Executing the Standard Algorithm for Three-Digit Division
Executing the Standard Algorithm for Three-Digit Division is a Grade 4 math skill that extends long division to three-digit dividends, applying the same divide-multiply-subtract-bring-down cycle to hundreds, tens, and ones in sequence. For 657 / 3, students first divide the hundreds (6/3 = 2), then bring down the tens (05, which is less than 3, so the tens quotient is 0), then divide the ones (57/3 = 19), giving the quotient 219. Covered in Chapter 13 of Eureka Math Grade 4, this skill is the capstone multi-digit division procedure for Grade 4.
Key Concepts
The standard algorithm for division is a step by step process to find a quotient and a remainder. The relationship is defined by: $Dividend = (Quotient \times Divisor) + Remainder$.
Common Questions
What are the steps of long division for a three-digit number?
Divide, multiply, subtract, and bring down — repeat for each digit. Start with the hundreds digit, then the tens, then the ones. When a partial dividend is less than the divisor, write 0 in the quotient and bring down the next digit.
How do I solve 657 / 3 using the standard algorithm?
Step 1: Divide 6 hundreds by 3 = 2, write 2 above the hundreds. Step 2: Multiply 2 x 3 = 6, subtract 6-6 = 0. Step 3: Bring down 5 (tens). 05 / 3 = 1, write 1 above the tens. Subtract 3 from 5, remainder 2. Step 4: Bring down 7, making 27. 27 / 3 = 9. Quotient: 219.
What do I do when a partial dividend is smaller than the divisor?
When the current partial dividend is smaller than the divisor, write 0 in that quotient position and bring down the next digit to form a larger number. For example, if dividing 5 by 6, since 5 < 6, write 0 and bring down the next digit.
How do I check my long division answer?
Multiply the quotient by the divisor and add any remainder. If the result equals the original dividend, your answer is correct. For 657 / 3 = 219: verify by computing 219 x 3 = 657.
What common mistakes occur in three-digit long division?
Common mistakes include forgetting to write a 0 in the quotient when a partial dividend is smaller than the divisor, misaligning digits in the quotient, and arithmetic errors in the multiply-and-subtract steps. Careful alignment and checking each step prevents these errors.
What chapter covers three-digit division in Eureka Math Grade 4?
Chapter 13: Division of Tens and Ones with Successive Remainders in Eureka Math Grade 4 develops long division systematically, culminating in three-digit and four-digit dividend problems.