If there are 30 lollipops and 54 candy bars for a gift bag, fill out all of the possible ratios of lollipops to candy bars that could be made.
To find all possible ratios of lollipops to candy bars, we need to determine the greatest common divisor (GCD) of 30 and 54. The GCD will help us simplify the ratios.
The prime factorization of 30 is 2 × 3 × 5.
The prime factorization of 54 is 2 × 3^3.
Thus, the GCD of 30 and 54 is 2 × 3 = 6.
Now, we can divide both 30 and 54 by 6 to simplify.
30 ÷ 6 = 5
54 ÷ 6 = 9
The simplified ratio is 5:9.
Therefore, the only possible ratio of lollipops to candy bars that could be made is 5:9.