Long Division
Learn to divide large numbers by 2-digit divisors using the long division method. Follow the steps: Divide, Multiply, Subtract, Bring down.
The DMSB Method
Long division follows four repeating steps. A helpful way to remember them is DMSB:
D
Divide
How many times does the divisor go in?
M
Multiply
Multiply divisor by the answer
S
Subtract
Subtract to find the remainder
B
Bring down
Bring down the next digit
Repeat these four steps until there are no more digits to bring down.
Step-by-Step: 756 ÷ 12
Step 1 (D): 12 goes into 7 zero times. Look at 75 instead. 12 goes into 75 six times (12 × 6 = 72).
Step 2 (M): 12 × 6 = 72. Write 72 below 75.
Step 3 (S): 75 - 72 = 3.
Step 4 (B): Bring down the 6 to make 36.
Step 5 (D): 12 goes into 36 exactly three times (12 × 3 = 36).
Step 6 (M): 12 × 3 = 36. Write 36 below.
Step 7 (S): 36 - 36 = 0. No remainder!
Answer: 756 ÷ 12 = 63
Division with Remainders
Sometimes the division does not work out evenly. The amount left over is called the remainder. We write it as r followed by the leftover amount.
Example: 500 ÷ 14
D: 14 into 50 goes 3 times (14 × 3 = 42)
M/S: 50 - 42 = 8. Bring down 0 to make 80.
D: 14 into 80 goes 5 times (14 × 5 = 70)
M/S: 80 - 70 = 10. No more digits to bring down.
Answer: 500 ÷ 14 = 35 r 10
Interpreting Remainders
In real life, what you do with a remainder depends on the situation:
Round Up
100 students need buses that hold 32 each. 100 ÷ 32 = 3 r 4. You need 4 buses (round up so no one is left behind).
Ignore the Remainder
You have $50 and each book costs $12. 50 ÷ 12 = 4 r 2. You can buy 4 books (you cannot buy part of a book).
Key Vocabulary
Dividend
The number being divided (e.g. in 756 ÷ 12, the dividend is 756).
Divisor
The number you are dividing by (e.g. in 756 ÷ 12, the divisor is 12).
Quotient
The answer to a division (e.g. 756 ÷ 12 = 63, the quotient is 63).
Remainder
The amount left over when a division does not work out evenly.
Worked Examples
Calculate 864 ÷ 24
Step 1: 24 into 86 goes 3 times (24 × 3 = 72). 86 - 72 = 14.
Step 2: Bring down 4 to make 144. 24 into 144 goes 6 times (24 × 6 = 144).
Answer: 36
A school has 475 students to split into teams of 15. How many full teams?
Step 1: 15 into 47 goes 3 times (15 × 3 = 45). 47 - 45 = 2.
Step 2: Bring down 5 to make 25. 15 into 25 goes 1 time (15 × 1 = 15). 25 - 15 = 10.
Answer: 31 full teams with 10 students left over.
Calculate 1 350 ÷ 25
Step 1: 25 into 13 goes 0 times. Look at 135. 25 × 5 = 125. 135 - 125 = 10.
Step 2: Bring down 0 to make 100. 25 into 100 goes 4 times (25 × 4 = 100). Remainder 0.
Answer: 54
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is 624 ÷ 12?
Question 2
What is 945 ÷ 15?
Question 3
350 lollies are shared equally among 16 children. How many does each child get, and how many are left over?
Question 4
In long division, what does the "B" in DMSB stand for?
Question 5
What is 1 200 ÷ 25?
Key Concepts Summary
- ●Long division follows four steps: Divide, Multiply, Subtract, Bring down (DMSB).
- ●The dividend is divided by the divisor to give the quotient.
- ●A remainder is the amount left over when the division is not exact.
- ●Always check your answer by multiplying the quotient by the divisor.
- ●In real life, decide whether to round up, round down, or keep the remainder.