Introduction to Variables
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What is a variable?

A variable represents a number that can change or that we don’t know yet. Because we don’t know the number, we use a letter to represent it. Most often we use x and y, but any letter or symbol can be used as a variable.

Just for Fun

Why do we often use X as a variable?

Much of what we know about mathematics originated in Persia and Arabia. The word algebra literally comes from the Arabic word al-jabr which means “the reunion of broken parts.” When Spanish scholars were translating Arabic mathematical texts, they often came across the Arabic word shay-un which means “something.” Since Spanish doesn’t have the “sh” sound, they used the Greek letter chi (X) instead. Later, these Spanish texts were translated into Latin, X became the standard symbol for something we don’t know. So today we use the letter X because Spanish doesn’t have the “sh” sound.

Gospel Connection

The example of X becoming the standard variable in algebra is an example of how texts can change over time through various translations. The 8th Article of Faith says that “we believe the Bible to be the word of God as far as it is translated correctly.” The Lord revealed to Joseph Smith in the Joseph Smith Translation of the Bible many clarifications for scriptures in the Bible that had lost their original meaning due to changes or mistakes in translation. Some of this can be found in Joseph Smith-Matthew in the Pearl of Great Price.

Introduction to variables

Video Source (02:31 mins) | Transcript

As we begin working with variables, we will often use x as a variable. Because of this, it’s confusing when we have multiplication represented by an x. The following video will explain the different ways we show multiplication.

Different ways to express multiplication

Video Source (02:39 mins) | Transcript

The following video shows how the different ways to express multiplication are used. This is done using variables and the order of operations.

Examples of multiplication written in different ways

Video Source (06:06 mins) | Transcript

Additional Resources

Practice Problems

1. Which of the following could be a variable? Select all that apply. (
Video Solution
Solution: b and c.

(Video Source | Transcript)
a. \(-1\)
b. \(y\)
c. \(A\)
d. \(7.5\)
2. Which of the following represents multiplication? Select all that apply. (
Solution: a, b, d, and e.
a. Is multiplication because it has the \(\times\) symbol of multiplication.
b. Is multiplication because the parentheses between the number and the variable implies multiplication.
c. Not multiplication
d. Is multiplication because a dot in the middle implies multiplication.
e. Is multiplication, because a number next to a variable implies multiplication.
a. \(4 \times n\)
b. \(4(n)\)
c. \(4 + n\)
d. \(4 \cdot n\)
e. \(4n\)

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