# Translate Words to Algebraic Expressions

Talking is always considered to be a great way of expressing one's self whether with spoken word or just flat out honest. But, what if you can turn your words into expressions? This is where algebraic expressions come in. There are various key words and phrases that come in handy when it comes to detailing common mathematical operations. When it comes to writing algebraic expressions and equations, just always make sure that you assign a variable [with \(x\) being the most common variable to use] to represent the unknown number.

Everything that you see bolded and italicized is actually either a key word or even a key phrase for that respective operation. Everything boxed will be written examples of algebraic phrases with all the hidden answers being algebraic expressions.

#### Contents

## Section \(A\): Addition

\[\boxed{\textup{A number \textbf{\textit{plus}} one.}}\]

\[x+1\]

\[\boxed{\textup{Two \textbf{\textit{more than}} a number.}}\]

\[x+2\]

\[\boxed{\textup{The \textbf{\textit{sum of}} a number and three.}}\]

\[x+3\]

\[\boxed{\textup{The \textbf{\textit{total of}} four and a number.}}\]

\[4+x\]

\[\boxed{\textup{A number \textbf{\textit{increased by}} five.}}\]

\[x+5\]

\[\boxed{\textup{Six \textbf{\textit{added to}} a number.}}\]

\[x+6\]

## Section \(B\): Subtraction

\[\boxed{\textup{A number \textbf{\textit{minus}} one.}}\]

\[x-1\]

\[\boxed{\textup{Two \textbf{\textit{less than}} a number.}}\]

\[x-2\]

\[\boxed{\textup{The \textbf{\textit{difference of}} a number and three.}}\]

\[x-3\]

\[\boxed{\textup{Four \textbf{\textit{less}} a number.}}\]

\[4-x\]

\[\boxed{\textup{A number \textbf{\textit{decreased by}} five.}}\]

\[x-5\]

\[\boxed{\textup{Six \textbf{\textit{subtracted to}} a number.}}\]

\[x-6\]

## Section \(C\): Multiplication

\[\boxed{\textup{Two \textbf{\textit{times}} a number.}}\]

\[2x\]

\[\boxed{\textup{The \textbf{\textit{product of}} three and a number.}}\]

\[3x\]

\[\boxed{\textup{\textbf{\textit{Twice}} a number.}}\]

\[2x\]

\[\boxed{\textup{\textbf{\textit{Double}} a number.}}\]

\[2x\]

\[\boxed{\textup{\textbf{\textit{Half}} a number.}}\]

\[\frac{1}{2}x\]

\[\boxed{\textup{A number \textbf{\textit{multiplied}} by negative four.}}\]

\[-4x\]

\[\boxed{\textup{Three fifths \textbf{\textit{of}} a number.}}\]

\[\frac{3}{5}x\]

## Section \(D\): Division

\[\boxed{\textup{The }\textup{\textbf{\textit{quotient of}} a number and two.}}\]

\[\frac{x}{2}\]

\[\boxed{\textup{Three }\textup{\textbf{\textit{divided by}} a number.}}\]

\[\frac{3}{x}\]

\[\boxed{\textup{The }\textup{\textbf{\textit{ratio of}} a number and four.}}\]

\[\frac{x}{4}\]

## Section \(E\): Power

\[\boxed{\textup{The }\textup{\textbf{\textit{square of}} a number.}}\]

\[x^2\]

\[\boxed{\textup{A number } \textup{\textbf{\textit{squared}}.}}\]

\[x^2\]

\[\boxed{\textup{The }\textup{\textbf{\textit{cube of}} a number.}}\]

\[x^3\]

\[\boxed{\textup{A number } \textup{\textbf{\textit{cubed}}.}}\]

\[x^3\]

## Section \(F\): Equals

\[\boxed{\textup{A number }\textup{\textbf{\textit{equals}} one.}}\]

\[x=1\]

\[\boxed{\textup{Two times a number }\textup{\textbf{\textit{is}} three.}}\]

\[2x=3\]

\[\boxed{\textup{Four }\textup{\textbf{\textit{is the same as}} five times a number.}}\]

\[4=5x\]

\[\boxed{\textup{Six subtracted from a number }\textup{\textbf{\textit{yields}} seven.}}\]

\[x+6=7\]

\[\boxed{\textup{Eight more than a number }\textup{\textbf{\textit{amounts to}} nine.}}\]

\[8+x=9\]

## Section \(G\): Combining Phrases into Expressions

When you're given some verbal descriptions, it is best to always keep in mind what goes first and what goes last along with what needs to be in parenthesis or with an exponent if written in the description.

\[\boxed{\textup{Ten times the sum of five and a number.}}\]

\[10(5+x)\]

\[\boxed{\textup{Twice the cube of a number.}}\]

\[2x^3\]

\[\boxed{\textup{Three times the difference of a number and seven is four times a number.}}\]

\[3(x-7)=4x\]

\[\boxed{\textup{Eight less than the quotient of three and a number is nine.}}\]

\[\frac{3}{x}-8=9\]

**Cite as:**Translate Words to Algebraic Expressions.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/translate-words-to-algebraic-expressions/