For more information, please see full course syllabus of Basic Math
For more information, please see full course syllabus of Basic Math
Discussion
Study Guides
Practice Questions
Download Lecture Slides
Table of Contents
Transcription
Related Books
Writing Equations
Related Links
- Equation: A math statement with two expressions that equal each other. It contains an equal (=) sign and uses numbers and variables.
- =: is
Writing Equations
Ten minus x is five
The product of eight and y is thirty two
- 8 ·y = 32
A number plus ten is eleven
y divided by 9 is 50
Eight is three more than x
The quotient of m and nine is five
6 + z = 9
9 · b = 27
The product of five and six is thirty
- 5 ·6 = 30
Nine is the sum of five and two
- 9 = 5 + 2
*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
Answer
Writing Equations
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
- Intro 0:00
- Equation 0:05
- Definition of Equation
- Examples of Equation
- Operations as Words 1:39
- Operations as Words
- Extra Example 1: Write Each as an Equation 3:07
- Extra Example 2: Write Each as an Equation 6:19
- Extra Example 3: Write Each as an Equation 10:08
- Extra Example 4: Determine if the Equation is True or False 13:38
Basic Math Online Course
Transcription: Writing Equations
Welcome back to Educator.com.0000
For the next lesson, we are going to be writing equations.0002
An equation is a math statement with two expressions equaling each other.0007
The previous lesson, we went over expressions, how to write expressions.0014
Remember an expression is a math statement that also uses numbers and variables.0017
An equation is when two of those expressions are equal to each other.0025
The main difference between expression and equation is that equation has an equal sign.0030
If you look at the first four letters of equation, it is almost the full word equal.0041
Think of equation as equal or having an equal sign whereas expressions do not.0051
If I just said A plus 3, A plus 3 without equaling 5, that would be considered an expression.0059
But if you see A plus 3 equal to 5, then that becomes an equation.0070
Here we are going to use words and operations into words to write this two ways,0079
as an equation using numbers and variables and using just words only.0091
To go over our different operations, this for addition, we can use plus.0101
We can use more than.0108
For the subtraction, we can use minus; we can use less than.0111
For multiplication, we can use times or product.0116
For division, we can say divided by; we can say quotient.0122
This one, when you see the word is, that means equals.0129
You can say A plus 3 equals 5; then you can say A plus 3 is 5.0136
Also to go over this, more than and less than, when you see the word than,0146
just like when we were writing expressions, you have to switch.0150
For example, if I say A more than B, more than means plus.0155
But instead of saying A plus B in that order, we have to switch those two.0167
Instead of A plus B, you are going to write B plus A.0174
It is for this one and this one.0180
Whenever you see the word than, you are going to switch them.0182
Let's do a few examples; write each as an equation.0188
For the first one, 10 minus A is 5.0192
We know that... we can write that...minus means minus; A.0197
Then is you know is equal; and 5.0205
That is it; that would be our equation; 10 minus A equals 5.0211
The second one, the product of 7 and 8 is X.0217
Product means times; 7 times 8 is X.0223
I know that this means times; this means product.0239
But when I start writing equations, I don't want to use this anymore.0244
I don't want to use the X to represent multiplication because, X, we use that as a variable.0248
Since we are using it as a variable, as an unknown number, unknown value,0257
I don't want to write it here because it looks like I have a variable.0261
Instead of using the X to represent times, you can either for now write the little dot.0269
But even this later on, you are not going to be able to do that anymore.0279
The best way to show two numbers being multiplied together is in parentheses.0284
To write each of them in parentheses.0290
That is the best way to represent multiplication, two numbers being multiplied together.0292
If you see two numbers written in parentheses like this, then that means times.0299
It means 7 times 8.0305
The next one, a number plus 4 is 10; here it just says a number.0310
A number plus 4 is 10; we know this is plus 4 equals 10.0317
But we don't know that that is; anything unknown, we write as a variable.0325
You can just pick whatever variable; you can say A.0333
You can say B; you can say D; whatever your favorite letter is.0336
You are going to write that as a number.0340
The next one, 6 is P divided by 3; 6 equals P divided by 3.0346
Or divided by can also be written as a fraction.0359
This can be 6 equals P divided by 3.0365
You can write it like this; or you can write it like that.0373
Let's do a few more; 12 is 2 more than A.0381
12 is 2 more than A; we know more than is plus.0387
But you see that word right there.0393
Instead of writing 2 plus A, I have to write A plus 2.0396
You are going to leave it like that.0405
A number multiplied by 2 is 20; a number; again we see that, a number.0409
I can say M multiplied, times, 2 is 20; M times 2 equals 20.0417
When it comes to multiplying letters and numbers together, you don't have to write it like this.0433
We can just stick them together with the number in front.0442
I can write M times 2 as 2M.0445
