Multiplication and Division Word Problems

Solving Word Problems

In elementary school, you're not just expected to solve word problems; you must also be able to identify and write equations to represent them. Every equation contains a variable, which represents the unknown part of the word problem. It's important to keep in mind that one word problem can be correctly represented by several different equations.

Multiplication

Your clue that a word problem requires multiplication is that it involves multiple groups of a given size. For example, three friends might bake 24 cookies each, or someone might pay $1.50 each for seven books. Then, you'll be asked to find the total number of cookies baked or the total cost of the books. To represent these two problems, we could write the following equations:

3 x 24 = ?

$1.50 x 7 = ?

Here, we can simply perform the multiplication to get the answers (72 cookies and $10.50). However, other multiplication word problems are not so straightforward. For instance, imagine you're asked this question:

Sally paid $10.50 for seven books. If all of the books were the same price, how much did she pay for each one?

This can be considered a division word problem because it can be represented like this: $10.50 ÷ 7 = ? However, it can also be expressed in any of the following ways:

7 x ? = $10.50

? x 7 = $10.50

$10.50 = ? x 7

$10.50 = 7 x ?

Any of these equations will be true if the correct answer, $1.50, is substituted for the '?'. The '?' can also be replaced with variables like 'x,' 'y' or other letters. It's important to understand that word problems can be represented by several different equations because multiple-choice tests may provide any one of them as the correct answer.

Division

Division word problems usually tell you about a group of items, and then they will ask you to figure out something about an individual item. As with the problem earlier, they might give you the total cost of a certain number of items and ask you to figure out the cost per item. They might also look like this:

Amanda's plant grew 14 inches in one week. If it grew the same amount each day, how many inches did it grow on Tuesday?

Since the plant grew 14 inches over one week (seven days), the number of inches that it grew each day can be represented by this equation: 14 ÷ 7 = ?. Since 14 ÷ 7 = 2, the plant grew two inches on Tuesday. However, the problem can also be represented by any of the equations listed below because substituting 2 for the '?' makes them true.

14 x ? = 7

? x 14 = 7

7 = ? x 14

7 = 14 x ?