Question

If there are 28 apples and 42 bananas for a fruit basket, fill out all of the possible ratios of apples to bananas that could be made.

Answer 1

28:42, 21:14, 7:10.5, 56:84

There are a lot more, but for the basics of ratios you only need to know this:

- The order is very important in the ratio, whatever number came first stays in that order.

- You can only multiply or divide the same numbers. For instance, if the ratio was 1:2, you would multiply or divide the numbers by the same number.

- When you multiply or divide the ratio/numbers, you cannot not only do whole numbers, but also decimals like 0.25 or mixed decimals like 1.5.

- Remember numbers are infinite, so you can multiply or divide your ratio/numbers by any decimal or number.

Hope this helps! :D

Answer 2

All the possible ratios of apples to bananas are multiples of
`\( (2)/(3) \)`.

To find all possible ratios of apples to bananas, we can express the ratio as a fraction and simplify it. The ratios can be written as
`\(\frac{\text{number of apples}}{\text{number of bananas}}\)`. In this case, the given quantities are 28 apples and 42 bananas.

1. Original Ratio:

- Apples to Bananas:
`\( (28)/(42) \)`

- Simplified Ratio:
`\( (2)/(3) \)`

2. Equivalent Ratios:

- We can multiply both the numerator and denominator of the original ratio by the same nonzero number to get equivalent ratios.

- For example, multiplying by 2:

-
`\( (28 * 2)/(42 * 2) = (56)/(84) \)`

- Simplified Ratio:
`\( (2)/(3) \)` (equivalent to the original)

- Multiplying by 3:

-
`\( (28 * 3)/(42 * 3) = (84)/(126) \)`

- Simplified Ratio:
`\( (2)/(3) \)` (equivalent to the original)

- Multiplying by 4:

-
`\( (28 * 4)/(42 * 4) = (112)/(168) \)`

- Simplified Ratio:
`\( (2)/(3) \)` (equivalent to the original)

...and so on.

All the possible ratios of apples to bananas are multiples of
`\( (2)/(3) \)`. These ratios are equivalent and represent different amounts of apples and bananas in the fruit basket.