then you just add the numerators together ( 2+2=42+2=4 ), and you add the denominators together ( 3+3=63+3=6 ). So the answer is 946946 . Unfortunately, Jonathan's strategy is incorrect. Solve this problem, and then briefly explain the flaw in Jonathan's reasoning. (4 points)

Question

onathan says that when you add 723723 to 223223 , you must add the whole numbers together first ( 7+2=97+2=9 ). Then you just add the numerators together ( 2+2=42+2=4 ), and you add the denominators together ( 3+3=63+3=6 ). So the answer is 946946 . Unfortunately, Jonathan's strategy is incorrect. Solve this problem, and then briefly explain the flaw in Jonathan's reasoning. (4 points)

Answer 1

To add two fractions, we need to have the same denominators.

Let's find the least common multiple (LCM) of 3 and 6, which is 6.

Now we can rewrite the fractions with a common denominator:

723723/6 + 223223/6 = (723723 + 223223) / 6 = 946946/6

However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2:

946946/6 = (946946 ÷ 2) / (6 ÷ 2) = 473473/3

Therefore, the correct answer is 473473/3.

Jonathan's flaw in reasoning is that he incorrectly assumes the fractions have the same denominator. While he correctly adds the numerators and denominators separately, he misses the crucial step of finding a common denominator before adding the fractions.