First, do you get the same sum when you use 18 rather than 9 as a common denominator for 2/3 and 4/9? Explain the answer.
Also what extra step will you have to perform if you do not use the least common denominator when adding fractions?
Please explain the answer.
You will get the same answer
The extra would be putting your answer in lowest terms
6/9 + 4/9 = 10/9
12/18 + 8/18= 20/18 = 10/9
To determine if using 18 instead of 9 as a common denominator for 2/3 and 4/9 results in the same sum, we first need to find the sum of the fractions using both denominators.
Using 9 as the common denominator, we can convert 2/3 to have a denominator of 9 by multiplying both the numerator and denominator by 3, giving us (2/3) * (3/3) = 6/9. The sum of 6/9 and 4/9 is 10/9.
Now, using 18 as the common denominator, we need to convert both fractions. To convert 2/3, we multiply both numerator and denominator by 6, resulting in (2/3) * (6/6) = 12/18. Similarly, for 4/9, we multiply both numerator and denominator by 2, resulting in (4/9) * (2/2) = 8/18. The sum of 12/18 and 8/18 is 20/18.
To compare these results, we need to simplify the fractions. The simplified form of 10/9 is (5/3) since 10 and 9 have a common factor of 1. The simplified form of 20/18 is (10/9) since 20 and 18 have a common factor of 2.
Comparing the two simplified fractions, we can see that 5/3 is not equal to 10/9. Therefore, using 18 instead of 9 as a common denominator for 2/3 and 4/9 does not result in the same sum.
If you do not use the least common denominator when adding fractions, an extra step you will need to perform is finding a common denominator for the fractions being added. This involves finding the least common multiple (LCM) of the denominators and then converting each fraction to have the same denominator.
Once you have a common denominator, you can add the fractions. However, the resulting fraction you obtain might not be in simplified form. To simplify the fraction, you will need to find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD.
By using the least common denominator, you can avoid this extra step of finding a common denominator and simplify the fraction more easily, as the numerator and denominator will likely have a common factor, which can be divided to simplify the fraction.