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The basics of mathematical operations such as addition, subtraction, multiplication, and division. It also covers the basics of equations and proportions. examples and step-by-step solutions to problems related to these topics.
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Basics of equations X + 23 = 45 Variable: X Constants: 23 and 45 =: equal sign/ fulcrum Because an equation represents a scale, it can also be manipulated Initial equation/problem X + 23 = 45 Subtract 23 from each side X + 23 - 23 = 45 - 23 result/ answer X = 22 Initial equation/ problem X + 23 = 2x + 45 Subtract X from each side X - X + 23 = 2x - x + 45 Result 23 = X + 45 Subtract 45 from each side 23 - 45 = X + 45 - 45 Result -22 = x Answer X = -
Using Division Recall: “ x + 23 = 3x + 45 “ applying addition and subtraction gave: 2x = - Divide by the coefficient of the variable since the coefficient of x is 2, we divide each side of the equation by 2 : After dividing by 2 1x = - Finally rewritten as x - Associative Property Associative property of addition Exp. 1: (14 + 6) + 7 = 14 + (6 + 7) 20 + 7 = 14 + 13 27 = 27 Exp. 2: (52 + 7) + 13 = 52 + (7 + 13) 69 + 13 = 52 + 19 72 = 72
Associative property of multiplication Exp. 3: (3 * 5) * 6 = 3 * (5 * 6) 15 * 6 = 3 * 30 90 = 90 Exp. 4: 2 * (18 * 10) = (2 * 18) * 10 2 * 180 = 36 * 10 360 = 366 Proportions Proportion Basics Compares two ratios to make an equivalent fractions 1 apple : 3 oranges For every apple, there are 3 oranges Exp. Apple orange 2 : 3
divide by 9 50 = x 50 =? 25/x = x/ X * X = 25 * 1 X squared = 5
