Standard Algorithm for Long Division with Four-Digit Dividends
Standard Algorithm for Long Division with Four-Digit Dividends is a Grade 4 math skill that extends long division to its most complex elementary form: dividing a four-digit number by a one-digit divisor. The algorithm applies the same divide-multiply-subtract-bring-down cycle four times, requiring careful alignment, handling of zero quotient digits, and multi-step regrouping. For example, 4,236 / 6 = 706. Covered in Chapter 13 of Eureka Math Grade 4, mastery of four-digit long division completes Grade 4 division fluency and prepares students for multi-digit divisor problems in Grade 5.
Key Concepts
To perform long division, we systematically divide the dividend by the divisor, place value by place value, from left to right. The relationship between the parts of a division problem is given by: $$(Quotient \times Divisor) + Remainder = Dividend$$.
Common Questions
How do I solve a four-digit long division problem?
Apply the divide-multiply-subtract-bring-down cycle starting with the thousands digit. When the partial dividend at any step is smaller than the divisor, write 0 in the quotient and bring down the next digit to form a larger number. Continue until all digits have been processed.
How do I solve 4,236 / 6?
Step 1: 4 thousands / 6 = 0 (too small), so include the next digit: 42 hundreds / 6 = 7. Write 7 above the hundreds. Subtract: 42 - 42 = 0. Bring down 3 (tens): 03 / 6 = 0, write 0. Bring down 6 (ones): 36 / 6 = 6. Quotient: 706.
What do I do when the partial dividend is smaller than the divisor?
Write 0 in that position in the quotient and bring down the next digit to form a two-digit (or larger) partial dividend. This is the same rule used in three-digit division, extended to four digits.
How do I check a four-digit division answer?
Multiply the quotient by the divisor and add any remainder. The result should equal the original dividend. For 4,236 / 6 = 706: check 706 x 6 = 4,236. If confirmed, the answer is correct.
What are common errors in four-digit long division?
Common errors: forgetting to write 0 in the quotient when the partial dividend is less than the divisor, misaligning digits in the quotient, and arithmetic mistakes in the multiply and subtract steps. Careful vertical alignment prevents most of these errors.
What chapter in Eureka Math Grade 4 covers four-digit division?
Chapter 13: Division of Tens and Ones with Successive Remainders in Eureka Math Grade 4 develops long division from two-digit to four-digit dividends, systematically building the algorithm's complexity.