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Dividing Whole Numbers

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Dividing Whole Numbers

How to Divide Whole Numbers:

  1. Divide the first digit of the dividend by the divisor.
     

    If the divisor is larger than the first digit of the dividend, divide the first two digits of the dividend by the divisor, and so on.

  2. Write the quotient above the dividend.
  3. Multiply the quotient by the divisor and write the product under the dividend.
  4. Subtract that product from the dividend.
  5. Bring down the next digit of the dividend.
  6. Repeat from Step 1 until there are no more digits in the dividend to bring down.
  7. Check by multiplying the quotient times the divisor.

Example

Divide \(2,596÷4.\) Check by multiplying:

Solution

Let’s rewrite the problem to set it up for long division.Dividing Whole Numbers
Divide the first digit of the dividend, 2, by the divisor, 4.Dividing Whole Numbers
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.Dividing Whole Numbers
Multiply the 6 in the quotient by the divisor 4 and write the product, 24, under the first two digits in the dividend.Dividing Whole Numbers
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.Dividing Whole Numbers
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.Dividing Whole Numbers
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.Dividing Whole Numbers
So \(2,596÷4=649\). 
Check by multiplying. 
Dividing Whole Numbers
 

It equals the dividend, so our answer is correct.

Extra:

Divide. Then check by multiplying: \(2,636÷4\)

Answer

659

Extra:

Divide. Then check by multiplying: \(2,716÷4\)

Answer

679

Example

Divide \(4,506÷6.\) Check by multiplying:

Solution

Let’s rewrite the problem to set it up for long division.Dividing Whole Numbers
First we try to divide 6 into 4.Dividing Whole Numbers
Since that won’t work, we try 6 into 45.
There are 7 sixes in 45. We write the 7 over the 5.
Dividing Whole Numbers
Multiply the 7 by 6 and subtract this product from 45.Dividing Whole Numbers
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.
Dividing Whole Numbers
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.
Dividing Whole Numbers
Check by multiplying.
Dividing Whole Numbers
 

It equals the dividend, so our answer is correct.

Extra:

Divide. Then check by multiplying: \(4,305÷5.\)

Answer

861

Extra:

Divide. Then check by multiplying: \(3,906÷6.\)

Answer

651

Example

Divide \(7,263÷9.\) Check by multiplying.

Solution

Let’s rewrite the problem to set it up for long division.Dividing Whole Numbers
First we try to divide 9 into 7.Dividing Whole Numbers
Since that won’t work, we try 9 into 72. There are 8 nines in 72.
We write the 8 over the 2.
Dividing Whole Numbers
Multiply the 8 by 9 and subtract this product from 72.Dividing Whole Numbers
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.
Dividing Whole Numbers
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.
Dividing Whole Numbers
Check by multiplying.
Dividing Whole Numbers
 

It equals the dividend, so our answer is correct.

Extra:

Divide. Then check by multiplying: \(4,928÷7.\)

Answer

704

Extra:

Divide. Then check by multiplying: \(5,663÷7.\)

Answer

809

So far all the division problems have worked out evenly. For example, if we had \(24\) cookies and wanted to make bags of \(8\) cookies, we would have \(3\) bags. But what if there were \(28\) cookies and we wanted to make bags of \(8?\) Start with the \(28\) cookies as shown in the figure below.

Dividing Whole Numbers

Try to put the cookies in groups of eight as in the figure below.

Dividing Whole Numbers

There are \(3\) groups of eight cookies, and \(4\) cookies left over. We call the \(4\) cookies that are left over the remainder and show it by writing R4 next to the \(3.\) (The R stands for remainder.)

To check this division we multiply \(3\) times \(8\) to get \(24,\) and then add the remainder of \(4.\)

\(\begin{array}{r}3 \\ ×8 \\ \hline 24 \\ +4 \\ \hline 28\end{array}\)

Example

Divide \(1,439÷4.\) Check by multiplying.

Solution

Let’s rewrite the problem to set it up for long division.Dividing Whole Numbers
First we try to divide 4 into 1. Since that won’t work, we try 4 into 14.
There are 3 fours in 14. We write the 3 over the 4.
Dividing Whole Numbers
Multiply the 3 by 4 and subtract this product from 14.Dividing Whole Numbers
Now bring down the 3 and repeat these steps. There are 5 fours in 23.
Write the 5 over the 3. Multiply the 5 by 4 and subtract this product from 23.
Dividing Whole Numbers
Now bring down the 9 and repeat these steps. There are 9 fours in 39.
Write the 9 over the 9. Multiply the 9 by 4 and subtract this product from 39.
There are no more numbers to bring down, so we are done.
The remainder is 3.
Dividing Whole Numbers
Check by multiplying.
Dividing Whole Numbers
 

So \(1,439÷4\) is \(359\) with a remainder of \(3.\) Our answer is correct.

Extra:

Divide. Then check by multiplying: \(3,812÷8.\)

Solution

476 with a remainder of 4

Extra:

Divide. Then check by multiplying: \(4,319÷8.\)

Solution

539 with a remainder of 7

Example

Divide and then check by multiplying: \(1,461÷13.\)

Solution

Let’s rewrite the problem to set it up for long division.\(13\overline{)1,461}\)
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.
Dividing Whole Numbers
Multiply the 1 by 13 and subtract this product from 14.Dividing Whole Numbers
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.
Dividing Whole Numbers
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.
Dividing Whole Numbers
Check by multiplying.
Dividing Whole Numbers
 

Our answer is correct.

Extra:

Divide. Then check by multiplying: \(1,493÷13.\)

Solution

114 R11

Extra:

Divide. Then check by multiplying: \(1,461÷12.\)

Solution

121 R9

Example

Divide and check by multiplying: \(74,521÷241.\)

Solution

Let’s rewrite the problem to set it up for long division.\(241\overline{)74,521}\)
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 into 745. 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.Dividing Whole Numbers
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.
Dividing Whole Numbers
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.
Dividing Whole Numbers
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.
Dividing Whole Numbers
 

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.

Extra:

Divide. Then check by multiplying: \(78,641÷256.\)

Solution

307 R49

Extra:

Divide. Then check by multiplying: \(76,461÷248.\)

Solution

308 R77

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