Arithmetic Notes

Book #1, Unit #1 Number Simplifying Fractions To change a fraction or a decimal into a percentage, multiply it by 100. To change a percentage into a fraction, rewrite % as division by 100. To write a fraction as a decimal, divide the top number by the number. To change 1/8 into a decimal: divide 1 by 8. 0.125 To change 7/20 into a percentage: multiply by 100. 7/20 x 100 = 35% To simplify 15/1.2: multiply top and bottom by 10. 150/12 = 25/2 = 12.5 Directed Numbers 3 + (-4) = 3 - 4 = - 1 3 - (-4) = 3 + 4 = 7 (-3) + (-4) = - 3 - 4 = - 7 (-3) - (-4) = - 3 + 4 = 1 6 x (-2) = - 12 6 / (-2) = 3 (-6) / (-2) = 3 (-6) x (-2) = 12 Order or Operation Brackets Indices Division and/or Multiplication Addition and/or Subtraction Percentages Multiplying Factor Method: If the original price is $60: For a profit of 30%, selling price y = 60 + (60 x 30/100) = 60 (1 + 30/100) = 60 x 1.30 = $78 For a profit of 30%, selling price = $78

For a loss of 30%, selling price y = 60 - (60 x 30/100) = 60 (1 - 30/100) = 60 x 0.7 = $42 For a loss of 30%, selling price = $42 Standard Form with Positive Indices 67000 = 6.7 x 104 0.00067 = 6.7 x 10-4 Significant Figures 34.779 to 3 significant figures = 34.8 0.0659 to 2 significant figures = 0.066 Decimal Places 2.0765 to 2 decimal places = 2.08 0.05296 to 3 decimal places = 0.053 Algebra Simplifying Algebraic Expressions 4ac means 4 x a x c You can only add or subtract like terms.

Solving Equations Do the same to both sides. 3x + 4 = 2(x + 3) 3x + 4 = 2x + 6 3x - 2x = 6 - 4 x=2 Check: 3 x 2 + 4 = 2(2 + 3) 3(x + 4) - (x - 7 = 25 (expand the brackets) 3x + 12 - x + 7 = 25 (simplify) 2x + 19 = 25 (subtract 19) (expand the brackets) (collect like terms) (simplify)

2x = 3 x=3 Check: 3(3 + 4) - (3-7) = 25

(divide by 2)

Graphs and Sequences Gradient of a Straight Line Straight-line Graphs Shapes and Space Basic Principles Constructions 60° angle (equilateral triangle) Draw arc from A to intesect AB at P. Keeping same radius, draw arc from P