Adam wants to compare the fractions 2/5. 1/6. and 1/3. He wants to order them from least to greatest and rewrite them so they all have the same denominator. Explain how Adam can rewrite the fractions.
30 is a common multiple of all the denominators
12/30
5/30
10/30
now order them
how did you get the denominators to be the same?
5/30,10/30,12/30
To compare fractions, Adam needs to rewrite them with a common denominator. Here are the steps he can follow:
1. Find the least common multiple (LCM) of the denominators in the fractions, which will be the common denominator.
2. Rewrite each fraction so that they all have the same denominator.
In this case, Adam wants to compare the fractions 2/5, 1/6, and 1/3.
Step 1: Finding the LCM
The denominators are 5, 6, and 3. To find the LCM, he can list the multiples of each number and look for the smallest common multiple. The multiples are:
- Multiples of 5: 5, 10, 15, 20, 25, ...
- Multiples of 6: 6, 12, 18, 24, 30, ...
- Multiples of 3: 3, 6, 9, 12, 15, ...
Adam can see that the smallest common multiple of 5, 6, and 3 is 30. Therefore, the LCM of the denominators is 30.
Step 2: Rewrite the fractions
To rewrite the fractions with the common denominator of 30, Adam needs to multiply the numerator and denominator of each fraction by the appropriate multiplier.
For 2/5:
- The multiplier is 6 (derived from LCM 30 / denominator 5).
- Therefore, 2/5 can be rewritten as (2 * 6) / (5 * 6) = 12/30.
For 1/6:
- The multiplier is 5 (derived from LCM 30 / denominator 6).
- Therefore, 1/6 can be rewritten as (1 * 5) / (6 * 5) = 5/30.
For 1/3:
- The multiplier is 10 (derived from LCM 30 / denominator 3).
- Therefore, 1/3 can be rewritten as (1 * 10) / (3 * 10) = 10/30.
Now, all the fractions have the same denominator of 30:
- 2/5 is now 12/30.
- 1/6 is now 5/30.
- 1/3 is now 10/30.
Adam can now order them from least to greatest:
1. 5/30 (1/6)
2. 10/30 (1/3)
3. 12/30 (2/5)
So, the fractions ordered from least to greatest are 1/6, 1/3, and 2/5, all with the same denominator of 30.