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Words to Math: Addition

In this section, we will learn to translate phrases into a mathematical expression by identifying keywords that indicate addition.

When talking about the process of adding, or addition, you will most likely see the terms "sum", "more than", "plus", "added to", "together", and "combined".

Let’s take a look at an example.

Nick owns a farm and he is trying to find an expression for the total number of animals in the farm.

Here is a diagram of the animals in the farm.

Looking at the image, we can see that there are $4$ chickens, $3$ sheep, and $2$ cows.

We know that the word "total" refers to addition, so the operator ‘$+$’ is required. Since we are totaling the number of animals, we can add them all using ‘$+$’.

Total Number of Animals = $4$ chickens + $3$ sheep + $2$ cows

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

Here are some phases translated into a mathematical expression.

1. $4$ plus $6$ equals to $10\quad\rightarrow\quad 4+6=10$
2. $5$ more than $9$ is $14\quad\rightarrow\quad 9+5=14$
3. The sum of a number and $7\quad\rightarrow\quad x+7$
4. $3$ combined with a number $\quad\rightarrow\quad 3+x$

We are now going to take a look at some of the types of problems you might encounter about words to math: addition.

We know that the term "plus" refers to addition, so the operator ‘$+$’ is required.

The term "is" refers to equality, so the operator ‘$=$’ can be used.

Replacing plus with ‘$+$’ and is with ‘$=$’, we can rewrite the phrase given into a mathematical expression.

$7$ plus $11$ is $18\quad\rightarrow\quad 7+11=18$

We know that the phase "combined" refers to addition, so the operator ‘$+$’ is required.

The phase "the same as" refers to equality, so the operator ‘$=$’ can be used.

Replacing combined with ‘$+$’ and the same as with ‘$=$’, we can rewrite the phase given into a mathematical expression.

$6$ combined with $3$ is the same as $9\quad\rightarrow\quad 6+3=9$

We know that the term "and" refers to addition, so the operator ‘$+$’ is required.

Since we are totaling the number of books to find the sum, the operator ‘$=$’ is also required.

Total Number of Books = $3$ Fiction Books + $2$ Biology Books + $5$ Math Books

(Video) Translating Phrases

by GVSUmath

This video by GVSUmath explains how to translate words to math.

$\large{\text{Summary}}$

The first sentence she looks at is: Three less than a number.

Take a look at the part that says less than. This tells us that we want to switch the order of the numbers to subtract. We see that three comes first in the sentence. Therefore, because it says less than, we want three to come second. So our sentence can be written as: $$n-3$$

The second sentence is: The difference of a number and $15$.

Here, difference means subtraction. Since we don't have a "than" like in the above problem, we subtract in the order in which the numbers are presented. Our sentence can be written as: $$n-15$$

The third sentence is: The sum of a number and $12$.

Sum indicates we want addition. Our sentence can be written as: $$n+12$$

The fourth sentence is: The product of a number and $7$.

Product indicates we want multiplication. Our sentence can be written as: $$n\times 7$$

The video contains more examples if you want more practice!

Word Problems with Addition

The key to solving word problems is to translate them into mathematical expressions. This is made easier if you can pick out key phrases that tell you what type of operation the problem is asking for. We'll call these signal words.

Let's try a few practice problems.

These signal words confirm that we will be doing addition. Now it's time to translate the word problem into a mathematical expression.