Writing Algebraic Expressions — Examples & Practice

(Videos) Translating Words to Algebraic Expressions

by mathman1024

Here's a video by mathman1024 where he shows you how to turn words into math. There are more videos further into the explanation.

$\large{\text{Summary}}$

When talking about addition you will most likely see the word sum or the phrase more than.

When talking about subtraction you will most likely see the word difference or the phrase less than.

When talking about multiplication you will most likely see the words product or times.

When talking about division you will most likely see the word quotient.

When talking about equality you will most likely see amounts, is, is the same as, or equals.

Finally, when talking about variables you will most likely see the number, some number, the missing/unknown number.

When you see the words sum, difference, product, and quotient your next step is to find the word and. This will be between the two numbers in your operation just like how $+$, $-$, $\times$, and $\div$ go between the two numbers.

$$\begin{array}{|c|c|} \hline \text{Words}&\text{Math}\\ \hline \text{sum}&+\\ \text{more than}&+\\ \text{difference}&-\\ \text{less than}&-\\ \text{product}&\times\\ \text{times}&\times\\ \text{quotient}&\div\\ \text{amounts}&=\\ \text{is}&=\\ \text{is the same as}&=\\ \text{equals}&=\\ \text{the number}&x\\ \text{some number}&x\\ \text{the missing number}&x\\ \text{the unknown number}&x\\ \hline \end{array}$$

He then gives some phrases which you have to translate into a mathematical expression.

1. Some number plus seventeen. $\rightarrow x+17$
2. The sum of a number and ten. $\rightarrow x+10$
3. The difference of a number and eight. $\rightarrow x-8$
4. Five more than some number. $\rightarrow x+5$
5. Seven less than some number. $\rightarrow x-7$

It's important to note in the last two examples that when you have more than or less than, the number that comes before the phrase goes after the operation.

Here's another video with more examples of phrases translated into mathematical expressions.

1. Twice a number. $\rightarrow 2x$
2. The sum of twice a number and three. $\rightarrow 2x+3$
3. Twice the sum of a number and three. $\rightarrow 2(x+3)$
4. Five times the difference of six and four times some number. $\rightarrow 5(6-4x)$

Learning how to do word problems is one of the most "real world useful" parts of math. While the most important thing is to just keep practicing, there are some guidelines that can make things easier.

Whenever I read a word problem, I note down all of the "facts" it's telling me. For example, if a problem says "Sydney is taller than Julie" I might write down:

$$\text{Height}_{\text{Sydney}} > \text{Height}_{\text{Julie}}$$

Be careful not to latch on to any one fact before you're done. Sometimes a word problem can include irrelevant pieces of information. These are called red herrings.

Read through the problem a couple of times and make sure you've pulled out all the information you can. You should be comfortable enough with the word problem to identify the most important piece of information. What is the problem asking?

Before doing any calculations, you need to know exactly what you are solving for. Solving for the wrong measurement wastes your time and effort!

Word problems are all about translation. English is one language, and math is another. Here's a list of some of the most common words and terms you'll want to know:

Writing expressions means translating words into math

Expressions are bits of math that you'll find on one side of an equation (or in the top part of a fraction, or within parentheses... etc.). You see them all the time on your homework or in math books, but it's also important that you're able to write them yourself.

You can think of writing expressions as translating the words you think in your head to mathematical symbols and numbers that you can work with on the page. There are lots of words that have pretty direct translations to math--so many that I can't even write them all here!--but you'll be able to catch on to some patterns pretty quick. Here are some translations though:

• Looking for the sum of two numbers means you need to add ($+$) them
• Looking for the difference between two numbers means you need to subtract ($-$) them
• Looking for the product of two numbers means you need to multiply ($\times$) them
• Looking for the quotient of two numbers means you need to divide $(\div)$ the first by the second.

Since we want the product of four ($4$) and $n$, we need to multiply them. Remember that when we multiple variables by numbers, we can just crowd them right next to each other: $4n$.

This expression has two operations in it, addition ("sum") and subtraction ("minus"). Remember to keep the terms in the right order: $17 + n - 4$.

This sentence could be either $4-3n$ or $(4-3)n$—which is an important difference, if you remember the order of operations. We have this problem because while difference always means that you subtract the second piece from the first piece and times always means multiply the terms around the word times, it's unclear if you're supposed to do the multiplication before or after the subtraction.

This won't happen too much, but remember to watch out for it!