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Words to Math: Division

In this section, we will learn to translate phrases into a mathematical expression by identifying key words that indicate division.

When talking about division, you will most likely see the terms "divide", "quotient", "percent" (divide by $100$). There are other terms to indicate addition, multiplication, or subtraction.

Let’s take a look at an example.

Nicole has $20$ cookies. She wants to divide the $20$ cookies equally between $4$ friends. How many cookies does each person receive?

We know that the term "divide" often refers to division, so the operator ‘$\div$ can be used. There is also an invisible equality sign. That's because we're looking for a number equal to how many cookies each person gets. Both sides of an equation are always equal. This problem is no different!

Nicole has $20$ cookies and there are $4$ people. So, we can rewrite this as a mathematical equation. Then perform the division of positive integers.

$20$ cookies $\div$ $4$ friends $=$ $5$ cookies each.

This problem is also illustrated with the following diagram.

When talking about equality, you will most likely see the terms "equal to", "is", "the same as", and "amounts to".

These phrases describe division as a mathematical expression.

1. $35$ divided by $7$ equals $5\quad\rightarrow\quad 35 \div 7= 5$
2. The quotient of $6$ and $3$ is $2\quad\rightarrow\quad 6 \div 3= 2$

Word Problems with Division

There is an important strategy for solving word problems. The key is to translate them into mathematical expressions. This is easier if you can pick out key phrases, called signal words. These that tell you what type of operation the problem is asking for. Each operation has its own set of signal words.

(Video) Solving Multiplication and Division Word Problems

by Ruth Erquiaga

Ruth Erquiaga has a great explanation and strategy on how to identify and approach word problems. This video focuses specifically on multiplication and division.

$\large{\text{Summary}}$

The key word that designates multiplication or division is "each". "Each" indicates that the groups being combined or split up need to be equal in size. This is true of multiplication and division, but not necessarily of addition and subtraction.

Other words like "total", "area", "in all", and "altogether" can designate multiplication or division. We need the context of the problem to allow you to work with equally sized groups.

The video covers a general strategy for translating word problems.

1. Read the whole problem (in fact, read it twice, just in case).
2. Find if the total is given. A given total means that the problem will be division or subtraction. No given total means the problem will be addition or multiplication. In the second case we usually want to find the total.
3. Find if the groups are equal. Equal groups will mean multiplication or division. Unequal groups will mean addition or subtraction.