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What Are Numerical and Algebraic Expressions? | Virtual Nerd

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Numerical Expression vs Algebraic Expression

Numerical expression and algebraic expression are a set of symbols and numbers that are formed to represent a certain number once they have been evaluated. They contain constants, variables, operations and relations and are used in simple or complex arithmetic operations.
Numerical Expression
A numerical expression involves purely numbers and mathematical operations. Also, it is a set of numerical values that are separated by the four mathematical operations, addition, subtraction, multiplication and division. The numbers may be positive or negative. Also, when evaluating numerical expressions, we need to evaluate them using the PODMAS or BODMAS method. Start with parenthesis (bracket), order (exponent), then dividing or multiplying, and lastly adding or subtracting.
Algebraic Expressions
Algebraic expressions, on the other hand, involve letters (pro-numerals) as well as numbers and mathematical operations. Numbers are called constants while letters are called variables. Even though the equation uses letters they still represent a certain number. In this case, though, the number they represent changes whenever you change the value of the variable. They still use the PODMAS method of evaluating expressions.
Difference between Numerical Expression and Algebraic Expression
So what are the differences between the numerical expressions and algebraic expressions? Well, to start, the latter uses letters as well as numbers. And therein lays the key difference. While numerical expressions are of fixed value, algebraic expressions can change depending on what you use for the variables. They are still solved using the same method, but algebraic expressions give you certain flexibility in juggling the equation. Also, to qualify as an expression, numerical or algebraic, the equation must be well-formed. That means, at the very least, everything must be in its correct place. For example, * 2/3 + is not a valid expression.

Algebraic expressions and numerical expressions are the cornerstones of our mathematical knowledge, as well as they are the basics of math itself. All those complex equations start from these simple terms and our understanding of what they are is crucial for their further study.

In brief:

* Numerical expressions are expressions containing numbers and math operations only. Numbers may be positive or negative while the operations are limited to addition, subtraction, multiplication and division.

* Algebraic expressions use letters as well as math operations. The letters are termed as variables while the numbers are called constants.

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Difference Between Numerical Expression and Algebraic Expression - DifferenceBetween.com

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Numerical Expression vs Algebraic Expression Numerical expression and algebraic expression are a set of symbols and numbers that are formed to represent a certain number once they have been evaluated. They contain constants, variables, operations and relations and are used in simple or complex arithmetic operations.

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Video transcript

Alan found 4 marbles to add to his 5 marbles currently in his pocket. He then had a competition with his friends and tripled his marbles. Write a numerical expression to model the situation without performing any operations. So let's think about what's going on. So he already had 5 marbles in his pocket. And then he found 4 more marbles to add to that. So we can add the 4 marbles to the 5 marbles. So 4 marbles plus the 5 marbles. So that's what happens after the first sentence. He found 4 marbles to add to his 5 marbles currently in his pocket. He then had a competition with his friends and tripled his marbles. So this is how many marbles he had before tripling. And now he's tripling his marbles. So we want to multiply 3 times the total number of marbles he has now-- times 4 plus 5. So this right over here is the numerical expression that models the situation without performing any operations. We, of course, could then actually calculate this. He has 9 marbles before tripling. And then you multiply it by 3 and he has 27. But this is what they're asking for. They want us to write this expression.

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Constructing numerical expressions (video) | Khan Academy

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Evaluate expressions (Pre-Algebra, Introducing Algebra) - Mathplanet

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Pre-Algebra Introducing Algebra: Operations in the correct order Pre-Algebra Introducing Algebra: Equations with variables Pre-Algebra Introducing Algebra: Coordinate system and ordered pairs Pre-Algebra Introducing Algebra: Inequalities

