Algebraic fractions can be simplified, added, subtracted, multiplied and divided just like fractions with numbers. The same principles behind performing operations on fractions can be extended to algebraic fractions, like cancelling fractions by finding a common factor or finding a common denominator with addition or subtraction. In addition to these principles, algebraic fractions require the expressions on the numerator or denominator to be factorised.
Cancelling algebraic fractions
Algebraic fractions can be cancelled if they have a common factor, this can be either a number or variable that divides into the numerator and denominator.
Example 1
Simplify
7x2y28x3y2
Write out the expressions on the numerator and denominator in full, then cancel down.
Algebraic fractions can be multiplied in a similar way to multiplying numerical fractions. Multiply the numerators together and multiply the denominators together and divide the two results. You can cancel down the algebraic fraction before or after the multiplication.
To divide algebraic fractions, change the divide sign into a muliplication sign and turn the second fraction upside down. Then perform the multiplication.
To add or subtract algebraic fractions, multiply up the fractions so that they have the same denominator. Then, add the numerators before simplifying the result.
How do you multiply or divide algebraic fractions?
Algebraic fractions can be multiplied in a similar way to multiplying numerical fractions. Multiply the numerators together and multiply the denominators together and divide the two results. To divide algebraic fractions, change the divide sign into a muliplication sign and turn the second fraction upside down, then calculate the multiplication.
How do you cancel algebraic fractions?
Algebraic fractions can be cancelled if they have a common factor, this can be either a number or variable that divides into the numerator and denominator.
What are algebraic fractions?
Algebraic fractions are fractions with algebraic terms or expressions in either the numerator or denominator. You can cancel, add, subtract, multiply and divide algebraic fractions just like numerical fractions.