Algebraic
Fractions
Algebraic Fractions – Core 3, Chapter 1
Session 1
LO:
Add, subtract, multiply and divide algebraic fractions.
Session 2
LO:
Write improper algebraic fractions as mixed numbers
using division or the remainder theorem.
Work out the answers to the following:
2 1
+
5 3
2 1
−
5 3
2 1
×
5 3
2 1
÷
5 3
Simplifying algebraic fractions
• Cancel down by finding common factors in the numerator and
the denominator.
• Factors must be common to ALL TERMS (no cancelling
randomly through addition signs).
• Remove fractions from numerators and denominators by
multiplying through by the appropriate number.
• If you see a quadratic, a good tip is to factorise that first. One of
its pair of brackets will usually cancel with another.
• Difference of two squares: (x – y)² = x² – y².
Multiplying and dividing algebraic fractions
• To multiply fractions, multiply the tops and multiply the
bottoms.
• To divide, flip the second fraction upside down and change to a
multiply (you’re using the reciprocal here).
• Cancel any common factors first – this will make it much easier.
• Think about factorising quadratics and again, difference of two
squares!
Adding and subtracting algebraic fractions
• To add and subtract fractions, the denominators must be the
same.
• You need to multiply each fraction (numerator and
denominator) by a number or expression to get a common
denominator.
• Write it out in full – don’t try to skip steps until you’re feeling
really confident!
• Expand brackets in the numerator and simplify where
possible.
• And again, FACTORISE QUADRATICS AND DIFFERENCE OF
TWO SQUARES!
Writing in ‘mixed’ number form
• Either use long division or the remainder theorem. You need to
be able to do both methods.
• Long division is just like in Core 2, but you will have a
remainder. This is always divided by the original denominator.
• Using the Remainder theorem:
• F(X) = (Ax² + Bx + C)(divisor) + D
• Substitute the value of x to make divisor = 0.
• Substitute x = 0 to give an equation in C and D.
• Equate coefficients in x³ and x².
• The remainder will always be of order one less than the
divisor (e.g. if the divisor is quadratic, the remainder will
be linear).