5.03 Translating expressions and equations
Mathematics is often referred to as a language. That's why we can take practical situations and translate them into algebraic expressions or equations and vice versa.
Translating phrases into expressions
In algebra, the variables that we write represent unknown values. It is these unknown values that we usually try to find.
Any operation can be used in algebraic expressions - in fact, any combination of operations can be used. To be able to turn written expressions into algebra, we can look for certain keywords to indicate addition, subtraction, multiplication, or division.
| Addition | Subtraction | Multiplication | Division |
|---|---|---|---|
|
plus the sum of increased by total more than added to |
minus the difference of decreased by fewer than less than subtracted from |
times the product of multiplied by of twice groups/lots of |
divided by the quotient of separated into equal parts split |
The letters $x$x and $n$n are popular choices for the unknown amount in a number sentence. However, if a letter is not specified, we can use any letter to represent the unknown number in an expression.
We can add or multiply in any order. However, for subtraction and division, the order is important.
For example, "$5$5 less than a number" is written as $n-5$n−5, not $5-n$5−n.
Similarly, "a number divided by $8$8" is written as $n\div8$n÷8 or $\frac{n}{8}$n8 not $\frac{8}{n}$8n.
Translating sentences into equations
An equation is a type of mathematical sentence that sets two expressions equal. It means that the two expressions have the same value. As with our four operations, we can look for key phrases that indicate equality.
| Equal |
|---|
|
is/are equals amounts to |
Worked example
Question 1
The sum of a number and $24$24 is $35$35. Set-up an equation for this scenario.
Think: We have an unknown, "the number", so let's call "the number" $x$x. We should note some keywords which can help us after we replace "a number" with $x$x. An equation must have an equals sign, unlike an expression which will not.
Do: Using our keywords, we can translate to an equation.
$x+24=35$x+24=35
Practice questions
Question 1
What does the algebraic expression $96q$96q represent?
96 times the number represented by q
Athe quotient of the number represented by q and 96
B96 less than the number represented by q
C96 more than the number represented by q
D
Question 2
Write an equation in simplest form for:
$y$y is $18$18 times $k$k.
Question 3
Roxanne has been out picking flowers, and has $40$40 in total. When she returns, she puts them in $5$5 different vases.
If she puts $p$p flowers in each vase, rewrite the following sentence using algebra:
"There are $5$5 groups of $p$p flowers, which make $40$40 in total."