How do you simplify?

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jennifer-taubenheim's profile pic

jennifer-taubenheim | Middle School Teacher | (Level 2) Assistant Educator

Posted on

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.

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jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

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 . 

ik9744's profile pic

ik9744 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

You can use PEMDAS

Paranthesis
Exponent
Multiplication
Division
Addition
Subtraction

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

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. 

acompanioninthetardis's profile pic

acompanioninthetardis | Student, Undergraduate | (Level 1) Valedictorian

Posted on

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.

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