Study Guide

# Basic Algebra - Translating Expressions and Equations

## Translating Expressions and Equations

Some words can be translated into math, and some math can be translated into words, and neither require the babel fish from The Hitchhiker's Guide to the Galaxy. When we translate words to math, most are replaced by symbols in the order that they're written.

To translate "seven plus a number," we replace the word seven with the number 7, replace the word plus with the addition sign, and replace the phrase "a number" with a variable like x to get:

7 + x

In the following phrases, we're told the operation first and then the two numbers in the operation. We just keep them in the order given.

The quotient of x and 7: The difference between x and 7: x – 7
The product of 3 and x: 3x

Some phrases tell us the numbers in reverse order. The most common is the phrase "less than," which first tells us what's being subtracted and then tells us what it's being subtracted from. For example, in the phrase "six less than a number," 6 is being subtracted from some given number, so the 6 goes at the end. It looks like this when we translate it into math:

x – 6

Finally, some phrases combine several operations into one long expression. We translate in the order everything is given, with the exception of "less than," and it often helps to include parentheses. For example:

"Three times the sum of a number and ten."

In this phrase, "three times…" means 3 is being multiplied by something. We can write the 3 and an empty set of parentheses waiting for whatever 3 is being multiplied by.

3( )

Next is "the sum of," so we know we'll be adding something inside the parentheses.

3( + )

Finally, "a number and ten" tells us we're adding a variable and ten.

3(x + 10)
Here are some common phrases and symbols. We'll need more practice before we go translating at the next international math conference, so be sure to check out the examples.