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.

least common multiple of

5
2*3
3
is
5*2*3 = 30
so use
2/5 = 12/30 (top and bottom by 6)
1/6 = 5/30 (top and bottom by 5)
1/3 = 10/30 (top and bottom by 10)
now put them in order :)

damon, how did you come up with the number 5 as least common multiple 1/6,1/3,2/5

30, it says 30 is least common multiple of 5, 6 which is 2*3 and 3

To compare fractions and order them from least to greatest, Adam needs to rewrite them so they all have the same denominator. Here's how he can do it:

Step 1: Find a common denominator
To find a common denominator, Adam needs to identify the least common multiple (LCM) of the denominators. In this case, the denominators are 5, 6, and 3. The LCM of these numbers is 30. Therefore, 30 will be the common denominator Adam will use to rewrite the fractions.

Step 2: Rewrite the fractions with the common denominator
To rewrite the fractions with a common denominator of 30, Adam needs to multiply both the numerator and denominator by a suitable factor. Here's how he can do it for each fraction:

For 2/5:
To make the denominator 5 become 30, Adam needs to multiply both the numerator and denominator by 6. So, the fraction becomes (2 * 6) / (5 * 6) = 12/30.

For 1/6:
To make the denominator 6 become 30, Adam needs to multiply both the numerator and denominator by 5. So, the fraction becomes (1 * 5) / (6 * 5) = 5/30.

For 1/3:
To make the denominator 3 become 30, Adam needs to multiply both the numerator and denominator by 10. So, the fraction becomes (1 * 10) / (3 * 10) = 10/30.

Now all three fractions have the same denominator of 30.

Step 3: Order the fractions from least to greatest
Now that Adam has rewritten the fractions with a common denominator, he can compare them in terms of their numerators. The fractions, from least to greatest, are:
5/30, 10/30, 12/30.

Therefore, the fractions 1/6, 1/3, and 2/5, when rewritten with a common denominator, can be ordered as 5/30, 10/30, and 12/30 respectively.