TABE Level D Math: Dividing Whole Numbers

Dividing is the reverse of multiplying. When you divide 20 by 5 you get 4, and 4 times 5 is 20. You have to be carefully when you say (or write) a division problem. You can also say, “Divide 5 into 20.” This changes the order of naming the two numbers. It does not mean the same as “Divide 5 by 20.” For example, if you have $20 to be divided among 4 people, each person gets $5. But if you have $5 to be divided among 20 people, each person only gets a quarter ($0.25). The answer to a division problem is called the quotient. In 20 divided by 5, 20 is called the dividend, 5 is called the divisor, and 4 is called the quotient.

There are two main ways of writing a division problem.

You can write the problem 20 divided by 5 equals 4 as or as .

The second form is usually the one used if you can’t do the problem in your head.

The division problems on TABE D have divisors with one or two digits.
You can think of whole number division as a way of separating a number of objects (dividend) into equal groups.

The divisor is the number of groups, and the quotient is the number objects in each group. If there are some objects left over after they are divided equally, this number is called the remainder.

Let’s look at some examples.

One-Digit Divisor:

Example A.

First divide 5 into the 7. It doesn’t go evenly, but it does go 1 time, so put 1 above the line, multiply 1 times 5 and put the answer 5 below the 7.
Then subtract 5 from 7 to get 2, and bring down the 8.

Repeat the process, this time dividing 5 into 28.
This goes 5 times, so put the 5 above the 8, multiply 5 times 5, and put the answer (25) under the 28.
Then subtract 25 from 28 to get 3, and bring down the 3.

Repeat the process again, this time divide 5 into 33.
This goes 6 times, so put the 6 above the 3, multiply 6 times 5, and put the answer (30) under the 33.
Then subtract 30 from 33 to get 3, the remainder.

The remainders (after the subtraction step) must always be smaller than the divisor.

Example B.

In this problem, 5 doesn’t divide into the first digit 1, so divide 5 into the first two digits 13.
This goes 2 times, so put the 2 above the 3, multiply 2 times 5, and put the answer (10) under the 13.
The subtract 10 from 13 to get 3 and bring down the 5.

Repeat the process, this time dividing 5 into 35.
This goes 7 times, so put the above the 5, multiply 7 times 5, and put the answer (35) under the 35.
When you subtract, you get 0, so there is no remainder (5 goes into 135 evenly).


Two-Digit Divisor:
As the next problem shows, division with a two-digit divisor is a little harder.
 

Example C.

The first digit of 23 (2) is less than the first digit of 38 (3), so you can just divide 2 into 3 and get 1.
Multiply 1 times 23, put the answer (23) under the 38, and subtract to get 15.

Bring down the 5, and repeat by dividing 23 into 155.
Unfortunately, the first digit of 23 (2) doesn’t go into the first digit of 155 (1), so you try 2 into the first two digits of 155 (15).
The 2 goes into 15 7 times, but when you multiply 7 times 23, you get 161, which is bigger than 155, so you have to reduce the 7 to a 6.
Then 6 times 23 is 138, so write that below the 155 and subtract to get a remainder of 17.

In summary, the quotient is 16 with a remainder of 17.

Practice Dividing Whole Numbers
You should write these problems using the form on a piece of paper and work them out there.

1. 16 ÷ 2

2. 48 ÷ 4

3. 84 ÷ 6

4. 85 ÷ 5

5. 108 ÷ 6

6. 136 ÷ 8

7. 272 ÷ 4

8. 322 ÷ 7

9. 96 ÷ 12

10. 312 ÷ 12

11. 425 ÷ 17

12. 506 ÷ 22

Answers: Practice Dividing Whole Numbers

1. 8

2. 12

3. 14

4. 17

5. 18

6. 17

7. 68

8. 46

9. 8

10. 26

11. 25

12. 23