3rd Grade - Divide 4-Digit Numbers

Multiplication and Division
Divide 4-Digit Numbers
Solve division problems in which a multi-digit number is evenly divided by a one-digit number (135 - 5=).
Number Sense: Division The ability to separate multidigit numbers into equal groups.

Building Blocks/Prerequisites


Sample Problems


Are there any special rules to division? Division is special when dividing by 0 and 1. A number divided by zero is not defined. Any number divided by one is equal to that number.


How do you divide a three-digit number by a one-digit number?

Place the divisor outside the division bracket and place the three-digit dividend inside the bracket. For example, 192/6; the first number of the dividend (1) is less than 6, so take the first two numbers of the dividend (19) to determine how many times 6 will go into 19. The 6 will go into 19 three times. Place the 3 above the 9 in the dividend. Multiply the 6 times the three and place that answer below the 19 in the dividend. Draw a line underneath it and subtract 18 from 19. 1 is the answer and bring down the 2 to make 12. Determine how many times 6 will go into 12 and place the answer (2) above the two in the dividend. Multiply the 2 x 6 and place the answer below the 12 (12). Subtract 12-12=0. There are no more numbers in the dividend to bring down next to the 0, therefore the answer is an even 32.


Is the order of numbers important? When dividing the order of the numbers is important: 40/5 does not equal 5/40.


How are division problems written?

There are two common ways to indicate division: c divided by b can be written as c/b or c÷b.


What are the names for the numbers in a division problem?

a=c—b, a is the quotient, c is the dividend, and b is the divisor. Quotient=dividend—divisor or quotient=dividend



Define dividend (the number to be divided), divisor (the number that divides the dividend), and quotient (the answer).

Learning Tips


Division requires following a certain procedure, just as multiplication by multiple digits does. But you want to be sure that your child understands why the procedures that we use in division are followed because then he/she is more likely to remember how to do this type of problem. For this example: 42 divided by 3, follow this procedure.

First, ask your child to count out 42 items. Pennies are particularly convenient to use; provide some small bags or envelopes to put them in. Once the 42 items are counted out, ask your child to group them in hundreds until there aren’t 100 left to group, then in tens until there aren’t ten to group, and to keep the rest out as “ones”. The grouped items can be placed in the envelopes or just stacked as this problem doesn’t require a large number of manipulatives.

Now, since the items will be divided into 3 groups, ask your child to divide up the largest group first. There won’t be any items in the hundreds stack, so your child’s attention should go to the 4 stacks/envelopes that make up the tens groups. Set 3 mats (pieces of paper are fine) out, since the problem asks that the items be divided into 3 groups and invite your child to divide the tens stacks. At this point he/she may NOT break a stack to divide it; only groups of ten may be divided. When finished, your child should find that there is one stack of ten on each mat, that there is one stack of ten that couldn’t be divided (since it can’t be split just yet) and there are those 2 loose items over in the ones pile.

Since the tens stack that remains couldn’t be divided into three, invite your child to open the stack and spread out the 10 pennies. Ask, “separated out like this, what does each penny stand for?” It can’t stand for 10 any longer; that group was broken up. Yes, each one is a “one” just like those 2 loose ones. If they are all ones, then they may be grouped together and then with the 12 ones available, your child should divide those onto the 3 mats. Each mat now has one stack of 10 and 4 loose ones. Remembering what you know about expanded notation, your 10 + 4 is the same thing as 14. You have divided 42 items into 3 groups and each group has 14 items.


After you have worked through this problem using the manipulatives, write the same problem using the standard division configuration to represent the problem: 3 | 43 (with the line on top, over the 43).

Now, repeat the division with the penny stacks that you did before. “Did you have enough stacks of 10 pennies to give each mat a stack?? (Yes, we had 4 so we put one 10-stack on each mat). Ask the child to show this work on the pencil/paper problem by writing a “1” over the 4. Now ask, “what did you do with the extra stack?” (We broke it out of the stack and put those 10 with the extra 2). Explain to your child that while you know he can do this one “in his head” because he just counted out pennies, he won’t always count pennies so you’ll show him how we can figure the same thing out on paper. Ask him to remember that he used one stack for each mat; since there were 3 mats, how many did you use? (1 x 3 = 3). Exactly. Point to the 3, which is the divisor in his paper/pencil version of the problem and the 1 which is the first digit in the answer and ask him to multiply the two numbers; you are multiplying one stack per group times the number of groups. Write the product (3) below the 4. Now, you remember that you had one stack of 10 left over, and we’re doing these calculations in the tens row, aren’t we? How could we show that 1? (Well, 4-3 is 1.) Right! Since that 1 is in the tens row, if we write the 2 that we see up in the ones row beside it, is 12 the number that we had when we divided up the remaining stack of 10? (The child should agree that this is so.) Now, can we divide that 12 into 3 groups? (Sure, there will be 4 in each group) As you’d expect, we’re dividing ones now, so we’ll write the 4 over the ones number in 43 (the three). Did you get the same result when you did this problem on paper as you got when you divided the pennies? (Yes.)

Lastly, ask your child if he/she imagines that things to be divided always come out “even” with every mat getting the same number and not having anything left over. (Probably not) So, what we do, is, we multiply how many ones we used for each mat x the number of groups—4 x 3 = 12) and write the 12 below the 12 in our problem. In this case it did “come out even” so we do not need to worry about any extras.


Do the same exercise over again with new numbers. This process, even when understood by children, takes a bit of practice to help the child feel confident about his/her ability to do this process. For third-graders, even simple division is probably the most complex process they have had to master. Your goal is to be very sure that your child understands why it is done the way it is because otherwise children are likely to forget what step comes next.


If your child is tempted to divide up the ones group first allow him/her to try. Eventually he/she will figure out that it often isn’t possible to work it out although for problems where every digit can be divided by the divisor, it will work just as well. The problem is, on larger problems, it isn’t possible to tell ahead whether or not this will be the case.


Provide much encouragement, help, and practice in short sessions. This is a complex process for third-graders and trying to do many, many problems in a row will tire and frustrate them.

Extra Help Problems


176/8= (22)


8,185x5= (40,925)


695/1= (695)


1815/3= (605) (some problems written vertically with the division bracket and others written horizontally).


Your mother buys a bag of bubble gum for you to share with your friends. When you open it and count the pieces, there are 67 pieces in the bag. One piece, however, has no wrapping on it, so you throw that piece into the trash. Two friends like bubble gum, and you like it too. How many pieces will each person get? Will there be any left over? (66 pieces to divide, 3 friends, 22 pieces each. )


220÷4 = (55)


450÷5 = (90)


189÷9 = (21)


273÷3 = (91)


126÷7 = (18)


639÷9 = (71)


77÷1 = (77)


95÷1= (95)


144÷2 = (72)


305÷5 = (61)


204÷4 = (51)


176÷8 = (22)


630÷7 = (90)


380÷5 = (76)


72÷6 = (12)


336÷7 = (48)


180÷4 = (45)


212÷4 = (53)


576÷8 = (72)


213÷3 = (71)


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