![]() The index laws were introduced for whole numbers in the module Multiples, Factors and Powers. People make different choices about how many middle steps to show − the important thing is to be accurate, particularly with the negative signs. Here are some further examples of substitution. Perhaps the substitution step should have been written asīut once we know about adding and subtracting negative numbers, the working is clearer when we do not worry about such distinctions. The third is a credit card account with a negative balance of −$3000. The first account is a savings account with a balance of $450, and the second is a term deposit with a balance $2000. ![]() The total amount $ T in the three accounts is given by the formula For example, suppose that I have three bank accounts with balances $ A, $ B and $ C. With many algebraic formulas, it is perfectly reasonable to substitute negative numbers for the pronumerals. This procedure is much simpler than the other standard methods of factoring and is covered in the final section. The first step in factoring is taking out the HCF of an algebraic expression - applying the distributive laws in reverse. The remaining two index laws are left until the next module, whose principal theme is the use of fractions in algebra.įactoring will later become an essential part of algebra for a variety of reasons, most obviously because it can help us find which substitutions make an algebraic expression zero. This module does not involve anything but very simple fractions, so it deals only with the three index laws involving products. Clearly the index laws need to be integrated into algebra. We saw the importance of the index laws when dealing with powers in the module, Multiples, Factors and Powers. These first four sections of this module provide all the skills needed to solve straightforward linear equations, without the constraints of avoiding negative coefficients. The present module extends the methods of that module to integers and to simple positive and negative fractions, covering in turn substitution, collecting like terms, taking products, and expanding brackets using the distributive law. The first of these modules, Algebraic Expressions, introduced algebra using only whole numbers for pronumerals. ![]() This module is the second of four modules that provide a systematic introduction to basic algebraic skills. The various uses of algebra require systematic skills in manipulating algebraic expressions.
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