example
Divide. Then check by multiplying.
- 42÷6
- 972
- 7)63
Solution:
1. |
|
|
42÷6 |
Divide 42 by 6. |
7 |
Check by multiplying.
7⋅6 |
|
42✓ |
|
2. |
|
|
972 |
Divide 72 by 9. |
8 |
Check by multiplying.
8⋅9 |
|
72✓ |
|
3. |
|
|
7)63 |
Divide 63 by 7. |
9 |
Check by multiplying.
9⋅7 |
|
63✓ |
|
What is the quotient when you divide a number by itself?
example
Divide. Then check by multiplying:
- 11÷11
- 119
- 1)7
Answer:
Solution:
1. |
|
|
11÷11 |
A number divided by itself is 1. |
1 |
Check by multiplying.
1⋅11 |
|
11✓ |
|
2. |
|
|
119 |
A number divided by 1 equals itself. |
19 |
Check by multiplying.
19⋅1 |
|
19✓ |
|
3. |
|
|
1)7 |
A number divided by 1 equals itself. |
7 |
Check by multiplying.
7⋅1 |
|
7✓ |
|
Suppose we have
example
Divide. Check by multiplying:
- 0÷3
- 010.
Answer:
Solution
1. |
|
|
0÷3 |
Zero divided by any number is zero. |
0 |
Check by multiplying.
0⋅3 |
|
0✓ |
|
2. |
|
|
10/0 |
Division by zero is undefined. |
undefined |
example
Divide
2,596÷4. Check by multiplying:
Answer:
Solution
Let's rewrite the problem to set it up for long division. |
 |
Divide the first digit of the dividend, 2, by the divisor, 4. |
 |
Since 4 does not go into 2, we use the first two digits of the dividend and divide 25 by 4. The divisor 4 goes into 25 six times. |
|
We write the 6 in the quotient above the 5. |
 |
Multiply the 6in the quotient by the divisor 4 and write the product, 24, under the first two digits in the dividend. |
 |
Subtract that product from the first two digits in the dividend. Subtract 25−24 . Write the difference, 1, under the second digit in the dividend. |
 |
Now bring down the 9 and repeat these steps. There are 4 fours in 19. Write the 4 over the 9. Multiply the 4 by 4 and subtract this product from 19. |
 |
Bring down the 6 and repeat these steps. There are 9 fours in 36. Write the 9 over the 6. Multiply the 9 by 4 and subtract this product from 36. |
 |
So 2,596÷4=649 . |
|
Check by multiplying.
 |
|
It equals the dividend, so our answer is correct.
example
Divide
4,506÷6. Check by multiplying:
Answer:
Solution
Let's rewrite the problem to set it up for long division. |
 |
First we try to divide 6 into 4. |
 |
Since that won't work, we try 6 into 45.
There are 7 sixes in 45. We write the 7 over the 5. |
 |
Multiply the 7 by 6 and subtract this product from 45. |
 |
Now bring down the 0 and repeat these steps. There are 5 sixes in 30. Write the 5 over the 0. Multiply the 5 by 6 and subtract this product from 30. |
 |
Now bring down the 6 and repeat these steps. There is 1 six in 6. Write the 1 over the 6. Multiply 1 by 6 and subtract this product from 6 |
 |
Check by multiplying.
 |
|
It equals the dividend, so our answer is correct.
example
Divide
7,263÷9. Check by multiplying.
Answer:
Solution
Let's rewrite the problem to set it up for long division. |
 |
First we try to divide 9 into 7. |
 |
Since that won't work, we try 9 into 72. There are 8 nines in 72. We write the 8 over the 2. |
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Multiply the 8 by 9 and subtract this product from 72. |
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Now bring down the 6 and repeat these steps. There are 0 nines in 6. Write the 0 over the 6. Multiply the 0 by 9 and subtract this product from 6. |
 |
Now bring down the 3 and repeat these steps. There are 7 nines in 63. Write the 7 over the 3. Multiply the 7 by 9 and subtract this product from 63. |
 |
Check by multiplying.
 |
|
It equals the dividend, so our answer is correct.
Watch this video for another example of how to use long division to divide a four digit whole number by a two digit whole number.
https://youtu.be/V7Korf09iWI
So far all the division problems have worked out evenly. For example, if we had
example
Divide and then check by multiplying:
1,461÷13.
Answer:
Solution
Let's rewrite the problem to set it up for long division. |
13)1,461 |
First we try to divide 13 into 1. Since that won't work, we try 13 into 14. There is 1 thirteen in 14. We write the 1 over the 4. |
 |
Multiply the 1 by 13 and subtract this product from 14. |
 |
Now bring down the 6 and repeat these steps. There is 1 thirteen in 16. Write the 1 over the 6. Multiply the 1 by 13 and subtract this product from 16. |
 |
Now bring down the 1 and repeat these steps. There are 2 thirteens in 31. Write the 2 over the 1. Multiply the 2 by 13 and subtract this product from 31. There are no more numbers to bring down, so we are done. The remainder is 5. 1,462÷13 is 112 with a remainder of 5. |
 |
Check by multiplying.
 |
|
Our answer is correct.
example
Divide and check by multiplying:
74,521÷241.
Answer:
Solution
Let's rewrite the problem to set it up for long division. |
241)74,521 |
First we try to divide 241 into 7. Since that won’t work, we try 241 into 74. That still won’t work, so we try 241 into745. Since 2 divides into 7 three times, we try 3. Since 3×241=723 , we write the 3 over the 5 in 745. Note that 4 would be too large because 4×241=964 , which is greater than 745. |
|
Multiply the 3 by 241 and subtract this product from 745. |
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Now bring down the 2 and repeat these steps. 241 does not divide into 222.
We write a 0 over the 2 as a placeholder and then continue. |
 |
Now bring down the 1 and repeat these steps. Try 9. Since 9×241=2,169 , we write the 9 over the 1. Multiply the 9 by 241 and subtract this product from 2,221. |
 |
There are no more numbers to bring down, so we are finished. The remainder is 52. So 74,521÷241 is 309 with a remainder of 52. |
|
Check by multiplying.
 |
|
Sometimes it might not be obvious how many times the divisor goes into digits of the dividend. We will have to guess and check numbers to find the greatest number that goes into the digits without exceeding them.
Watch the video below for another example of how to use long division to divide whole numbers when there is a remainder.
https://youtu.be/UPUcShGCBOs