Adding and Subtracting Rational (Fractional) Expressions
Fractions are fractions!
It doesn’t matter if the fractions are made up of numbers, or of algebraic variables, the rules are the same!
The Basic RULE for Adding and Subtracting Fractions:
Get a Common Denominator!
Examine the basic process:
Add: 1/3+1/4
You CANNOT reduce (cancel) those 3’s!!!!
Get a common denominator – the smallest number that both denominators can divide into without remainders. In this case, the number is 12.
To change the denominator of 3 into 12 requires multiplying by 4. To change the denominator of 4 into 12 requires multiplying by 3.
With each fraction, whatever is multiplied times the bottom must ALSO be multiplied times the top.
1/3. 4/4 + 3/4 .3/3
1/3. 4/4 + 3/4 .3/3 = 4/12 + 9/12 = 13/12 = 1 (1/12)
Multiplying the top and bottom by the same number is multiplying by
the multiplicative identity element (which is = 1) and therefore does not change the fraction.
Now, apply this basic process to algebraic fractions:
