Reading and writing algebraic expressions

Algebra has a small vocabulary; once you know it you can translate any everyday statement into symbols.

Idea

Here are the most common phrases you will meet, with their algebraic translations:

A small but important point: order matters for subtraction and division. "$3$ less than $y$" is $y - 3$, not $3 - y$. Read carefully.

Going the other way , from symbols to words , also helps. The expression $4n + 7$ reads "four times $n$, plus seven" or "seven more than four times $n$".

Brackets in algebra work just like in arithmetic: they force priority. For example, "twice the sum of $x$ and $5$" is $2(x + 5)$ , not $2x + 5$. The bracket changes the meaning completely.

Worked examples

Example 1. Translate: "the sum of $x$ and $9$, multiplied by $2$".

Sum first: $x + 9$. Then "multiplied by $2$": $2(x + 9)$.

Example 2. Translate: "$5$ less than three times $y$".

Three times $y$: $3y$. $5$ less than that: $3y - 5$.

Example 3. Express in words: $\dfrac{a}{2} + 7$.

"Half of $a$, plus $7$" or "$7$ more than half of $a$".

Example 4. A taxi charges a base fare of $\rupee 50$ and $\rupee 12$ per kilometre. Write the cost expression for $x$ km.

Base $50$, plus $12$ per km, so cost $= 12x + 50$.

Try it yourself

1. Translate "the difference of $a$ and $7$".
2. Translate "twice the sum of $x$ and $4$".
3. Translate "$10$ more than the product of $3$ and $n$".
4. Express in words: $5x - 8$.
5. Write an expression for the perimeter of a rectangle of length $l$ and breadth $b$.
6. The age of a child today is $a$ years. What will it be after $5$ years? $3$ years ago?
7. A boy has $\rupee n$. He spent $\rupee 30$. How much is left?
8. Translate: "one-third of the difference of $x$ and $9$".

Activity

Bring a recipe (your favourite snack!) and rewrite its quantities using a single letter $n$ standing for "number of servings". For example, "$2n$ tablespoons of oil" instead of "$2$ tablespoons for one serving". This is exactly how a chef scales a recipe.