Final answer:
To retain the same value, the number of longs needed when there are 4 flats is 5.
Step-by-step explanation:
To retain the same value, we can use the concept of equivalency. In the given collection of base ten pieces, 5 flats, 6 longs, and 8 units represent a certain value. To find the number of longs needed when there are 4 flats, we can set up a proportion: (Number of longs needed) / 6 = 4 / 5. Cross-multiplying, we get (Number of longs needed) * 5 = 6 * 4. Simplifying, we find that (Number of longs needed) = 24 / 5 = 4.8.
Since we can't have a fraction of a long, we need to round to the nearest whole number. In this case, when rounding up or down, we use the rule that if a number is 5 or greater, we round up, but if it's less than 5, we round down. In this case, since 0.8 is greater than 0.5, we round up to 5.
Therefore, the answer is 5 longs (Option b) to retain the same value.