Algebraic Fractions and Formulae

Chapter 9 Algebraic Fractions and Formulae

Learning Objectives
1 master the operations of algebraic fractions.
2 know some common formulae and substitute values into formulae.
3 perform change of subject of a formula

Title page story, oral and dictation
A school holds a chess competition. Every participant has to play against all other participants for a round each. It is given that a total of 10 rounds are required to be held if there are altogether n participants and T rounds, write down the relation

between T and n.
4 x 5 divided by 2 = 10
(n-1) x n divided by 2 = T

Hints
1 simplify the following questions and find the patterns.
2 Find that T = 10 when n = 5 according to the following.
3 Figure out the relation between T and n according to the following.

Preview
Basic technique
Methods of factorization
1 Taking out common factor ab+ac=a(b+c)
2 Group terms ax+ay+bx+by=a(x+y)+b(x+y) =(x+y)(a+b)
a=1 b=2 x=3 y=4 1x3+1x4+2x3+2x4=1(3+4)+2(3+4) =(3+4)(1+2) =21
3 Using identities

9.1 Simple Algebraic fractions
9.2 Addition and Subtraction of Algebraic Fractions
9.3 Formulae and Substitution
9.4 Change of Subject of a Formula
In a formula, when a variable is expressed in terms of other variables, it is called the subject of the formula.

**Chapter Summary
Term Introduced
1 Algebraic fraction: P over Q, where P and Q are polynomials and Q involves variables.
2 Formula: An algebraic equality to express the relation among variables.
3 Subject of a formula: A variable in a formula which is expressed in terms of the other variables.

Additional Questions
2 The dosage of medicine for a child is usually less than that for an adult. A manufacturer calculates the dosage of a medicine for a child using the formula ?????, where C stands for the dosage of a child, y stands for the age of a child under 13 and a stands for the dosage for an adult.

Repeat and check carefully again
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