If there are 18 apples and 30 bananas for a fruit basket, fill out all of the possible ratios of apples to bananas that could be made.
To find all possible ratios of apples to bananas, we need to determine all the possible ways we can divide the total number of apples and bananas.
The ratio of apples to bananas can be expressed as a fraction using the following format: apples:bananas.
To simplify the ratios, we can divide both the number of apples and bananas by their greatest common divisor (GCD).
The GCD of 18 and 30 is 6. So, we obtain:
18 ÷ 6 = 3 apples
30 ÷ 6 = 5 bananas
Therefore, the simplified ratio of apples to bananas is 3:5.
However, we should consider all possible combinations by multiplying the numerator and denominator by different positive integers.
Here are all the possible ratios of apples to bananas:
1) 3:5 (the simplified ratio)
2) 6:10 (multiply both numbers by 2)
3) 9:15 (multiply both numbers by 3)
4) 12:20 (multiply both numbers by 4)
5) 15:25 (multiply both numbers by 5)
6) 18:30 (the initial ratio)
7) 21:35 (multiply both numbers by 7)
8) 24:40 (multiply both numbers by 8)
9) 27:45 (multiply both numbers by 9)
10) 30:50 (multiply both numbers by 10)
Therefore, there are 10 possible ratios of apples to bananas that could be made.