# The Numerical Value in Algebraic Expressions

πPractice algebraic expression domain

An algebraic expression is a combination of constant numbers (or 'integers'), unknown variables represented by letters, and basic operations. When we assign numerical values to each of the unknown variables, we can reduce the expression to a numerical value.

If you are unsure about these terms, you can click on the link for more information about variables in algebraic expressions.

For example:

If we take the algebraic expression $X+5$ and assign the variable $X$ a value equal to $3$, then the value of the algebraic expression will be $8$.

• Algebraic expression:
$X+5$
• Algebraic expression after having given the variable $X$ a value of $3$:
$5+3$
• Therefore, the value (result) of the algebraic expression is $8$:
$5+3=8$

If the same variable appears several times in an algebraic expression, each has the same numerical value.

## Test yourself on algebraic expression domain!

What will be the result of this algebraic expression:

$$5x-6$$

if we place

$$x=8$$

For example:

If we want to give $X$ a value of $3$ in the expressions below, we will obtain the following:

a) $X+5-X=3+5-3=5$

b)$-10+X\times\left(\frac{4}{X}\right)=-10+3\times\left(\frac{4}{3}\right)=-10+3\times\frac{4}{3}=-10+4=-6$

c) $X+Y-5=3+Y-5$

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## Exercises: Finding the Numerical Value

### Exercise 1

Find the numerical value of the following expression if $X=4$:

$8+X+8X+12:3$

Solution:

We replace $X$ with the number $4$ and solve.

$8+4+8\cdot4+12:3=48$

$48$

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### Exercise 2

Find the numerical value of the following expression if $X=2.5$:

$\frac{(X+X)3}{3}$

Solution

First, we substitute $2.5$ in the place of $X$ and then perform the various operations.

$\frac{(2.5+2.5)3}{3}=5$

$5$

### Exercise 3

Find the numerical value of the following expression given that $X=10$ and $Y=7$:

$XΒ²+YΒ²+1000$

Solution

We simply replace $X$ and $Y$ with the given numbers and solve.

$100+49+1000$

$10Β²+7Β²+1000=1149$

$1149$

Do you know what the answer is?

### Exercise 4

Find the numerical value of the following expression if $X=12$ and $Y=9$:

$\frac{X}{6}+\frac{Y}{6}$

Solution

We substitute the given numbers for $X$ and $Y$ and then solve.

$\frac{12}{6}+\frac{9}{6}$

$2+\frac{3}{2}$

$2\frac{3}{2}$

### Exercise 5

Find the numerical value of the following expression if $X=4$, $Y=8$, and $Z=2$:

$X\cdot\frac{Y}{Z}+XΒ²+\frac{Y}{2}+200$

Solution

We replace $X,Y$ and $Y$ with the given numbers and solve.

$4\cdot\frac{8}{2}+4Β²+\frac{8}{2}+200$

$4\cdot4+16+4+200$

$4\cdot4+16+4+200=236$

$236$

## Review Questions

What are algebraic expressions?

An algebraic expression is a combination of constant numbers (or 'integers'), unknown variables represented by letters, and basic operations. For example:

a) $x+3$

b) $2x+y$

c) $a^2 -6a+1$

d) $(x+1)(x-2)$

e) $m^2 -n^2 -1$

### How to calculate the numerical value of an algebraic expression or polynomial?

To calculate the numerical value of an algebraic expression or a polynomial, we must assign each variable with a value. Then we substitute these values into the expression and perform all the operations indicated. The result obtained will be the numerical value of the expression for the assigned values of the variables.

Do you think you will be able to solve it?

### What is the numerical value of an algebraic expression?

The numerical value of an algebraic expression is the value to which the expression is reduced once we have assigned all of the variables with a value and performed the operations.

#### Example 1

If $x = 2$, then what is the value of $x^2 β 3x + 7$?

Solution

Replace x with its assigned value and perform the operations.

$(2)^2 -3(2)+7 = 4 β 6 + 7 = 11 - 6 = 5$

#### Example 2

Given that $m = 4$ and $n = 10$, find the value of $(m+3)(n-6)$.

Solution

$(4 + 3)(10 - 6) = (7)(4) = 28$

### What does the numerical value of an expression indicate?

Algebraic expressions are used to represent unknown quantities in a given problem, but once we know these values it is no longer necessary to represent them using algebraic expressions. The numerical value indicates the quantity that is represented by the expression.

### How can you tell if you are falling behind with the subject material?

Are there any geometry topics that you don't fully understand? Well, if the answer is 'yes', then don't worryβit's normal! There are topics that you will learn easily and there will be others that take you longer to grasp.

Important: Try not to fall behind with the subject material, as the pace at which most students learn mathematics is very fast. The problem is that many topics are based on what has been taught before, meaning that if you try to move on to a new subject while your knowledge of the previous one still has holes in it, you will likely struggle with it.

### What are the indictors that you have fallen behind?

• You find it difficult to maintain your concentration in class, as you find it hard to understand the teacher.
• You have difficulty doing your homework.
• You have received a very low grade on an exam.

Do you know what the answer is?

### What can you do in this case?

• You can ask a classmate to explain what you don't understand.
• Ask your mathematics teacher to help you with the topic you don't understand.
• You can hire a private tutor to explain the topic you don't understand from the beginning.

## examples with solutions for algebraic expression domain

### Exercise #1

What will be the result of this algebraic expression:

$8a-b(7+a)$

if we place

$a=50,b=0$

### Step-by-Step Solution

Let's present the data in an expression as given:

8*50-0(7+50) =
400-0*57 =
400-0 =
400

$400$

### Exercise #2

What will be the result of this algebraic expression:

$5x-6$

if we place

$x=8$

34

### Exercise #3

What will be the result of this algebraic expression:

$5x-6$

if we place

$x=0$

### Video Solution

$-6$

### Exercise #4

What will be the result of this algebraic expression:

$5x-6$

if we place

$x=-3$

### Video Solution

$-21$

### Exercise #5

What will be the result of this algebraic expression:

$5x-6$

if we place

$x=-2$

### Video Solution

$-16$