How Many Pears are in the Partially Filled Tray When a Farmer Packs 49 Pears into Trays Holding 7 Pears Each?

When it comes to packing fruits like pears, farmers often use trays to organize and transport their produce. These trays are designed to hold a specific number of fruits to ensure they are not damaged during transportation. In this scenario, a farmer has 49 pears and each tray can hold 7 pears. The question that arises is, how many pears are in the partially filled tray? To answer this, we need to understand the concept of division and remainders in mathematics.

Understanding Division and Remainders

Division is one of the four basic operations in arithmetic, along with addition, subtraction, and multiplication. When we divide a number (the dividend) by another number (the divisor), we get a quotient and sometimes a remainder. The remainder is the amount left over after division. In this case, we are dividing 49 (the number of pears) by 7 (the number of pears each tray can hold).

Calculating the Number of Trays

To calculate the number of trays needed, we divide the total number of pears by the number of pears each tray can hold. Using the division operation, 49 divided by 7 equals 7. This means that the farmer can fill 7 trays completely with 7 pears each.

Identifying the Partially Filled Tray

Since the total number of pears (49) is an exact multiple of the number of pears each tray can hold (7), there is no remainder. This means that all the trays are completely filled and there is no partially filled tray. In other words, every tray has 7 pears and none of them is partially filled.

Conclusion

Understanding the concept of division and remainders is crucial in solving problems like this. In this case, the number of pears perfectly fits into the trays, leaving no partially filled tray. However, if the total number of pears was not an exact multiple of the number of pears each tray can hold, there would be a remainder, indicating a partially filled tray. For example, if the farmer had 52 pears, dividing by 7 would give a quotient of 7 and a remainder of 3. This would mean that 7 trays are completely filled and one tray is partially filled with 3 pears.