📚 Study helper: This page helps you learn and practice for school. Read it, listen to it, and try to say the four steps in order!
Long division is a way to split a big number into equal groups.
You use the same four steps again and again.
Step one is Divide.
Step two is Multiply.
Step three is Subtract.
Step four is Bring down.
You repeat the steps until there is nothing left to bring down.
What is left at the end is the remainder.
If nothing is left, the remainder is 0.
Elementary: One Worked Example, Step by Step
Let us do one problem together, slowly.
Our problem is 96 ÷ 4.
We share 96 into 4 equal groups.
The answer is called the quotient.
Follow each numbered step. Do not skip a step.
First round: work on the 9
Step 1. Divide. How many times does 4 go into 9? It goes in 2 times. Write 2 on top. It is the first digit of the quotient.
Step 2. Multiply. 2 × 4 = 8. Write 8 under the 9.
Step 3. Subtract. 9 − 8 = 1. Write 1 below.
Step 4. Bring down. The next digit in 96 is 6. Bring the 6 down next to the 1. Now you have 16.
Second round: work on the 16
Step 5. Divide. How many times does 4 go into 16? It goes in 4 times. Write 4 on top, next to the 2. The top now reads 24.
Step 6. Multiply. 4 × 4 = 16. Write 16 under the 16.
Step 7. Subtract. 16 − 16 = 0. Write 0 below.
Step 8. Bring down. There is nothing left to bring down. You are done.
The answer and the check
So 96 ÷ 4 = 24.
Check your work. Multiply the quotient by the divisor.
24 × 4 = 96.
You get back to 96, the number you started with. The answer is right.
Middle School: Longer Problems and a Remainder
In middle school the numbers get longer, but the cycle does not change.
For each digit position you divide, multiply, subtract, and bring down, in that exact order, and you keep careful track of place value so each quotient digit lands above the right part of the dividend.
The check also grows up: dividend = divisor × quotient + remainder. If that equation balances, your work balances.
Example 1: 952 ÷ 7 = 136
Step 1. Divide. 7 goes into 9 one time. Write 1 on top.
Step 2. Multiply. 1 × 7 = 7. Write 7 under the 9.
Step 3. Subtract. 9 − 7 = 2.
Step 4. Bring down. Bring down the 5 next to the 2. You now work with 25.
Step 5. Divide. 7 goes into 25 three times, because 3 × 7 = 21 and 4 × 7 = 28 is too big. Write 3 on top. The top now reads 13.
Step 6. Multiply. 3 × 7 = 21. Write 21 under the 25.
Step 7. Subtract. 25 − 21 = 4.
Step 8. Bring down. Bring down the 2 next to the 4. You now work with 42.
Step 9. Divide. 7 goes into 42 six times. Write 6 on top. The top now reads 136.
Step 10. Multiply. 6 × 7 = 42. Write 42 under the 42.
Step 11. Subtract. 42 − 42 = 0. There is nothing left to bring down, so the division ends with remainder 0.
Check: 136 × 7 = 952. That matches the dividend, so 952 ÷ 7 = 136 is correct.
Example 2, with a remainder: 377 ÷ 5 = 75 remainder 2
Sometimes the divisor does not fit into the first digit at all. That is what happens here, and handling it cleanly is the main new skill in this example.
Step 1. Divide. 5 goes into 3 zero times. It does not fit. So you look at the first two digits together and start with 37 instead.
Step 2. Divide. 5 goes into 37 seven times, because 7 × 5 = 35 and 8 × 5 = 40 is too big. Write 7 on top, above the 7 in 37.
Step 3. Multiply. 7 × 5 = 35. Write 35 under the 37.
Step 4. Subtract. 37 − 35 = 2.
Step 5. Bring down. Bring down the last 7 next to the 2. You now work with 27.
Step 6. Divide. 5 goes into 27 five times, because 5 × 5 = 25 and 6 × 5 = 30 is too big. Write 5 on top. The top now reads 75.
Step 7. Multiply. 5 × 5 = 25. Write 25 under the 27.
Step 8. Subtract. 27 − 25 = 2.
Step 9. Bring down. There is nothing left to bring down. The 2 that remains cannot make another full group of 5, so 2 is the remainder.
Check: 75 × 5 + 2 = 375 + 2 = 377. That matches the dividend, so 377 ÷ 5 = 75 remainder 2 is correct. Notice the remainder, 2, is smaller than the divisor, 5. A remainder must always be smaller than the divisor.
What to watch for
If a subtraction gives you a number that is as big as the divisor or bigger, your divide step was too small. Try a bigger quotient digit.
If you get a negative result, your divide step was too big. Try a smaller quotient digit.
Always finish with the check. It catches most mistakes in one line.
Divide: Divide means to split a number into equal groups, or to ask how many times one number fits into another number.
Divisor: The divisor is the number you divide by. It is the size of each group. In 96 ÷ 4, the divisor is 4.
Dividend: The dividend is the big number you are splitting up. In 96 ÷ 4, the dividend is 96.
Quotient: The quotient is the answer to a division problem. In 96 ÷ 4 = 24, the quotient is 24.
Remainder: The remainder is what is left over at the end when nothing is left to bring down and the left-over part is too small for one more full group.
Bring down: Bring down means to copy the next digit of the dividend down next to the result of your subtraction, so you have a new number to divide.
📚 Study helper: Great job! Now try this. Say the four steps out loud in order: Divide, Multiply, Subtract, Bring down. Then work 96 ÷ 4 on paper by yourself and check it with 24 × 4 = 96. You can do it!
Mathematics LibreTexts, Santa Ana College — Mathematics Concepts and Skills for Elementary School Teachers, Section 4.3: Embracing Diversity of Algorithms for Multiplication and Division (division algorithm and standard algorithm of division; quotient and remainder check a = b × q + r): https://math.libretexts.org/Courses/Santa_Ana_College/Mathematics_Concepts_and_Skills_for_Elementary_School_Teachers/04:_Strengthening_Number_Sense_-_Strategies_Algorithms_and_Estimation/4.03:_Embracing_Diversity_of_Algorithms_for_Multiplication_and_Division
All worked examples on this page were computed and checked step by step for this page: 24 × 4 = 96; 136 × 7 = 952; 75 × 5 + 2 = 377.