# 4.03 Translating expressions and equations

Lesson

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.

plus

the sum of

increased by

total

more than

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.

Careful!

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 $n-5$n5, not $5-n$5n.

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?

1. 96 times the number represented by q

A

the quotient of the number represented by q and 96

B

96 less than the number represented by q

C

96 more than the number represented by q

D

96 times the number represented by q

A

the quotient of the number represented by q and 96

B

96 less than the number represented by q

C

96 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:

1. "There are $5$5 groups of $p$p flowers, which make $40$40 in total."

### Outcomes

#### 6.1

Represent relationships between quantities using ratios, and will use appropriate notations, such as a/b , a to b, and a:b

#### 6.13

Solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable