First Step In Division Problem 8 Divided By 6288

In the realm of mathematics, division stands as a fundamental operation, essential for solving a myriad of problems ranging from basic arithmetic to complex equations. When faced with a division problem, especially one involving larger numbers, it's crucial to approach it systematically to ensure accuracy and efficiency. This article delves into the first step in solving a specific division problem: $8 \longdiv { 6 2 8 8 }$. We'll dissect the options provided, elucidate the correct approach, and provide a comprehensive understanding of the underlying principles of division.

Dissecting the Division Problem: $8 \longdiv { 6 2 8 8 }$

When presented with the problem $8 \longdiv { 6 2 8 8 }$, the immediate task is to determine how to initiate the division process. The problem essentially asks: "How many times does 8 fit into 6288?" To answer this, we embark on a step-by-step journey, focusing on manageable segments of the dividend (6288). The given options present different approaches, but only one aligns with the correct initial step in long division.

Option A: Divide 8 into 62 to get 7

This option suggests that the first step involves dividing 8 into 62, resulting in 7. This is a valid consideration because we are looking at how many times 8 can fit into the first two digits of the dividend, which is 62. To assess this, we consider the multiples of 8. We know that 8 multiplied by 7 equals 56, which is less than 62. So, 7 is a plausible quotient for this initial step. Therefore, option A correctly identifies the first operation: dividing 8 into 62.

Option B: Divide 8 into 62 to get 8

Similar to Option A, this option directs us to divide 8 into 62. However, it proposes that the result is 8. While the operation is correct, the result needs careful verification. Multiplying 8 by 8 gives 64, which is greater than 62. This indicates that 8 is too large a quotient for this step. Therefore, while the initial operation is correct, the suggested result is inaccurate, making option B incorrect.

Option C: Multiply 8 by 7 to get 56

This option shifts the focus to multiplication, specifically multiplying 8 by 7 to get 56. While this multiplication is accurate and relevant to the division process (as it helps us determine how many times 8 fits into 62), it's not the first step. Multiplication comes into play after we've made an initial estimate of the quotient. So, while important, this step is subsequent to the initial division.

Option D: Multiply 8 by 8 to get 62

This option presents a multiplication (8 by 8), but the result (62) is inaccurate. Eight multiplied by eight equals 64, not 62. Additionally, similar to Option C, multiplication is not the very first step in the division process. We first need to determine the initial quotient by dividing. Thus, option D is incorrect due to both the inaccurate result and the misplacement of the step in the division sequence.

The Correct First Step: Option A in Detail

The correct first step, as identified in Option A, is to divide 8 into 62. This is the logical starting point for long division because we are assessing how many times the divisor (8) fits into the initial portion of the dividend (62). Here’s a detailed breakdown:

1. Identify the Part of the Dividend: We start by considering the first two digits of the dividend, 62, because 8 does not fit into 6 (the first digit) alone.
2. Estimate the Quotient: We need to estimate how many times 8 goes into 62. Thinking about multiples of 8, we know:
   • 8 x 7 = 56
   • 8 x 8 = 64
3. Determine the Initial Quotient: Since 56 is less than 62 and 64 is greater, 7 is the correct initial quotient. This means 8 fits into 62 seven times.

Therefore, the first step is indeed to divide 8 into 62, resulting in 7. This forms the foundation for the subsequent steps in long division.

Long Division: A Step-by-Step Process

To further clarify the importance of this initial step, let's outline the complete process of long division for the problem $8 \longdiv { 6 2 8 8 }$:

1. Divide 8 into 62: As we've established, 8 goes into 62 seven times. Write the 7 above the 2 in the quotient.
2. Multiply: Multiply the quotient (7) by the divisor (8): 7 x 8 = 56. Write 56 below 62.
3. Subtract: Subtract 56 from 62: 62 - 56 = 6. This is the remainder from the first division.
4. Bring Down: Bring down the next digit from the dividend (8) next to the remainder (6), forming the new number 68.
5. Divide 8 into 68: Determine how many times 8 goes into 68. Eight goes into 68 eight times (8 x 8 = 64).
6. Write the Quotient: Write the 8 next to the 7 in the quotient.
7. Multiply: Multiply the new quotient digit (8) by the divisor (8): 8 x 8 = 64. Write 64 below 68.
8. Subtract: Subtract 64 from 68: 68 - 64 = 4. This is the new remainder.
9. Bring Down: Bring down the last digit from the dividend (8) next to the remainder (4), forming the number 48.
10. Divide 8 into 48: Determine how many times 8 goes into 48. Eight goes into 48 six times (8 x 6 = 48).
11. Write the Quotient: Write the 6 next to the 78 in the quotient.
12. Multiply: Multiply the new quotient digit (6) by the divisor (8): 6 x 8 = 48. Write 48 below 48.
13. Subtract: Subtract 48 from 48: 48 - 48 = 0. The remainder is 0, indicating a complete division.

Therefore, $8 \longdiv { 6 2 8 8 } = 786$.

Why Understanding the First Step Matters

The first step in long division is pivotal because it sets the stage for the entire process. A correct initial step ensures that the subsequent steps are based on a sound foundation. An incorrect initial step, on the other hand, can lead to a cascading series of errors, resulting in an inaccurate final answer. By meticulously dividing the divisor into the appropriate segment of the dividend, we establish the correct magnitude of the quotient, which is crucial for accurate calculations.

Moreover, mastering the first step fosters a deeper understanding of the division process. It reinforces the concept of how many times one number fits into another, a fundamental aspect of division. This understanding is transferable to other mathematical contexts and is essential for problem-solving skills.

Conclusion

In summary, when solving the division problem $8 \longdiv { 6 2 8 8 }$, the first step is to divide 8 into 62, which gives us 7. This initial step is not merely a procedural action; it is the cornerstone of the entire division process. By accurately determining how many times the divisor fits into the initial segment of the dividend, we pave the way for a successful and accurate solution. Understanding this principle is crucial for mastering division and enhancing overall mathematical proficiency. This detailed explanation highlights the significance of option A and underscores the importance of a methodical approach to solving division problems.

Therefore, option A, "Divide 8 into 62 to get 7," is the correct answer. This is the logical and accurate first step in solving the long division problem $8 \longdiv { 6 2 8 8 }$.

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