Turning Words into Algebra

In short: To turn a word problem into algebra, choose a letter for the unknown, write the other amounts using it, and use the facts to make an equation. Sum means add, difference means subtract, product means multiply and quotient means divide.

Before you start

Collecting like terms and expanding brackets (earlier chapters in this unit).
Solving equations such as $2 u - 9 = 53$ (see Solving Equations).
Perimeter is the distance around a shape. Average is the total divided by how many there are.

Word to symbol dictionary

Words	Algebra
sum of $a$ and $b$ , $a$ plus $b$ , $b$ more than $a$	$a + b$
difference, $b$ less than $a$ , $a$ take away $b$	$a - b$
product of $a$ and $b$ , $a$ times $b$	$ab$
quotient, $a$ divided by $b$ , $a$ shared among $b$	$\frac{a}{b}$
double $a$ , twice $a$	$2 a$
half of $a$	$\frac{a}{2}$ or $\frac{1}{2} a$
3 times as many as $a$	$3 a$
the square of $a$	$a^{2}$

Writing expressions

Writing and solving equations

Choose a letter for the thing you do not know. Say what it means.
Write the other amounts using that letter.
Use the fact in the question to make an equation.
Solve it, then answer the question in words.

Words into algebra

Dictionary

sum, more than: +
difference, less than: -
product, times: x
quotient, shared: ÷

Expressions

Prices: $3 z$
Ages: $y + 12$
Perimeter: $2 x + 14$

Equations

Name the unknown
Use the fact to write =
Solve and answer in words

Traps

5 less than $n$ is $n - 5$
Everyone ages together

Quick summary

Choose a letter for the unknown and say what it means.
Learn the key words: sum means add, difference means subtract, product means multiply and quotient means divide.
5 less than $n$ means $n - 5$ .
Write other amounts using the letter, then use the fact in the question to make an equation.
In age problems, everybody gets older by the same amount.
Finish by answering the actual question in words.

Quiz

13 questions with instant marking. It is free, and your scores are saved to your account so you can carry on from any device.

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Try 3 questions now

A pen costs $p$ dollars. What do 6 pens cost?
1. A $p + 6$
2. B $6 p$
3. C $\frac{p}{6}$
4. D $6 + p$ dollars
Show answer
B: $6 p$
6 pens cost 6 lots of $p$ , which is $6 p$ dollars.
Leo is $z$ cm taller than Bob, who is 143 cm tall. How tall is Leo?
1. A $143 - z$
2. B $143 + z$
3. C $143 z$
4. D $z - 143$
Show answer
B: $143 + z$
Taller means more, so add: $143 + z$ cm.
How do you write 7 less than $m$ in algebra?
1. A $7 - m$
2. B $7 m$
3. C $m - 7$
4. D $m + 7$
Show answer
C: $m - 7$
Start with $m$ and take 7 away.