6.01 Represent algebraic equations

In algebra, the variables that we write represent unknown values. It is these unknown values that we usually try to find or solve for.

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.

The letters x and n are popular choices for the unknown amount in an equation. However, if a letter is not specified, we can use any letter to represent the unknown number.

We can add or multiply in any order. However, for subtraction and division, the order is important.

For example, "5 less than a number" is written as n-5, not 5-n. Similarly, "a number divided by 8" is written as n\div8 or \dfrac{n}{8} not \dfrac{8}{n} .

An equation is a type of number sentence that sets two expressions equal to each other. It means that the two expressions have the same value. As with our four operations, we can look for key phrases that indicate equality.

For example: "5 less than a number is equal to 28", is represented by the equation n - 5 = 28.

Examples

Example 1

The sum of a number and 24 is 35. Set-up an equation for this scenario.

Worked Solution

Create a strategy

Express the unknown number as a variable. The word "is" indicates equality, the word "sum" indicates addition.

Apply the idea

Using our keywords, we can translate to an equation: x+24=35

Example 2

Write an equation in simplest form for: y is 18 times k.

Worked Solution

Create a strategy

The word "times" indicates multiplication, while "is" indicates equality.

Apply the idea

\displaystyle y	\displaystyle =	\displaystyle 18 \times k	Translate the phrase into equation
\displaystyle y	\displaystyle =	\displaystyle 18k	Simplify

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Example 3

Roxanne has been out picking flowers, and has 40 in total. When she returns, she puts them in 5 different vases. If she puts p flowers in each vase, rewrite the following sentence using algebra:

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

Worked Solution

Create a strategy

The words "groups of" are used to mean multiplication.

Apply the idea

\displaystyle 5 \times p	\displaystyle =	\displaystyle 40	Translate the sentence into an equation
\displaystyle 5p	\displaystyle =	\displaystyle 40	Simplify

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