When you have a number in front of a variable like that, it means multiply them.0450
This is 2 times M; you can write it in that way.0456
Here they said a number first; a number multiplied by 2.0461
You would think you write it like that.0467
But when you have a number times a variable, you always write the number in front.0469
You don't have to write anything between them.0477
You don't have to write the dot; you don't have to write parentheses.0478
Only when it comes to numbers with variables.0481
Or you can do it with variable to variable also.0485
If it is M times N, then you can just write them together like that.0487
Just be careful, you cannot write it with a number being multiplied to a number.0493
If I want to say 2 times 3, if I put them together like that, then that just becomes 23.0497
That doesn't say 2 times 3 so you can't write it like that.0505
Only when you are multiplying a number with a letter, a variable, or variable with variable.0509
Only when a variable is involved, you can write them together.0517
M times 2 equals 20; this can be written as 2M equals 20.0522
The quotient of a number and 4 is 40; quotient is divide.0532
Quotient of... what are the two things that we are dividing?--a number and 4.0541
A number again is just a variable; you can say Z.0548
Z divided by 4 equals 40; again we can write this as a fraction.0556
This can be Z over 4 equals 40; Z divided by 4 equals 40.0569
The last one, 2 added to a number is 21.0581
2 added to a number P equals 21.0588
Again you can use whatever variable you want; 2 plus P equals 21.0598
Write the equations using words.0610
You can write this several ways because we know that addition, we can use plus.0614
We can use added; we can use the sum.0619
Here we can say 5 plus Z is 9; I am going to use sum.0628
I am going to say the sum of 5 and Z.0636
If you use sum, then you have to write the two things that you are going to be adding together.0648
5 and Z, those are the two things; equals translates to is; 9.0654
The sum of 5 and Z is 9.0666
Here 3; this is is; 18; 18 minus A.0671
You can also say 3 is A less than 18.0691
Remember that here, I had to switch these because of this.0706
The next one, the product of 2 and B; or you can say 2 times B.0714
The product of 2... be careful, you are not going to say 2 times B because you already said product.0726
You already used that word to show operation; here you are going to write and.0739
You are saying between this and B; this is... and then 10.0748
The product of 2 and B is 10.0762
The fourth one, 36 divided by 3 is 12.0768
Or I can say the quotient of 36 and 3 is 12.0772
It is okay if yours is a little bit different than what I wrote as long as you use the words correctly.0797
Make sure if you are going to use less than or more than here, then you are going to switch.0804
You can say Z more than 5 is 9.0810
We are going to determine if the equation is true or false.0820
The first one, 12 is the sum of 10 and 2.0824
I am going to write it as an equation first.0831
12 equals... we know is is equals... the sum... we are going to add.0832
We are going to be adding what and what?--10 and 2.0840
10 plus 2; is this true?--12 equals 10 plus 2?--yes it is true.0844
Number two, the product of 6 and 3 is 15.0857
Product means we are going to be multiplying.0861
6 and 3, remember if you are going to multiply two numbers,0866
the best way for you to write that is to write them each in parentheses.0869
6 and 3, is, equals, 15; 6 times 3 we know is not 15.0875
This one is false.0888
The next one, 8 minus 10 is 2; equals 2.0895
This may look right; this may look true.0906
But it is actually not because here this is 8 minus 10.0909
If I had 10 minus 8, this equals 2.0916
But that is not the equation; it is 8 minus 10.0923
Remember this number is smaller than this number.0926
If I have a number line, this is 0; say this is 8.0935
If I am going to start at 8 and then go backwards 10 because that is what minus says,0947
then I am going to be... all the way to here is... that is 8.0953
I moved 8 spaces; but then I have to move 2 more.0959
Where am I going to land?--if I move 10 spaces, then I am going to land at -2.0964
Then this is not true; this is false because 8 minus 10 is -2.0972
Again you are starting at +8 and then you are going to move backwards 10 spaces on the number line.0979
You are going to land at -2; so this is false.0986
You can also think of this as +8 and -10.0997
Remember minus and negative is the same thing.1002
If you want, you can circle this sign with that number.1006
This is +8 and -10; we know that this is the bigger number.1010
We have to give this the sign of that number if you remember from going over integers; +8 minus 10.1018
Another way you can think of this for integers, if you have 8 apples.1028
It is a +8; you have something; you have 8 apples.1035
But let's say you need 10 apples.1039
Say you are going to bake an apple pie or something.1042
You need 10 apples; negative means that you need it or you borrowed it.1044
You have 8; you need 10; are you short?--do you have 2 left?1052
No, you don't have 2 apples left.1059
You used up all of your apples and you need 2 more.1060
That would be a -2 because you are short 2; that is a -2.1065
It would be 8 minus 10 would be -2.1072
That is it for this lesson; thank you for watching Educator.com.1080
1 answer
Last reply by: Milan Ray
Sun Jun 1, 2014 3:50 PM
Post by Rishabh Kasarla on January 22, 2012
what if you have 4 numbers in the perenteces
would you multiply all of them?