Divide Numbers up to 4 Digits by a Two-Digit Whole Number Using the Formal Written Method of Long Division 4 - Reasoning

Leanna and Tia are engaged in a practical application of their mathematical skills as they tackle the task of making necklaces from a collection of 3,762 beads. Each necklace they plan to create requires 36 beads. The challenge lies in determining how many complete necklaces can be made from their bead stash. Leanna asserts that they can make 104 necklaces, while Tia believes they can create 105. Upon applying the formal written method of long division to divide 3,762 by 36, it becomes apparent that the correct answer is 104 necklaces, with a remainder of 18 beads left over. Therefore, Leanna's calculation is accurate, as the leftover beads are insufficient to complete another necklace.

The reasoning behind the correct answer involves understanding the process of long division and recognizing that any remainder does not constitute a full unit—in this case, a complete necklace. Even though there are extra beads remaining after making 104 necklaces, these 18 beads do not meet the required number to form an additional necklace. Hence, while Tia's suggestion of 105 necklaces is optimistic, it is not feasible with the given number of beads. This exercise highlights the importance of precision in mathematical operations, particularly when it comes to real-world scenarios where the results have practical implications, such as in the crafting of jewellery.