Algebraic Fractions Algebraic Fractions Core 3 Chapter 1

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.

$Simplifying algebraic fractions • Cancel down by finding common factors in the numerator and$

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.

$Multiplying and dividing algebraic fractions • To multiply fractions, multiply the tops and multiply$

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!

$Adding and subtracting algebraic fractions • To add and subtract fractions, the denominators must$

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).