Does 1/3 + 5/9 - 5/12 = 5/9 + 5/12 - 1/3 ? Explain
Thank you :p
1/3 + 5/9 - 5/12 =
12/36 + 20/36 - 15/36 = 17/36
5/9 + 5/12 - 1/3
20/36 + 15/36 - 12/36 = 23/36
To determine if 1/3 + 5/9 - 5/12 is equal to 5/9 + 5/12 - 1/3, we need to evaluate each expression separately and compare the results.
First, let's calculate 1/3 + 5/9 - 5/12:
To add fractions with different denominators, we need to find a common denominator. In this case, the smallest common denominator is 36 (3 * 3 * 4). To convert 1/3 to have a denominator of 36, we multiply the numerator and denominator by 12: (1/3) * (12/12) = 12/36. The other fractions already have denominators of 36.
Now we can add the fractions:
12/36 + 5/36 - 15/36 = (12 + 5 - 15) / 36 = 2/36 = 1/18.
Now, let's calculate 5/9 + 5/12 - 1/3:
Using the same process, we find a common denominator of 36 (3 * 3 * 4). To convert 5/9 to have a denominator of 36, we multiply the numerator and denominator by 4: (5/9) * (4/4) = 20/36. The other fractions already have denominators of 36.
Now we can add the fractions:
20/36 + 5/36 - 12/36 = (20 + 5 - 12) / 36 = 13/36.
Comparing the two results, we can see that 1/3 + 5/9 - 5/12 is not equal to 5/9 + 5/12 - 1/3. Therefore, the answer to the equality is false.