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Simplification

Sometimes you will come across mathematical expressions with fractions. Then you need to be able to deal with them.

Examples of addition of fractions

frac{1}{a}+frac{2}{3a}=frac{3}{3a}+frac{2}{3a}=frac{3+2}{3a}=frac{5}{3a}

When you want to add fractions together, the first thing you do is to find the equivalent fractions satisfying that both of them have the same denominator, the common denominator, in this case 3a. Then we just add the numerators.

Simplifying a fraction
You simplify a fraction by dividing numerator and denominator by the same number:

frac{2}{4a}=frac{2\div2}{4a\div2}=frac{1}{2a}

The fraction above can be simplified, because the numerator and the denominator can be divided evenly by 2.


Here is an example of a more complicated simplification
frac{2x}{x^2+x}=frac{x*(2)}{x*(x+1)}

The denominator x^2+x is rewritten to x*(x+1) according to the distributive property, saying that: a*(b+c)=ab+ac.

Then it’s obvious that we can simplify the fraction by dividing the fraction by x, and we end up with:

frac{x*(2)}{x*(x+1)}=frac{2}{x+1}

Example of two fractions being multiplied together

frac{1}{2}*frac{2x}{3y}=frac{1*2x}{2*3y}=frac{2x}{6y}=frac{x}{3y}