The four steps of long division
The four steps of long division—Divide, Multiply, Subtract, and Bring Down—are the repeating cycle for solving multi-digit division problems in Grade 4, Saxon Math Intermediate 4 Chapter 8. Students apply this cycle to each digit of the dividend until no digits remain. For example, dividing 974 by 4: divide 9 by 4 equals 2, multiply 2 times 4 equals 8, subtract 9 minus 8 equals 1, bring down 7 to make 17, and repeat. The final leftover after the last subtraction is the remainder. Precise alignment of quotient digits above the dividend is critical.
Key Concepts
To perform long division, repeat these four steps in order: Step 1: Divide. Step 2: Multiply. Step 3: Subtract. Step 4: Bring down. This cycle continues until no digits remain to bring down. The final leftover number, if any, is the remainder. This structured process breaks down large division problems into manageable parts.
For $4 \overline{)974}$: Divide 9 by 4 is 2. Multiply $2 \times 4 = 8$. Subtract $9 8 = 1$. Bring down 7 to make 17. Repeat: Divide 17 by 4 is 4. Multiply $4 \times 4 = 16$. Subtract $17 16 = 1$. Bring down 4 to make 14. Repeat: Divide 14 by 4 is 3. Multiply $3 \times 4 = 12$. Subtract $14 12 = 2$. The answer is 243 R 2. For $6 \overline{)1512}$: Divide 15 by 6 is 2. Multiply $2 \times 6 = 12$. Subtract $15 12 = 3$. Bring down 1 to make 31. Repeat: Divide 31 by 6 is 5. Multiply $5 \times 6 = 30$. Subtract $31 30 = 1$. Bring down 2 to make 12. Repeat: Divide 12 by 6 is 2. The answer is 252.
Think of long division as a dance with four moves: Divide, Multiply, Subtract, and Bring Down! You just keep repeating this dance routine for each digit in your big number until you run out of partners to bring down. It’s the same rhythm every time, making huge problems easy to solve step by step!
Common Questions
What are the four steps of long division?
Divide, Multiply, Subtract, and Bring Down. Repeat this four-step cycle for every digit in the dividend.
How do I use the four steps to solve 974 divided by 4?
Divide 9 by 4 equals 2. Multiply 2 times 4 equals 8. Subtract 9 minus 8 equals 1. Bring down 7 to make 17. Divide 17 by 4 equals 4. Multiply 4 times 4 equals 16. Subtract 17 minus 16 equals 1. Bring down 4 to make 14. Divide 14 by 4 equals 3. Multiply 3 times 4 equals 12. Subtract 14 minus 12 equals 2. Answer: 243 R 2.
What does bring down mean in long division?
Bring down means taking the next unused digit from the dividend and placing it to the right of the current remainder to form a new number for the next division step.
How do I know when long division is complete?
Long division is complete when you have brought down and processed every digit of the dividend and have no more digits to bring down.
Why is alignment important in long division?
Each quotient digit must be written directly above the last digit of the portion of the dividend being divided. Misalignment produces digits in the wrong place value.