Compare fractions-write in order least to greatest. My daughter wrote them incorrectly at first, then we found what the answer should be, but can you explain to her why the answers are what they are. Thank you.

1. 2/5, 1/10, 3/20
answer----1/10, 3/20, 2/5

2. 1/3, 3/8, 2/9
answer----2/9, 1/3, 3/8

If you plug them into a calculator, you would get decimals. You can use those decimals to see which is least or greater. Atleast that is how I do it.

Convert all the fractions so that they all have the same denominator (the number below the line). That way, you can tell how big they are relative to one another just by looking at the numerator (the number above the line).

(#1.)

2/5, 1/10, and 3/20 can all be converted so that they have a common denominator of 20:

2/5, when you multiply both the top and bottom by 4, becomes 8/20.

1/10, when you multiply both the top and bottom by 2, becomes 2/20.

3/20 already has a denominator of 20.

2/20 < 3/20 < 8/20
so 1/10 < 3/20 < 2/5

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(#2.)

Do the same thing as in #1, except now make the common denominator 72, since 9, 3, and 8 can all go into 72 evenly.

To compare fractions and put them in order from least to greatest, you can follow these steps:

1. Find a common denominator: To compare fractions, you need to make sure they have the same denominators. Look for the smallest common multiple of the denominators in the set of fractions.

For example:
1. In the first set of fractions (2/5, 1/10, 3/20), the smallest common multiple of 5, 10, and 20 is 20.
2. In the second set of fractions (1/3, 3/8, 2/9), the smallest common multiple of 3, 8, and 9 is 72.

2. Convert fractions to have the same denominator: Once you have a common denominator, you need to convert the fractions to have that denominator.

For example:
1. In the first set, convert the fractions:
2/5 becomes 8/20 (multiplied numerator and denominator by 4)
1/10 becomes 2/20 (multiplied numerator and denominator by 2)
3/20 remains as is since it already has the common denominator.

2. In the second set, convert the fractions:
1/3 becomes 24/72 (multiplied numerator and denominator by 24)
3/8 becomes 27/72 (multiplied numerator and denominator by 9)
2/9 becomes 16/72 (multiplied numerator and denominator by 8)

3. Compare the numerators: Now that the fractions have the same denominator, you can compare the numerators to determine their order.

For example:
1. In the first set of fractions (8/20, 2/20, 3/20), the numerators are 8, 2, and 3 respectively. So the order from least to greatest is 2/20, 3/20, 8/20, which simplifies to 1/10, 3/20, 2/5.

2. In the second set of fractions (24/72, 27/72, 16/72), the numerators are 24, 27, and 16 respectively. So the order from least to greatest is 24/72, 16/72, 27/72, which simplifies to 2/9, 1/3, 3/8.

These steps help you compare fractions and determine their order from least to greatest.