Lecture3: Signed Numbers and Operation on Series of Numbers

SIGNED NUMBERS & OPERATION IN SERIES OF NUMBERS

SIGNED NUMBERS

·        These are numbers preceded by a plus (+) or minus ( – ) sign including zero.

·        Another term for integers.

FOUR FUNDAMENTAL OPERATIONS WITH SIGNED NUMBERS

ADDITION

R1. In adding signed numbers having common sign, add the numbers and affix the common sign.

e.g.:

1.)  2 + 4 + 6 = 12            2.)    (-12) + (-6) + (-8) = -28

R2. In adding signed numbers having unlike sign, subtract the two numbers from the largest to the smallest and affix the sign of the larger number.

e.g.:

1.)  5 + (-3) = 2                2.)    -5 + 3 = -2                   3.)    12 + (-15) = -3

SUBTRACTION

R1. In subtracting signed numbers, change the sign of the subtrahend and proceed as in addition.

e.g.:

1.)  115 – 3 = 112            2.)    25 – 75 = -50             3.)    -2 – (-3) = 1

4.)     (-15) – (-2) = -13   5.)    -2 – 13 = -15              6.)   14 – (-2) = 16

MULTIPLICATION

R1. In multiplying signed numbers with like sign, multiply the numbers and always affix the positive sign to the result.

e.g.:

1.)  25 * 4 = 100             2.)   -8 * -9 = 72

R2. In multiplying signed numbers with unlike sign, multiply the numbers and always affix the negative sign to the result.

e.g.:

1.)  15 * (-3) = -45          2.)   -6 * 4 = -24

DIVISION

R1. In dividing signed numbers with like sign, divide the numbers and always affix the positive sign to the result.

e.g.:

1.)  18 / 2 = 9                 2.)   -25 / -5 = 72

R2. In dividing signed numbers with unlike sign, divide the numbers and always affix the negative sign to the result.

e.g.:

1.)  15 / (-3) = -5             2.)   -81 / 3 = -27

OPERATION IN SERIES OF NUMBERS

·        In performing operations in series of numbers in mathematics the GEMDAS rule must be applied.

·        GEMDAS is the order of operation in mathematics which stands for Grouping symbol, Exponents, Multiplication, Division, Addition and Subtraction.

·        There are various grouping symbols in mathematics like ( ) parenthesis, [ ] brackets, { } curly braces and         vinculum.

·        In applying the GEMDAS rule, the inner grouping symbol must be simplified first.

e.g.:

1.)  2 + 2 / 2

= 2 + 1

= 3

2.)  16 / 8 + 4 * 2 – 2

=16 / 8 + 8 – 2

=2 + 8 – 2

=10 – 2

=8

3.)  – [2 + 4(3) – 2] + 3 [13(2 – 5 + 12) – 8]

= – [2 + 12 – 2] + 3 [13(9) – 8]

= – [2 + 12 – 2] + 3 [117 – 8]

= – [12] + 3 [109]

= – 12 + 327

= 315

4.)  6 + {2 – [5 – 6 + 3(2 – 4 + 5)] – 2 + [18 – 8 / 2 + 6(4 – 8)]}

= 6 + {2 – [5 – 6 + 3(3)] – 2 + [18 – 8 / 2 + 6(–4)]}

= 6 + {2 – [5 – 6 + 9] – 2 + [18 – 8 / 2 –24]}

= 6 + {2 – [5 – 6 + 9] – 2 + [18 – 4 –24]}

= 6 + {2 – [8] – 2 + [–10]}

= 6 + {2 – 8 – 2 – 10}

= 6 + {– 18}

= 6 – 18

= – 12