Final answer:
Calculating 3120 divided by 48 results in 65 with no remainder. The process can be simplified mentally by dividing by factors of 48. Checking the result via multiplication confirms accuracy and reflects the diversity of paths to a solution in mathematics.
Step-by-step explanation:
Understanding Division with Remainders
To calculate 3120 divided by 48, one can use long division or consider factors that simplify the process. If we assess the division mentally, recognizing that 48 is divisible by 8 could help. For example, 48 can be re-expressed as 6×8, a product of smaller, more manageable numbers. Following this logic, 3120 can be divided by these numbers sequentially.
Let's divide 3120 by 6 first: we get 520. Now take 520 and divide that by 8, which equals 65. Therefore, 3120 divided by 48 is 65 without any remainders.
The question mentions division with remainders, but in this case, there is no remainder. However, it is still crucial to understand how to determine a remainder. If a number does not divide evenly, the remainder is the difference between the last subtracted multiple and the dividend. In mathematical terms, the remainder is the value that is left over after the division is complete, expressed as 'Dividend = Divisor × Quotient + Remainder.'
Here's a simplified example: 20 divided by 6. The quotient is 3, and the remainder is 2, because 6×3=18 and 20-18=2.
Furthermore, you can check your answer using multiplication. In our case, the result of 65 times 48 should equal 3120, ensuring there are no remainders. This approach demonstrates that math offers multiple paths to the same solution, an important concept that enables verification and reinforces understanding.