Grade 5 → Operations with Whole Numbers ↓
Long Division
Long division is a method used to divide large numbers into smaller, easier-to-manage pieces. It is an essential mathematical technique that helps break down the division process into a series of easy steps. In this explanation, we will cover every aspect of long division and provide simple instructions with text and visual examples for a deeper understanding.
Understanding the basics
In division you have a dividend, a divisor, a quotient, and sometimes a remainder. Here's what each term means:
- The dividend is the number you want to divide by.
- The divisor is the number you are dividing by.
- The quotient is the result of division.
- The remainder is what is left after division if the division is not exact.
Steps of long division
Let us understand the steps of long division using a simple example: Divide 652 by 4.
Step 1: Divide the first number of the dividend by the divisor. Step 2: Multiply the divisor by the quotient. Step 3: Subtract the result from the first number of the dividend. Step 4: Bring down the next number of the dividend. Step 5: Repeat the process until you reach the final number of the dividend.
Now, we will apply these steps to our example.
Visual example
Step-by-step lesson example
Step 1: See how many times 4 can go into the first digit 6 of 652. It goes into 1 time. Write 1 over 6.
1 , 4 | 6 5 2
Step 2: Multiply 1 by 4. The answer is 4. Write it under 6.
1 , 4 | 6 5 2 - 4
Step 3: Subtract 4 from 6. The answer is 2. Write it under 4.
1 , 4 | 6 5 2 - 4 , 2
Step 4: Bring down the next digit of the dividend, which is 5. You now have 25.
1 , 4 | 6 5 2 - 4 , 2 5
Step 5: Determine how many times 4 can go into 25. It goes into 6 times. Write 6 next to the 1 in the quotient.
16 , 4 | 6 5 2 - 4 , 2 5
Step 6: Multiply 6 by 4. The answer is 24. Write it under 25.
16 , 4 | 6 5 2 - 4 , 2 5 - 2 4
Step 7: Subtract 24 from 25. The answer is 1. Write it under 24.
16 , 4 | 6 5 2 - 4 , 2 5 - 2 4 , 1
Step 8: Bring down the next digit of the dividend, which is 2. You now have 12.
16 , 4 | 6 5 2 - 4 , 2 5 - 2 4 , 1 2
Step 9: Determine how many times 4 can go into 12. It goes into 3 times. Write the 3 next to 16 in the quotient.
163 , 4 | 6 5 2 - 4 , 2 5 - 2 4 , 1 2
Step 10: Multiply 3 by 4. The answer is 12. Write it under the 12.
163
,
4 | 6 5 2
- 4
,
2 5
- 2 4
,
1 2
-1 2
,
0
We have no remainder, and the quotient is 163.
Practice makes perfect
Now that you've learned the steps of long division, let's practice with some additional examples. You can check your work by multiplying the quotient by the divisor to see if you got a dividend.
Example 1
Divide 847 by 5.
169 R2
,
5 | 8 4 7
- 5
,
3 4
- 3 0
,
4 7
-4 5
,
2
Answer: 169 R2
Example 2
Divide 2345 by 3.
781 R2
,
3 | 2 3 4 5
- 2 1
,
2 4
-2 4
,
0 5
-0 3
,
2
Answer: 781 R2
Tips for success
Doing long division can be challenging at first, but it gets easier with practice. Here are some tips to help you master long division:
- Practice regularly to get more comfortable with the steps.
- Write your numbers clearly to avoid confusion.
- Be patient and take one step at a time.
- Check if you received the original dividend by multiplying your work back.
Conclusion
Learning long division is an essential skill because it allows you to divide large numbers accurately. It's important to understand each step in the process, and using both text and visual examples can help. With consistent practice and patience, you'll gain confidence in performing long division and solving complex problems with ease.
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