Whole number word problems

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In the previous section you were given the size of a set (or group) and the number of sets (or groups) and asked to calculate the product of these two figures. What if you were given the size of each set(or group) and the product, and asked to calculate the number of sets needed to reach this end figure? That is basically the definition of division, and as you can see it is intrically tied to multiplication.

Rather than try to understand this concept in the abstract, let's review some of the division problems we performed on the arithmetic section of this unit. Remember that the answer to a division problem is called the quotient. The number that we are dividing is called the dividend. And the number that we are "dividing by" is called the divisor.

You know that at a certain school each classroom contains 32 students. How many classrooms will you need for 384 students?

Each classroom holds 32 students. So we can think of the size of each of our sets as 32. Our divisor is 32.
The total amount of students is 384. The dividend is 384.
This problem is basically asking "How many sets of 32 do you need to equal 384?" In other what is 384 divided by 32?
384 ¸ 32 = 12
There you need 12 groups of 32 to reach 324.
Each of these groups represented a classroom.
Conclusion: You need 12 classes for the 384 students.
You could also think of this problem along with its solution as follows:
"12 classes of 32 students each would equal 384."

You are traveling at a constant speed of 55 miles per hour. How long will it take to travel 220 miles?

Each hour you are traveling 55 miles (i.e. 55 miles per hour). So we can think of the size of each of our sets as 55. Our divisor is 55.
The total amount of miles traveled is 220. The dividend is 220.
This question is basically asking "How many groups of 55 will it take to equal 220?"
220 ¸ 55 = 4
Thus it will take 4 hours of drivung at a constant rate of 55 miles per hours to travel 220 miles.
You could also think of this problem along with its solution as follows:
"If you travel for 4 hours at 55 miles per hour, you will cover 220 miles."

Remember back when I wrote that "15/5 = 3" and "15/3=5" were two division problems relating to equivalent multiplication problems? At that time I told you that you could switch the divisor and the quotient of any division problem.

This relationship gives division a second meaning when it comes to solving word problems.

If you know the number of items that you have, and you know the number of groups that these items will be separated into, then the size of each group will equal the "total amount" divided by "the number of groups."

This will be illustrated for you in the next three examples

You are planning to drive 1,200 miles over the course of three days. You plan to drive the same number of miles each day. How many miles will you have to drive each day?

In this example the total amount of miles is 1,200. This is our dividend.
The size of our groups (or if you prefer the size of each set) would be the number of miles driven each day of your trip. We do not currently know this figure.
However we do know that this trip will last three days. So we can think of this as being three groups of a yet to be undetermined size.
The size of each group will equal "the total amount" divided by "the number of groups."
1200 / 3 = 400
Conclusion: You will have to drive 400 each day.

The dividend (i.e. the total amount of miles) was 1,200.
The size of each group (i.e. the amount of miles driven each day) was 400.
The number of groups (i.e. the number of days) was 3.
So by multiplying the size of each group by the number of groups, we should get the dividend.
400 x 3 = 1,200
Therefore our solution has been verified.

You just baked 14 cupcakes for your son's birthday party. There will be 7 children at this party including your son. How many cupcakes will each child receive? I hope your son has a happy birthday.

In this example the total amount of cupcakes is 14. That is our dividend.
The size of our groups (or if you prefer the size of each set) would be the number of cupcakes given to each child. We do not currently know this figure.
However we do know that there will be 7 children. So we can think of this as being 7 groups of a yet to be undetermined size.
The size of each group will equal "the total amount" divided by "the number of groups."
14 / 7 = 2
Conclusion: Each child will receive two cupcakes.

The dividend (i.e. the number of cupcakes) was 14.
The size of each group (i.e. the amount of cupcakes given to each child) was 2.
The number of groups (i.e. the number of children) was 7.
So by multiplying the size of each group by the number of groups we should get the dividend.
7 x 2 = 14
Therefore our solution has been verified.

At that party you bought a package of children's books to distribute to the 7 children as party favors. There were 16 books in the package. How many books will each child receive?

In this example the total amount of books is 16. That is our dividend.
The size of our groups (or if you prefer the size of each set) would be the number of books given to each child. We do not currently know this figure.
However we do know that there will be 7 children. So we can think of this as being 7 groups of a yet to be undetermined size.
The size of each group will equal "the total amount" divided by "the number of groups."
16 / 7 = 2r2 (2 with a remainder of 2)
Conclusion: Each child will receive two books and you will have 2 left over. I suggest that you put them aside for some special occasion in the future.

The dividend (i.e. the number of books) was 16.
The size of each group (i.e. the amount of books given to each child) was 2.
The number of groups (i.e. the number of children) was 7.
The remainder (i.e. the amount of books left over) was 2.
So by multiplying the size of each group by the number of groups, and then adding the remainder we should get the dividend.
7 x 2 = 14 and 14 + 2 = 16.
Therefore our solution has been verified.

Now it's time for you to practice division word problems. To see a word problem, click on the "generate a division word problem" button.

Work out the problem and place your answer in the text box. Then click the "check my answer" button. The computer will then tell you whether or not your answer was correct. You will get additional instructions if your answer was incorrect.

After you complete the problem you can generate another word problem by clicking the "reset" button and then clicking the "generate a division word problem" button once again.
Continue as many times as you wish, and then:

Section 2-WHOLE NUMBER WORD PROBLEMS