The four steps of division
The four steps of division are the repeating procedure for long division: Divide, Multiply, Subtract, Bring Down. In Grade 4 math from Saxon Math Intermediate 4 Chapter 7, students apply this four-step cycle for each digit in the dividend—for example, 6)147 → quotient 24 R 3. After the last subtraction, any remaining amount becomes the remainder, written as R before the number. Mastering this procedure is essential for all multi-digit division in upper elementary and middle school.
Key Concepts
Property: The method for dividing has four steps that are repeated until the division is complete: 1. Divide, 2. Multiply, 3. Subtract, and 4. Bring down. After the last subtraction, the number left over is the remainder, which is written with an uppercase 'R' in front of it.
For $6\overline{)147}$: First, divide 14 by 6 to get 2. Multiply $2 \times 6 = 12$. Subtract $14 12 = 2$. Bring down 7 to make 27. Then, divide 27 by 6 to get 4. Multiply $4 \times 6 = 24$. Subtract $27 24 = 3$. The answer is 24 R 3. For $97 \div 4$: First, divide 9 by 4 to get 2. Multiply $2 \times 4 = 8$. Subtract $9 8 = 1$. Bring down 7 to make 17. Then, divide 17 by 4 to get 4. Multiply $4 \times 4 = 16$. Subtract $17 16=1$. The answer is 24 R 1.
Think of long division as a repeating four step dance routine for numbers. First, you divide a part of the dividend. Then, you multiply that result back. Next, you subtract to find the leftover amount. Finally, you bring down the next digit to start the dance all over again until you run out of partners to dance with.
Common Questions
What are the four steps of long division?
Divide, Multiply, Subtract, Bring Down—repeated for each digit in the dividend. Remember the cycle with the mnemonic Does McDonald Sell Burgers? (Divide, Multiply, Subtract, Bring down).
How do you apply the four steps to 6 divided into 147?
Divide 14 by 6 = 2. Multiply 2 × 6 = 12. Subtract 14 − 12 = 2. Bring down 7 to make 27. Divide 27 by 6 = 4. Multiply 4 × 6 = 24. Subtract 27 − 24 = 3. No more digits, so the answer is 24 R 3.
What is a remainder in division?
A remainder is the amount left over after dividing as evenly as possible. It is always less than the divisor and is written with an R. For 147 ÷ 6 = 24 R 3, the remainder is 3.
When do Grade 4 students learn long division?
The four-step long division method is introduced in Chapter 7 of Saxon Math Intermediate 4 as students extend basic division facts to multi-digit dividends.
What happens when you bring down and the result is smaller than the divisor?
Write a 0 in the quotient and bring down the next digit. For example, dividing 3 into 525: after finding 1 in the hundreds, bring down 2; since 5 does not go into 2, write 0, bring down 5 to get 25, and divide to get 5.
How does long division connect to fractions?
A fraction like 7/3 means 7 ÷ 3. Performing long division gives 2 R 1, which means 7/3 = 2 + 1/3 = 2 and one-third as a mixed number.