Write each fraction in simplest form.
#18
(-5x^3y^3)/(-20xy^4)
my answer is: (3x^2)/(4y)
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Write each expression in simplest form.
#24
(4x-28)/(5x-35) = (4(x-7))/(5(x-7))
MY answer= (4)/(5)
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Write each expression in simplest form
(4r^2-25s^2)/(2r^2+3rs-20s^2)
MY answer: (2r+5s)/(r+4s)
Where did you get the "3" in your answer for #18 ?
The rest look OK!
16/100
To simplify fractions, we can follow these steps:
Step 1: Find the greatest common factor (GCF) of the numerator and the denominator.
Step 2: Divide both the numerator and the denominator by the GCF.
Let's apply these steps to each fraction:
#18:
(-5x^3y^3)/(-20xy^4)
Step 1: GCF of -5x^3y^3 and -20xy^4 is 5xy^3.
Step 2: Divide both the numerator and the denominator by 5xy^3.
((-5x^3y^3)/(5xy^3)) / ((-20xy^4)/(5xy^3))
= (-5x^3y^3) * (5xy^3) / (-20xy^4) * (5xy^3)
= -25x^4y^6 / -100x^2y^7
= (25x^4y^6)/(100x^2y^7)
Now, let's further simplify by canceling out common factors:
(25x^4y^6)/(100x^2y^7)
= (25/100) * (x^4/x^2) * (y^6/y^7)
= (1/4) * x^(4-2) * y^(6-7)
= (1/4) * x^2 * y^(-1)
= x^2/(4y)
Therefore, the simplified form of (-5x^3y^3)/(-20xy^4) is x^2/(4y).
Now let's move on to #24.
(4x-28)/(5x-35)
Step 1: GCF of 4x-28 and 5x-35 is 4.
Step 2: Divide both the numerator and the denominator by 4.
((4x-28)/4) / ((5x-35)/4)
= (4(x-7))/4 / (5(x-7))/4
= (x-7)/(5(x-7))
Now, we can cancel out the common factor of (x-7):
(x-7)/(5(x-7))
= 1/5
Therefore, the simplified form of (4x-28)/(5x-35) is 1/5.
For the last expression, let's simplify it:
(4r^2-25s^2)/(2r^2+3rs-20s^2)
Step 1: Factoring the numerator and the denominator.
(2r+5s)(2r-5s) / (2r-5s)(r+4s)
Step 2: Cancel out the common factor of (2r-5s):
(2r+5s)/(r+4s)
Therefore, the simplified form of (4r^2-25s^2)/(2r^2+3rs-20s^2) is (2r+5s)/(r+4s).
Regarding your comment about the "3" in my answer for #18, I apologize for the mistake. It should be (1/4) instead of (3). Thank you for bringing it to my attention.