For example:
If we want to give X a value of 3 in the expressions below, we will obtain the following:
a) X+5βX=3+5β3=5
b)β10+XΓ(X4β)=β10+3Γ(34β)=β10+3Γ34β=β10+4=β6
c) X+Yβ5=3+Yβ5
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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+8β
4+12:3=48
Answer:
48
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Exercise 2
Find the numerical value of the following expression if X=2.5:
3(X+X)3β
Solution
First, we substitute 2.5 in the place of X and then perform the various operations.
3(2.5+2.5)3β=5
Answer:
5
Exercise 3
Find the numerical value of the following expression given that X=10 and Y=7:
X2+Y2+1000
Solution
We simply replace X and Y with the given numbers and solve.
100+49+1000
102+72+1000=1149
Answer:
1149
Do you know what the answer is?
Exercise 4
Find the numerical value of the following expression if X=12 and Y=9:
6Xβ+6Yβ
Solution
We substitute the given numbers for X and Y and then solve.
612β+69β
2+23β
Answer:
223β
Exercise 5
Find the numerical value of the following expression if X=4, Y=8, and Z=2:
Xβ
ZYβ+X2+2Yβ+200
Solution
We replace X,Y and Y with the given numbers and solve.
4β
28β+42+28β+200
4β
4+16+4+200
4β
4+16+4+200=236
Answer:
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) a2β6a+1
d) (x+1)(xβ2)
e) m2βn2β1
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 x2β3x+7?
Solution
Replace x with its assigned value and perform the operations.
(2)2β3(2)+7=4β6+7=11β6=5
Example 2
Given that m=4 and n=10, find the value of (m+3)(nβ6).
Solution
(4+3)(10β6)=(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 worryβit'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 The Domain of an Algebraic Expression
Exercise #1
What will be the result of this algebraic expression:
5xβ6
if we place
x=0
Video Solution
Step-by-Step Solution
Usually we don't know the value of the unknown and need to find it,
However, in this case they give us a value, so the first action will be to substitute it into the expression,
Meaning, replace every place where X is written with 0.
5*0-6=
0-6=-6
Therefore, the result is -6.
Answer
Exercise #2
What will be the result of this algebraic expression:
5xβ6
if we place
x=β3
Video Solution
Step-by-Step Solution
The first step is to substitute X in the exercise, resulting in:
5(β3)β6
When we have two numbers with different signs, meaning one number is negative and the other is positive or vice versa,
the result of multiplication or division will always be negative.
5Γβ3=β15
β15β6=β21
Answer
Exercise #3
What will be the result of this algebraic expression:
8aβb(7+a)
if we ascertain that:
a=50,b=0
Video Solution
Step-by-Step Solution
Let's insert the given data into the expression:
8*50-0(7+50) =
400-0*57 =
400-0 =
400
Answer
Exercise #4
What will be the result of this algebraic expression:
5xβ6
if we place
x=8
Video Solution
Answer
Exercise #5
What will be the result of this algebraic expression:
5xβ6
if we place
x=β2
Video Solution
Answer