Divide Numbers up to 4 Digits by a Two-Digit Whole Number Using the Formal Written Method of Long Division 5 - Reasoning

Esin has diligently saved up 8,034 pence and is looking to purchase a pencil using all of her money. However, she faces a dilemma in choosing between two pencils, one green and one red, each priced differently. Through the use of formal written methods of long division, we can determine which pencil would allow her to receive change back. The green pencil costs 78 pence, and when we divide Esin's savings by this amount, we get an exact quotient of 103, meaning she would use all her money with no change remaining. On the other hand, the red pencil is priced at 76 pence. Dividing her savings by the cost of the red pencil, we find that she would be left with a remainder, specifically 105 pencils with 54 pence change.

Based on these calculations, if Esin wishes to have some money left over after her purchase, she should opt for the red pencil. The reasoning behind this is clear: buying the red pencil for 76 pence each would not exhaust her savings completely, leaving her with 54 pence as change. This exercise not only helps Esin make a decision but also demonstrates the practical application of long division in real-life scenarios, where understanding remainders is crucial for financial decisions such as making purchases and expecting change.