Carry The Two

Positive + Positive = Positive Negative + Negative = Negative Subtracting a Negative is the same as adding: 8 - (-3) = 8 + 3 = 11 The sum of a negative and a positive: Use the sign of the large number and then subtract: Example 1 8 + (-12) = -4 Example 2 (-7) + 17 = 10 Example 3 7 + (-3) = 4 Example 4 18 + (-20) = -2 Positive x Positive = Positive Negative x Negative = Negative Positive x Negative = Negative Negative x Positive = Negative Positive  ÷ Positive = Positive Negative  ÷ Negative = Positive Negative  ÷ Positive = Negative Positive  ÷ Negative = Positive

Definition The percent error expresses the difference between an approximate or measured value and the exact value.  To find the percent error you must first find the greatest possible error. Approximate Error v. Exact Error Exact error is found by subtracting the approximate value from the exact value.  Negative signs should be ignored.  If I made an approximation of $350 and the actually value is $400: 350 - 400 = -50 We would ignore the negative sign therefore the exact error is 50. Percentage Error The percentage error allows you to see the error as a percent of the exact value.  To find the percentage error, we divide the exact error by the exact value: 50/400 = .125 or 12.5%

ONE Use your notes and homework.  Rework the problems.  Many teachers recycle questions.  Treat your homework and classwork questions like a warm-up for the actual exam.  Do not skip problems. TWO Use your resources! You Youtube and Google everything else, why wouldn't you do the same for an Algebra concept that you do not understand? THREE Practice makes perfect.  When you think you got it, the studying has just began.  Set aside more time in order to master the material. FOUR Do not cram.  You have to plan strategically if you want the grade that you desire.  Do not wait until the last minute! FIVE Use flash cards to memorize formulas and rules.  This does not mean make them and set them aside.  Use them!

The midpoint is the point on a line segment that divides it into two equal parts. The midpoint formula is as follows: Example The endpoints of a line are (4, 8) and (4, 0).  Find the coordinates of the midpoint. Plug the points into the midpoint formula: x: ((4 + 4) / (2)) = 4 y: ((8+0) / (2)) = 4 Therefore the midpoint is (4, 4)

Natural Number - positive integers (whole numbers) 1, 2, 3... 'Counting numbers' used when you are counting one to one objects Whole Number - not fractions nor decimals.  Unlike natural numbers, we include 0 when referring to whole numbers Integers - a number that is not a fraction whole numbers; integers can also be negative whole numbers: ...-2, -1, 0, 1, 2... Rational Number  - a number that can be written as a ratio; a number that can be written as a fraction with the numerator and denominator expressed as whole numbers: 7/1, 9/2 Irrational Number  - Real numbers that cannot be expressed as simple fractions;  π is irrational because it cannot be written as a simple fraction Real Number  - rational and irrational numbers; any number that can be found on a number line. Infinity is not a real number.  Imaginary numbers are also not considered real numbers Imaginary Number  - A number that, when squared, gives a negative result; imaginary numb...

Equivalent Ratios Two ratios are equivalent if their cross products are equal.  Compare the cross products by cross multiplying: Multiply the denominator of one fraction by the numerator of the other fraction.  If the cross products are equal then the ratios are equivalent. Another Method Ratios are used in order to find how two or more quantities are related.  In order determine whether you have equivalent ratios, you must multiply or divide both sides by the same number. The first two problems use the first method above whereas the last two problems use the second method above. Problems #1 Are the following ratios equivalent? 2:3 and 10:12 Step 1 Determine the cross products by multiplying the numerator of the first fraction by the denominator of the second: 2 x 12 = 24 Step 2 Determine the second cross product by multiplying the denominator of the first fraction by the numerator of the second: 3 x 30 = 90 Step 3 Compare the cross products to d...

Slope The slope of a line tells you how steep the line is. Formula To find the slope of a line, we take the change in y divided by the change in x: Some call this equation "rise over run": Therefore, in order to find the slope, you divide the difference of the y-coordinates of a point or a line by the difference of the x-coordinates. Problem #1 What is the slope? Step 1 Select any 2 points on the line Point 1: (-1, -2) Point 2: (2, 2) Step 2 Put those point into the slope formula Therefore: = 4/3 Answer: The slope of the line is 4/3 Problem #2 What is the slope? Step 1 Select any 2 points on the line Point 1: (-2, 5) Point 2: (-4, 4) Step 2 Put those point into the slope formula Therefore: = -1/-2 which equals: 1/2 Answer: The slope of the line is 1/2