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Variable Expressions

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A symbol for a number whose value is not known.

For example:

The statement x + 5 means a number plus 5.

This is called a variable expression.

The answer depends on what number the variable (x) stands for.

To figure out the value of the expression, you must be aware of the value of the variable.

x = ??

When you know what it equals, you simply substitute it into the expression and find the answer.

Finding the value of algebraic expression

Example 1

 

x + 5, if x = 3

This statement says to add 5 to whatever x equals.

Since x = 3, simply substitute 3 in place of x in the given expression. That means just replace the x with the number 3.

x + 5

3 + 5

8.

The answer is obviously 8 since 3 + 5 = 8.

 

Example 2

 

9n if n = 2

Whenever a number and a variable are written right next to each other with no space in between, this means multiplication.

 

So this statement says to multiply 9 by whatever n equals.

Since n = 2, simply substitute 2 in place of n in the given expression. That means just replace the variable n with number 2.

9 x n

9 x 2

18

The answer is 18 since 9 multiplied by 2 is 18.

Can we write our own variable expression from a statement ???

You can write your own variable expression from a statement. You need to think about what the statement is saying and then translate it into mathematical expression.

Here are a few key words you must remember :-

  • "a number" means a variable (like x) because you don't know which number they mean.
  • Sum, more than, increased by, plus, and together all mean addition (+)
  • Difference, less than, decreased by, and minus all mean subtraction (-)
  • Product, times, and of mean multiplication (X)
  • Quotient and divided by mean division (÷)
 

Example 3

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12 more than a number.

Take each word and translate it to math.

12 is obviously 12

More than means '+'

A number means a variable. Let's use x.

12 more than a number in mathematical form is :

12 + x

Or, you could also say x + 12 since the order does not change the sum.

 

Example 4

 

A number decreased by 2.

Translate each word to math.

A number means a variable. We'll use n this time.

Decreased by means '-'

subtracting the variable by 2.

A number decreased by 2 in mathematical form is :

n - 2


Example 5

 

A number divided by 6.

Translate each word to math.

A number means a variable.

Let's use 'y' this time.

Divided by means '÷'

Dividing the variable by 6.

A number divided by 6:

y ÷ 6


Example 6


Alexis has 5 more pencils than Sadie has. Write an expression to describe how many pencils Alexis has. Use s to represent Sadie's pencils.

This problem is a little different since it's a real-world scenario. But we know that s represents Sadie's pencils (since we don't know how many pencils she has.)

Number of pencils with Sadie is represented by 's'.

We also know that Alexis has 5 more pencils.

More means addition, so we'll use a '+' sign.

Hence, Alexis has "s + 5" pencils.


Example 7


Adam has twice as much money as his brother Rand does. Write an expression to describe how many dollars Adam has if Rand has r dollars.

'r' represents how many dollars Rand has.

Adam has twice as much as Rand.

That means he has 2 times as much.

This can be written as 2 x r.

So, Adam's money can be represented as "2 x r or 2r".

Summary
  • Variable : A symbol for a number whose value is not known.
  • To find the value of a variable expression, substitute the value of the unknown variable in the mathematical statement and simplify.
  • To frame a variable expression from a statement, following key points are used :

  • "a number" means a variable (like x) because you don't know which number they mean.
  • Sum, more than, increased by, plus, and together all mean addition (+)
  • Difference, less than, decreased by, and minus all mean subtraction (-)
  • Product, times, and of mean multiplication (x)
  • Quotient and divided by mean division (÷)

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