# Multiplication and Division Word Problems

Word problems are fun and challenging to solve because they represent actual situations that happen in our world. As students, we are always wondering why we should learn one skill or another, and word problems help us see the practical value of what we are learning.

Read the tips and guidance and then work through the multiplication and division word problems in this lesson with your children. Try the three worksheets that are listed within the lesson (you will also find them at the bottom of the page.)

## Solving Multiplicative Comparison Word Problems

### Multiplication as Comparing

In multiplicative comparison problems, there are two different sets being compared. The first set contains a certain number of items. The second set contains multiple copies of the first set.

Any two factors and their product can be read as a comparison. Let’s look at a basic multiplication equation:  4 x 2 = 8.

 8 is the same as 4 sets of 2 or 2 sets of 4. 8 is 4 times as many as 2, and 2 times as many as 4.

### What Operation to Use: Multiply? Divide? Add? Subtract?

The hardest part of any word problem is deciding which operation to use. There can be so many details included in a word problem that the question being asked gets lost in the whole situation. Taking time to identify what is important, and what is not, is essential.

Use a highlighter on written problems to identify words that tell you what you are solving, and give you clues about which operations to choose. Make notes in the margins by these words to help you clarify your understanding of the problem.

Remember: If you don't know what's being asked, it will be very difficult to know if you have a reasonable answer.

### Different Types of Problem

There are three kinds of multiplicative comparison word problems (see list below). Knowing which kind of problem you have in front of you will help you know how to solve it.

• Product Unknown Comparisons
• Set Size Unknown Comparisons
• Multiplier Unknown Comparisons

The rest of this lesson will show how these three types of math problems can be solved.

### Multiplication Problems: Product Unknown

In some multiplicative comparison word problems, you are given the number of items in one set, and you are given the "multiplier" amount. The multiplier amount tells you how many times bigger (or more) the second set is than the first. "Bigger" can also mean "longer," or "wider," or "taller" in problems involving measurement, or "faster" in problems involving a rate of speed.

These problems in which you know both the number in one set, and the multiplier are called “Product Unknown” comparisons, because the total is the part that is unknown.

In order to answer the question you are being asked, you need to multiply the number in the set by the multiplier to find the product.

#### Multiplication Problems: Product Unknown - Example

The problem below includes color-coding to help analyze the Product Unknown Comparison. Notice also how the importance of fully stating the answer and also of checking if the answer makes sense.

Try the word problems on the worksheet below (the worksheet is also listed towards the bottom of this page)

### Multiplication Problems: Set Size Unknown

In some multiplicative comparison word problems, the part that is unknown is the number of items in one set. You are given the amount of the second set, which is a multiple of the unknown first set, and the “multiplier” amount, which tells you how many times bigger (or more) the second set is than the first. Remember, “bigger” can also mean “longer,” or “wider,” or “taller” in problems involving measurement, or “faster” in problems involving a rate of speed.

These problems in which you know both the number in the second set, and the multiplier are called “Set Size Unknown” comparisons, because the number in one set is the part that is unknown.

In order to answer the question you are being asked, you need to use the inverse operation of multiplication: division. This kind of division is “partition” or “sharing” division. Dividing the number in the second set by the multiplier will tell you the number in one set, which is the question you are being asked in this kind of problem.

#### Multiplicative Comparison Problems: Set Size Unknown - Example

Try the word problems on the worksheet below (the worksheet is also listed towards the bottom of this page)

### Multiplicative Comparison Problems: Multiplier Unknown

In some multiplicative comparison word problems, you are given the number of items in one set, and you are given the number of items in the second set, which is a multiple of the first set. The “multiplier” amount is the part that is unknown.

The multiplier amount tells you how many times bigger (or more) the second set is than the first. “Bigger” can also mean “longer,” or “wider,” or “taller” in problems involving measurement, or “faster” in problems involving a rate of speed.

These problems in which you know both the number in one set, and the number in the second set are called “Multiplier Unknown” comparisons, because the multiplier is the part that is unknown.

In order to answer the question you are being asked, you need to use the inverse operation of multiplication: division. This kind of division is called “measurement” division.