Final answer:
To rewrite fractions (13/30) and (9/20) with a common denominator, find their least common multiple (60), then convert each fraction—(26/60) and (27/60). Now, we can easily order or compare the fractions.
Step-by-step explanation:
To rewrite the fractions (13/30) and (9/20) with a common denominator, we first need to find a number that both denominators can divide into, that is, the least common multiple (LCM) of 30 and 20. The LCM of 30 and 20 is 60. Therefore, we need to convert each fraction to an equivalent fraction with a denominator of 60.
To convert (13/30) to a fraction with a denominator of 60, we need to determine what number multiplies by 30 to get 60. We find that 30 multiplied by 2 equals 60, so we must also multiply the numerator 13 by 2. This gives us (13 * 2)/(30 * 2) which simplifies to (26/60).
In the case of (9/20), we need to figure out what number multiplies by 20 to make 60. Multiplying 20 by 3 gives us 60, so the numerator 9 should also be multiplied by 3. Thus, we get (9 * 3)/(20 * 3) which simplifies to (27/60).
Now, (13/30) and (9/20) are rewritten as (26/60) and (27/60), respectively. With a common denominator, we can easily compare or order these fractions.