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Determine the number of solutions for each of these equations, and they give us three equations right over here. And before I deal with these equations in particular, let's just remind ourselves about when we might have one or infinite or no solutions. You're going to have one solution if you can, by solving the equation, come up with something like x is equal to some number. Let's say x is equal to-- if I want to say the abstract-- x is equal to a. Or if we actually were to solve it, we'd get something like x equals 5 or 10 or negative pi-- whatever it might be. But if you could actually solve for a specific x, then you have one solution. So this is one solution, just like that. Now if you go and you try to manipulate these equations in completely legitimate ways, but you end up with something crazy like 3 equals 5, then you have no solutions. And if you just think about it reasonably, all of these equations are about finding an x that satisfies this. And if you were to just keep simplifying it, and you were to get something like 3 equals 5, and you were to ask yourself the question is there any x that can somehow magically make 3 equal 5, no. No x can magically make 3 equal 5, so there's no way that you could make this thing be actually true, no matter which x you pick. So if you get something very strange like this, this means there's no solution. On the other hand, if you get something like 5 equals 5-- and I'm just over using the number 5. It didn't have to be the number 5. It could be 7 or 10 or 113, whatever. And actually let me just not use 5, just to make sure that you don't think it's only for 5. If I just get something, that something is equal to itself, which is just going to be true no matter what x you pick, any x you pick, this would be true for. Well, then you have an infinite solutions. So with that as a little bit of a primer, let's try to tackle these three equations. So over here, let's see. Maybe we could subtract. If we want to get rid of this 2 here on the left hand side, we could subtract 2 from both sides. If we subtract 2 from both sides, we are going to be left with-- on the left hand side we're going to be left with negative 7x. And on the right hand side, you're going to be left with 2x. This is going to cancel minus 9x. 2x minus 9x, If we simplify that, that's negative 7x. You get negative 7x is equal to negative 7x. And you probably see where this is going. This is already true for any x that you pick. Negative 7 times that x is going to be equal to negative 7 times that x. So we already are going into this scenario. But you're like hey, so I don't see 13 equals 13. Well, what if you did something like you divide both sides by negative 7. At this point, what I'm doing is kind of unnecessary. You already understand that negative 7 times some number is always going to be negative 7 times that number. But if we were to do this, we would get x is equal to x, and then we could subtract x from both sides. And then you would get zero equals zero, which is true for any x that you pick. Zero is always going to be equal to zero. So any of these statements are going to be true for any x you pick. So for this equation right over here, we have an infinite number of solutions. Let's think about this one right over here in the middle. So once again, let's try it. I'll do it a little bit different. I'll add this 2x and this negative 9x right over there. So we will get negative 7x plus 3 is equal to negative 7x. So 2x plus 9x is negative 7x plus 2. Well, let's add-- why don't we do that in that green color. Let's do that in that green color. Plus 2, this is 2. Now let's add 7x to both sides. Well if you add 7x to the left hand side, you're just going to be left with a 3 there. And if you add 7x to the right hand side, this is going to go away and you're just going to be left with a 2 there. So all I did is I added 7x. I added 7x to both sides of that equation. And now we've got something nonsensical. I don't care what x you pick, how magical that x might be. There's no way that that x is going to make 3 equal to 2. So in this scenario right over here, we have no solutions. There's no x in the universe that can satisfy this equation. Now let's try this third scenario. So once again, maybe we'll subtract 3 from both sides, just to get rid of this constant term. So we're going to get negative 7x on the left hand side. On the right hand side, we're going to have 2x minus 1. And now we can subtract 2x from both sides. To subtract 2x from both sides, you're going to get-- so subtracting 2x, you're going to get negative 9x is equal to negative 1. Now you can divide both sides by negative 9. And you are left with x is equal to 1/9. So we're in this scenario right over here. We very explicitly were able to find an x, x equals 1/9, that satisfies this equation. So this right over here has exactly one solution.

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Number of solutions to equations | Algebra (video) | Khan Academy

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Determine the number of solutions for each of these equations, and they give us three equations right over here. And before I deal with these equations in particular, let's just remind ourselves about when we might have one or infinite or no solutions.

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00:00

Thank you multistep equations with variables on both sides ah

00:07

la shmoop running the reindeer has always tried to follow

00:10

in the footsteps of his brother rudolf every year rudolph

00:14

by santa and expensive new hat out of the goodness

00:18

of his heart rudolph gives running exactly half his cash

00:22

so they'll have the same amount to spend on christmas

00:25

gifts on the way to the sugar plum all acute

00:28

victim recognizes rudolph and offers to give him seven dollars

00:32

to take a photo with he and his famous knows

00:35

rudolph doesn't want running to feel left out so he

00:37

pays the vixen two dollars to take a photo with

00:40

running in his slightly less famous schnoz Well rudolph even

00:43

asked the vixen teo give the seven dollars to running

00:46

instead we'll check out running has exactly enough money to

00:49

purchase two hats while rudolph has exactly enough to buy

00:53

one Can you determine the price of one of these

00:57

hats Hoof a lot of information Well it'll help to

01:00

be able to solve this sort of problem however because

01:02

the type of situation that pops up a lot in

01:04

real life first we need to determine the variable we're

01:07

going to use way don't know how much money each

01:09

reindeer started with but we do know that they started

01:12

with the same amount since the problem tells us that

01:15

rudolph gave half is cash to running before they headed

01:19

out So let's call their starting cash ex same for

01:22

both Then rudolph gave two dollars to the cute vixen

01:26

so ex minus two running on the other hand received

01:30

seven dollars from his fangirl So x plus seven goes

01:34

there However we're also told that running is able to

01:37

buy twice as many hats Is rudolph after this little

01:40

exchange which means that we'd have to multiply the expression

01:43

for rudolph by two has set he's equal to one

01:47

another So two times the quantity x minus two equals

01:51

x plus seven multiplying that two on the left hand

01:54

side we get to x minus four equals x plus

01:57

seven Of course we want to get x by itself

02:00

so we know how much cash all of these guys

02:02

started with so we can subtract x from both sides

02:05

to get x minus four equals seven then had four

02:08

to each side to get x equals eleven And there

02:11

we have it Each ranger started their shopping trip with

02:14

eleven bucks but that's not what the questions asking We

02:18

know that rudolph gave away two dollars and still had

02:20

exactly enough money to buy one hat itself He started

02:24

with eleven bucks and gave way to box leaving himself

02:26

with nine box Then each hat must run nine dollars

02:31

on the button We can double check to see if

02:33

that's correct by plugging the same number in the runnings

02:35

equation We started with eleven dollars and the vixen gave

02:38

him another seven giving him eighteen dollars total And sure

02:42

enough eighteen divided by nine is too meaning Running would

02:45

have had exactly enough cash to buy two hats It's

02:49

like santa has a new favorite this year This allergy 00:02:52.87 --> [endTime] season strikes

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Algebra Basics: Solving Basic Equations Part 1 - Math Antics

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Algebra Basics: Solving Basic Equations Part 2 - Math Antics