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Translating Math into Words

We spend a lot of time talking about how to solve word problems by translating the words into mathematical expressions: addition, subtraction, multiplication, or division.

The useful thing about translation is that it can go both ways. Just like we can translate words into mathematical expressions, we can translate mathematical expressions back into words.

That's what we'll focus on here—going from math to words.

One of the most helpful things to start with is the translation of the operation in a mathematical expression.

Here are some possible translations:

Sometimes, math problems can be pretty scary to look at. There might be numbers and symbols and parentheses everywhere which make equations/expressions practically unreadable.

One useful trick to try and understand math equations is to try to convert them to words. We can even do this for algebraic expressions.

Let's try a small example to start: $$7y+9$$

We can say this in a few different ways:

1. $9$ more than $7y$
2. $7y$ more than $9$
3. The sum of $7y$ and $9$

All these statements are saying the same thing, so feel free to figure out what way makes the most sense to you!

Now, let's see if we can try something a little more complicated like follows: $$3y-8 = 2 \cdot (y-2)$$

For something like this, it might be better to almost think of a small story. We want the variable to represent an object. We might say something like "I started with $y$ dogs and $2$ were taken away, then the number of dogs I had was doubled! After that, it was the same amount of dogs as if I had first tripled the number of dogs I had then taken $8$ away."

In this type of situation, the algebraic equations are represented in stories.

For this specific problem, we want to figure out how many dogs I originally had. I'll leave it to you to solve the equation and answer the question we started with. Here's a hint, though: use the distributive property on the right-hand side.

Try to get creative with the ways you convert equations to words and see what phrases you're most comfortable interpreting math as. Then read the problem once more for good measure. This will help ensure you don't miss any important details. Good luck!

(Video) Translating Math to Word Statements

by MuchoMath

Here's a video by MuchoMath that teaches you how to turns mathematical equations into words.

$\large{\text{Summary:}}$

The first example he looks at is: $$3+8$$

When translating math into words, we want to look at the operation being used. Here, it's addition. One way to write addition is "the sum of". $$\text{The sum of }$$ Next, we write the numbers being used in the expression. These will be $3$ and $8$. $$\text{The sum of three and eight.}$$

Let's look at an equation now. $$-2+8=6$$ Again, our operation is addition. $$\text{The sum of}$$ Our numbers next to the operation are $-2$ and $8$. $$\text{The sum of negative two and eight}$$ We can use the word "is" to refer to an equal sign. $$\text{The sum of negative two and eight is}$$ Finally, our last number is $6$. $$\text{The sum of negative two and eight is six.}$$