## Dividing Whole Numbers

Contents

### How to Divide Whole Numbers:

- 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.

- Write the quotient above the dividend.
- Multiply the quotient by the divisor and write the product under the dividend.
- Subtract that product from the dividend.
- Bring down the next digit of the dividend.
- Repeat from Step 1 until there are no more digits in the dividend to bring down.
- 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. | |

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 6 in 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.

### 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. | |

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.

### 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. | |

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. | |

Multiply the 8 by 9 and subtract this product from 72. | |

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.

### 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.

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

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. | |

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. | |

Multiply the 3 by 4 and subtract this product from 14. | |

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. | |

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. | |

Check by multiplying. |

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. | |

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.

### 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. | |

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.

### Extra:

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

#### Solution

307 R49

### Extra:

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

#### Solution

308 R77