Algebraic fractions
Clement Radcliffe, Contributor

The St. Andrew High School for Girls presents 'An Evening of Culture: Abundantly Blessed, The Legacy Continues', in celebration of their 80th anniversary held at The Little Theatre, Tom Redcam Avenue, on Sunday, October 23. - Winston Sill Photo

LET US begin this week's lesson by reviewing the answers to last week's homework.

1. State each of the following numbers correct to the number of decimal places given in brackets.

a) 5.05 (1 d.p.) = 5.1
b) 286.598 (2 d.p.) = 286.60
c) 0.0088 (3 d.p.) = 0.009

2. Write each of the following numbers correct to the number of Significant Figures indicated in each bracket.

a) 46.93106 (2 significant figure) = 47
b) 45.37 (1 significant figure) = 50
c) 37.8567 (3 significant figure) = 37.9

3. Write in Standard Form:

a) 0.003921 = 3.92 x 10-³

b) 49376.82 = 4.94 x 104

Please be reminded that you may check your answer by converting the standard form to a decimal fraction.

4. Expand the following:

a) (m + 1) (m - 1) = m² - m + m - 1 = m² - 1
b) (k - 3) (k + 1) = k² + k - 3k - 3 = k² - 2 k - 3
c) (X + y) (X - y) = X² - Xy +Xy - y2 = X² - y²

We will now return to ALGEBRA by reviewing ALGEBRAIC FRACTIONS.

ALGEBRAIC FRACTIONS

The method of simplifying algebraic fractions is the same as that used for vulgar fractions. This is also true for addition or subtraction of algebraic fractions. It follows then that you must know the method used to find L.C.M.

EXAMPLE 1

The L.C.M. of the denominator is 10

(I am sure that you recall that the negative sign in front of the brackets will change the sign within the bracket when you evaluate)

EXAMPLE 2

The L.C.M. of the denominator is x(2x - 3).

Now attempt the following

LINEAR EQUATIONS

The inclusion of the EQUAL sign differentiates an EQUATION from an algebraic expression. This point is commonly missed by students who sometimes attempt to solve algebraic expressions. Do not fall into this trap.

The following points should be noted:

* Equations identify either the relationship between variables or the value of a variable.

* The value of the variable is maintained by performing identical operations on both sides of the equation.

* The methods of expanding brackets and simplifying algebraic expressions are usually required to find solution of equations.

EXAMPLE 3

(June 1996, No. 2 (d))

Consider the left hand side first:

ALTERNATIVELY You may multiply all terms by the L.C.M. of the denominators.

Remember, practice is important if you are to succeed. I urge you to find examples in your textbooks and work them.

* Clement Radcliffe is principal of Glenmuir High School in Clarendon.