Listing fractions from the least to the greatest of 1/3,4/9, 3/4, 5/6, 5/8, 2/3, 3/12, 2/5
Change all of the fractions to decimals. That will make it clear which order they should be in.
To list the fractions from least to greatest, you need to compare them and determine which ones are smaller and which ones are larger. Here are the steps to do it:
1. Start by converting the fractions to a common denominator. To do this, find the least common multiple (LCM) of the denominators. In this case, the LCM of 3, 9, 4, 6, 8, 3, 12, and 5 is 36. So, we need to convert all the fractions to have a denominator of 36.
2. Convert each fraction to have a denominator of 36:
- 1/3 becomes 12/36 (multiply numerator and denominator by 12).
- 4/9 becomes 16/36 (multiply numerator and denominator by 4).
- 3/4 becomes 27/36 (multiply numerator and denominator by 9).
- 5/6 remains the same since 6 is already a factor of 36.
- 5/8 becomes 22.5/36 (multiply numerator and denominator by 4.5).
- 2/3 becomes 24/36 (multiply numerator and denominator by 12).
- 3/12 becomes 9/36 (multiply numerator and denominator by 3).
- 2/5 becomes 14.4/36 (multiply numerator and denominator by 7.2).
3. Now that all the fractions have a common denominator, you can compare the numerators to determine their relative sizes.
- 12/36 < 16/36 < 27/36 < 30/36 < 22.5/36 < 24/36 < 9/36 < 14.4/36
4. Simplify the fractions if possible. In this case, 12/36 can be simplified to 1/3, 16/36 becomes 4/9, 27/36 becomes 3/4, 24/36 becomes 2/3, and 9/36 becomes 1/4.
So, in the final order from least to greatest, the fractions are: 1/3, 4/9, 3/4, 5/6, 2/3, 1/4, 22.5/36, 14.4/36.