GCSE Algebraic Fractions Dr J Frost jfrosttiffin kingston

GCSE: Algebraic Fractions Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths. com GCSE Revision Pack Ref: 53 ii, 53 iii, 92 Last modified: 31 st August 2015

$GCSE Specification (Using revision pack reference numbers) 53 ii. Simplify algebraic fractions. 53 iii.$

GCSE Specification (Using revision pack reference numbers) 53 ii. Simplify algebraic fractions. 53 iii. Add and subtract algebraic fractions. 92. Solve equations involving algebraic fractions which lead to quadratic equations.

Starter Are these algebraic steps correct? 40 - x = x + 4 3 Fail (Click your answer) 40 = 2 x + 4 3 Win! 2(4) = 5 x - 2 2(4 – 2 x) = 3 x - 2 Fail Win!

Starter Are these algebraic steps correct? Fail Win! (Click your answer)

Starter To cancel or not to cancel, that is the question? y 2 + x 2+x Fail Win! (2 x+1)(x – 2) x– 2 Fail Win! (Click your answer) s(4 + z) s Fail Win! pq(r+2) + 1 pq Fail Win! 1+r -1 2 Fail Win!

What did we learn? Bro Tip #1: You can’t add or subtract a term which is ‘trapped’ inside a bracket, fraction or root.

Simplifying Algebraic Fractions Bro Tip: Just factorise top and bottom, then cancel! ? ? ?

Test Your Understanding Bro Tip: Sometimes they’ve done part of the factorising for you! ? ? ?

Negating a difference ? ? ? ?

Exercise 1 1 ? 8 2 ? 9 ? 3 4 5 6 7 ? ? ? 10 11 ? ? ? 12 13 ? ?

$Adding/Subtracting Fractions What’s our usual approach for adding fractions? ? Sometimes we don’t need$

Adding/Subtracting Fractions What’s our usual approach for adding fractions? ? Sometimes we don’t need to multiply the denominators. We can find the Lowest Common ? Multiple of the denominators. ?

$Adding/Subtracting Algebraic Fractions The same principle can be applied to algebraic fractions. ! ?$

Adding/Subtracting Algebraic Fractions The same principle can be applied to algebraic fractions. ! ? ? Bro Tip: Notice that with this one, we didn’t need to times x and x 2 together: x 2 is a multiple of both denominators.

Further Example ? ? ? Bro Tip: Be careful with your negatives! Bro Tip: The numerator needn’t be expanded out because it is factorised – you get the marks either way.

Test Your Understanding ? ? ? “To learn the secret ways of the ninja, add fractions you must. ”

$Exercise 2 Write as a single fraction in its simplest form. 1 ? 8$

Exercise 2 Write as a single fraction in its simplest form. 1 ? 8 3 10 ? ? 4 12 ? 6 ? ? ? ? 11 ? 5 7 9 ? 2 ? N 1 N 2 ? ? ?

Solving Equations with Algebraic Fractions ? ?

Test Your Understanding ? ? ?

Exercise 3 Give exact answers unless otherwise specified. 1 2 3 4 5 ? 6 ? 7 ? 8 ? ? ?