A student claims that 2/3 = 6/7 because if you add 4 to both the top and the bottom of a fraction, the fraction does not change. How do you respond?
I am a bit confused. Don't you need to have a common denominator?
http://www.mathsisfun.com/equivalent_fractions.html
Note that you need to use division or multiplication, not addition, to form or identify equivalent fractions.
The link you posted made it clear! Thank you Thank you!
You're very welcome!
You're absolutely right! While it is true that adding the same number to both the numerator (the top) and denominator (the bottom) of a fraction does not change its value, it does not mean that two fractions with different denominators can be considered equivalent.
In order to determine if two fractions are equal, we need to have a common denominator. The denominator represents the number of equal parts in a whole, so different denominators mean different numbers of equal parts.
To compare fractions, we need to find the least common multiple (LCM) of the denominators, which is the smallest number that is divisible by both denominators. Then, we can convert the fractions to have the same denominator and make an accurate comparison.
In this case, 2/3 and 6/7 have different denominators (3 and 7), so we cannot immediately assert their equality by adding 4 to both the numerator and denominator. To compare them accurately, we need to find a common denominator.
The LCM of 3 and 7 is 21, so we can convert both fractions to have a denominator of 21:
2/3 = (2/3) * (7/7) = 14/21
6/7 = (6/7) * (3/3) = 18/21
Now that both fractions have the same denominator, we can confidently compare them. As you can see, 2/3 is not equal to 6/7, so the student's claim is incorrect.