Long Division with Remainders
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Learning Objectives
- 1Divide a 2-digit or 3-digit dividend by a 1-digit divisor using the long-division algorithm
- 2Apply the four-step cycle of divide, multiply, subtract, and bring down until the dividend is finished
- 3Identify the quotient and the remainder in a division problem and write the answer in the form Q R r
- 4Check a division answer by multiplying quotient times divisor and adding the remainder
Mini Lesson
Long division splits a big sharing problem into a series of small steps. You divide one place-value column at a time, repeating the same four moves until you run out of digits. When the divisor does not go in evenly, the leftover amount is called the remainder.
The Four-Step Cycle
- Divide: ask how many times the divisor fits into the current digit (or pair of digits) of the dividend.
- Multiply: multiply that quotient digit by the divisor and write the result under the dividend digits used.
- Subtract: take the product away from the digits above to find what is left.
- Bring down: pull the next digit of the dividend down beside the difference, then start the cycle again.
- Stop when there are no more digits to bring down — whatever is left after the last subtraction is the remainder.
Worked Example: 87 / 4
- Divide: 4 goes into 8 two times. Write 2 above the 8.
- Multiply: 2 x 4 = 8. Write 8 under the 8.
- Subtract: 8 - 8 = 0.
- Bring down: pull the 7 down to make 07 (just 7).
- Divide again: 4 goes into 7 one time. Write 1 above the 7.
- Multiply: 1 x 4 = 4. Write 4 under the 7.
- Subtract: 7 - 4 = 3. No more digits to bring down, so 3 is the remainder.
- Final answer: 87 / 4 = 21 R 3.
What is the Remainder?
- The remainder is what is left over after the divisor has been taken out as many whole times as it can.
- The remainder must always be smaller than the divisor — if it is bigger, you missed a step.
- Write it as R followed by the leftover number, for example 21 R 3.
- Real life: 87 cookies shared by 4 friends gives each friend 21 cookies, with 3 cookies left over.
Checking Your Answer
- Multiply the quotient by the divisor: 21 x 4 = 84.
- Add the remainder: 84 + 3 = 87.
- If the result equals the dividend, your answer is correct.
- Formula: dividend = (quotient x divisor) + remainder.
Memory Aid for the Steps
- Some learners remember the order with: Does McDonalds Sell Burgers?
- D = Divide, M = Multiply, S = Subtract, B = Bring down.
- Repeat that sentence in your head every time you start a new column.
Tip: line up each new digit you bring down directly under the dividend digit it came from. Keeping straight columns prevents place-value mistakes that turn a correct quotient into a wrong one.
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