basics - Maths Fundamentals(for MA11 Andrew Roberts 4th...

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Maths Fundamentals (for MA11) Andrew Roberts 4th November 2003 Arithmetic Whilst this document will not delve into the most basic arithmetic (tens and units, etc.), people often forget how to correctly calculate with negative num- bers. m - ( - n ) = m + n (e.g., 10 - ( - 5) = 15) m × - n = - ( m × n ) (e.g., 10 × - 5 = - 50) - m × n = - ( m × n ) (e.g., - 10 × 5 = - 50) - m × - n = m × n (e.g., - 10 × - 5 = 50) m ÷ - n = - ( m ÷ n ) (e.g., 10 ÷ - 5 = - 2) - m ÷ n = - ( m ÷ n ) (e.g., - 10 ÷ 5 = - 2) - m ÷ - n = m ÷ n (e.g., - 10 ÷ - 5 = 2) And finally, let’s not forget the golden rule when multiplying numbers by zero: n × 0 = 0. Fractions For the addition and subtraction of fractions, always remember that the de- nominator (bottom) must be the same for each fraction involved. Then, simply apply the following (for subtraction, simply substitute the pluses for minuses): n p + m p = n + m p (e.g., 2 7 + 3 7 = 2+3 7 = 5 7 ) Unfortunately, you will not always be given fractions with a common de- nominator. It will therefore be necessary to perform some extra calculations to get the expression into the required format, before addition/subtraction can take place. 1 3 + 2 9 1
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In the above example, the lowest common denominator is 9. The fraction on the right can be left as we found it, as its denominator is already 9. To convert the left-hand fraction, we simply multiply the top and bottom numbers by some constant that will result in the new denominator being 9. In this case, we must multiply by 3. The addition can then be carried out as normal: 1 3 + 2 9 = 1 × 3 3 × 3 + 2 9 = 5 9 The next eventuality is when neither dominator shares a common factor.
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