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Simplifying Rational Expressions
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Learn to simplify fractions that contain variables.
Fractions with variables can also be described as rational expressions.
Transcript
Hi welcome to MooMooMath Today we are going to learn how to simplify expressions with variables.
This expression is a fraction which is another name for a rational, so sometimes you will hear them called a rational expression, which are just fractions.
Our first example is 24x^5y^6/15x^2y^4
The first thing I will do is create a factor tree for the numerator.
Step one of the factor tree will be 24 breaks down to 4 x 6 which breaks down to 2 x2x2 x3
I will next take those factors and rewrite them here.
Now lets look at the variables of this fraction. I have x times x times x times x times x which is x to the fifth. I also have six y's because it is y to the sixth. Those are all of the factors of 24x^5y^6 I will next do the same thing to the denominator. 15 and draw a factor tree and that is just 5 times 3 and I will bring that up here. x^2 is x times x, and y^4 is y y y y
Now I get to do the fun part. I get to cancel, because any value divided by itself is one. The threes will cancel, Two x's cancel, I next go to the y variable and four of them cancel. What do I have left? I will take all of the factors and multiply them back together to get my final answer. So 2 x 2 = 4 x 2 = 8 and I have two y's left so I have y^2. In my denominator the only value I have is the 5 The final answer to this rational expression is 8x^3y^2/5 or you can write is as 8/5 x^3y^2
Lets try one more rational expressions
Lets create a factor tree of 16 which is 2 x 8 2 x4 and 2 x 2 so we are left with 2 * 2 *2 *2 and a^5 is a*a*a*a*a and b and c to the fifth I will write five c's
This will be my numerator.
Lets next take our denominator.
We have 20 which is 2 x 10 and 10 is 2 times 5 so I have 2 *2 *5 in the denominator. Lets write out our factors for a^2 which is a *a and b^3 is b*b*b, and c ^5 is 5 c's
Now we have our factors so we can now cancel out, because any number divided by itself is one. Here are all the coefficients I can cancel. I will go to the a's and I can cancel one, and I can take off one b and I can cancel all of the c's
Lets see what I'm left with.
I have 2 on top and another 2 which equals 4, and a cubed and my b is gone, and my c.
On the bottom I have a 5 left.
So my final answer is 4a^3/5b^2
So that is my final answer.
Hope this video was helpful on learning how to simplfy expressions with variables
-~-~~-~~~-~~-~-
Please watch: "Study Skills Teacher's Secret Guide to your Best Grades"
-~-~~-~~~-~~-~-
Learn even more about fractions with this fraction playlist that covers the basics of fractions!!
Fractions with variables can also be described as rational expressions.
Transcript
Hi welcome to MooMooMath Today we are going to learn how to simplify expressions with variables.
This expression is a fraction which is another name for a rational, so sometimes you will hear them called a rational expression, which are just fractions.
Our first example is 24x^5y^6/15x^2y^4
The first thing I will do is create a factor tree for the numerator.
Step one of the factor tree will be 24 breaks down to 4 x 6 which breaks down to 2 x2x2 x3
I will next take those factors and rewrite them here.
Now lets look at the variables of this fraction. I have x times x times x times x times x which is x to the fifth. I also have six y's because it is y to the sixth. Those are all of the factors of 24x^5y^6 I will next do the same thing to the denominator. 15 and draw a factor tree and that is just 5 times 3 and I will bring that up here. x^2 is x times x, and y^4 is y y y y
Now I get to do the fun part. I get to cancel, because any value divided by itself is one. The threes will cancel, Two x's cancel, I next go to the y variable and four of them cancel. What do I have left? I will take all of the factors and multiply them back together to get my final answer. So 2 x 2 = 4 x 2 = 8 and I have two y's left so I have y^2. In my denominator the only value I have is the 5 The final answer to this rational expression is 8x^3y^2/5 or you can write is as 8/5 x^3y^2
Lets try one more rational expressions
Lets create a factor tree of 16 which is 2 x 8 2 x4 and 2 x 2 so we are left with 2 * 2 *2 *2 and a^5 is a*a*a*a*a and b and c to the fifth I will write five c's
This will be my numerator.
Lets next take our denominator.
We have 20 which is 2 x 10 and 10 is 2 times 5 so I have 2 *2 *5 in the denominator. Lets write out our factors for a^2 which is a *a and b^3 is b*b*b, and c ^5 is 5 c's
Now we have our factors so we can now cancel out, because any number divided by itself is one. Here are all the coefficients I can cancel. I will go to the a's and I can cancel one, and I can take off one b and I can cancel all of the c's
Lets see what I'm left with.
I have 2 on top and another 2 which equals 4, and a cubed and my b is gone, and my c.
On the bottom I have a 5 left.
So my final answer is 4a^3/5b^2
So that is my final answer.
Hope this video was helpful on learning how to simplfy expressions with variables
-~-~~-~~~-~~-~-
Please watch: "Study Skills Teacher's Secret Guide to your Best Grades"
-~-~~-~~~-~~-~-
Learn even more about fractions with this fraction playlist that covers the basics of fractions!!
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