I assume that you are talking about simplifying fractions?
Simplifying (or reducing) fractions means to make the fraction as simple as possible. Why say four-eighths (4/8) when you really mean half (1/2) ? Try dividing both the top and bottom of the fraction until you can't go any further (try dividing by 2,3,5,7,... etc).
Simplifying can also mean turning an improper fraction into a mixed number. For example, 3/2 into 1 1/2.
Simplifying is basically just reducing . If you're simplifying a fraction you should make both the numerator and denominator divisible by the same number . For example if you're simplifying 20 / 12 . You are able to divide 20 by 4 and 12 by 4 . By doing that you'll get 5 / 3 which is is the simplified version of 20 /12 .
Now to simplify equations it can either be finding the answer or reducing the equation as much as you can until there is nothing else to reduce . For example , for the equation
2x + 5x + 2y + 10y = 20y + 9 + 10 First let's add the 2x and the 5x together
By adding 2x and 5x together, you should get
7x + 2y + 10y = 20y + 9 + 10 now , let's add the 2y with the 10y
By adding the 2y and the 10y together , you should get
7x + 12y = 20y + 9 + 10 now let's combine the 9 and 10 on the right side of the equation
By combining the 9 and the 10 , you should get
7x +12y = 20y + 19 now subtract 20y on both sides , that way all the " y " would be together
By doing that , you should get
7x - 8y = 19 Now this is basically the reduce equation of the earlier equation , but you can also subtract the 19 on both sides making the equation equal to 0 , so it would be 7x - 8y -10 = 0 . It basically depends on what the questions asks you to do .
You can use PEMDAS
For simplifying equations use Please Excuse My Dear Aunt Sally. (Parenthesis, Exponents, Multiplication, Division, Addition and Subtraction). And if you encounter brackets, they are just like parenthesis in terms of operator priority.
Also, don't forget log and exponent rules that can be useful when simplifying messy irrational fractions with multiple exponents.
You simplify fractions by looking at what number is a common denominator or common multiple of the top and bottom numbers. Then divide by it and keep dividing until you can no longer simplify.
As far as simplifying equations goes use PEMDAS. It can be looked at as (Parentheses)(Exponents)(Multiplication Division)(Addition Subtraction)
The reason the last 4 letters are grouped into twos is because those can be interchangeable. But you follow the pemdas rule by first completing whatever is in the parenthesis then doing the exponents then going from left to right doing the miltiplication or division whichever one comes first and then finally the addition and subtraction which ever comes first.