Yosemite Trip Participants

Transcription

1 Yosemite Trip Participants During your trip you will have the opportunity to enjoy many exciting and new experiences. Because of the myriad of activities planned, you will probably not have any time to even think about our Algebra class. However, during the week you are in Yosemite, the class will continue its course of study in Chapter 5 as well as complete the two sections skipped in chapter 2. Your assignment, listed below, is a shortened version of the actual class assignment for the week of October It is your responsibility to continue your understanding and learning of this material, even if you are absent from the class. Although you will have until Thursday, November 10, 2016 to complete the following assignment, please plan accordingly. You will have to keep up with the homework the week we return and we will have a midchapter test shortly after you return. The Magic Number Project due date is October 31 - so make sure it is close to being completed before you leave!! Please don t leave it to the weekend we return!! Your project will NOT come together well, if you do that We are covering topics that you learned in prior years: Section 2-6 Ratios & Proportions. Page 114 # 1-8 all odd all Section 2-7 Percent of Change Page all all Section 5-1 Solving Inequalities by Adding/ Subtracting Page 288 #1-11 all Section 5-2 Solving Inequalities by Mult/ Dividing Page odd odd all Some Notes to help you: 2-6Ratios & Proportions A ratio is a comparison of two things. Comparisons: Say you are a dog walker and you want the ratio of large dogs to small dogs to remain at 8 small dogs to 2 large dogs for your business. 3 ways to write a ratio:

2 8 small dogs to 2 large dogs or 8 small dogs : 2 large dogs or 8 small dogs /2 large dogs You can also reverse the order and put the large dogs first. Just as with fractions, since a ratio functions like a fraction, you ALWAYS SIMPLIFY the ratio: 4 small dogs to 1 large dog or 4 small dogs : 1 large dog or 4 small dogs /21 large dog Proportions: A proportion is 2 EQUAL ratios. You can use CROSS PRODUCTS or SIMPLIFYING to determine if two ratios are equivalent. Means: The means in a proportion are the two middle terms if written with a : or the denominator of the 1st term and the numerator of the 2nd term. Extremes: The extremes in a proportion are the two outside terms if written with a : or the numerator of the 1st term and the denominator of the 2nd term. CROSS PRODUCTS PROPERTY: The product of the MEANS is always equal to the product of the EXTREMES Rate: A ratio with 2 DIFFERENT units of measure like miles per gallon Unit Rate: A rate with a denominator of 1 unit that is found by dividing the numerator by the denominator of a rate Scale Rate: A rate that is used to make a model bigger or smaller of an actual sized item that is usually too big to draw or use Example: a building sketch or a map. Remember: It s all about the labels! After setting up the proportion, you have your choice of 3 methods: 1) equivalent fraction method (doesn t always work- the numbers must be compatible)

3 3/5 = y/15 y = 9 because 5(3) = 15 must multiply 3(3) to get numerator in second fraction 2) balancing equation method (always works) multiply by the multiplicative inverse 3/5 = y/15 multiply both sides by 15 ( the multiplicative inverse of 1/15 3) cross products method (this is the only time that name is accurate) Multiply the corners making an X. Same example but this time you would set up the cross product equation or 5y = 3(15). Don t be too quick to multiply 3(15). Divide by 5 first. It may simplify. 315 y so y = Percent of Change Percent of change is the ratio of the change over the original amount. It can be an increase or a decrease. Sometimes you know the percent of increase or decrease and you want to find either the original amount or the new amount. Simply plug in the given information and solve for the missing item. REAL LIFE APPLICATIONS OF PERCENTS OF CHANGE: Percent of Decrease: Sales Tax or Discount Sometimes a store will not tell you the percent off merchandise is Instead, they ll tell you the amount off. You can find the discount % by looking at it as a percent of change. Example: A laptop is $100 off of the original price of $700. What is the discount percent? The amount off is the change. 100/ or 14.3% Percent of Increase: Markups To make a profit, stores must mark up what they manufacture or buy to their customers. That markup is an increase. Example: A company makes something that costs them $500 to produce. They mark it up $200 and sell it. What is their markup percent? The $200 is the increase. 200/500 =.4 or 40% markup

4 5-1 Solving Inequalities by Adding or Subtracting Graphing an inequality - open dot is < or > Closed dot mean less than or EQUAL or greater than or EQUAL (think of the = sign as a crayon that you can use to COLOR IN THE DOT!) Different from equations: Inequalities have many answers (most of the time an infinite number!) Example: n > 3 means that every real number greater than 3 is a solution! (but NOT 3) n 3 means still means that every real number greater than 3 is a solution, but now 3 is also a solution Graphing an equation's solution is easy 1) Say you found out that y = 5, you would just put a dot on 5 on the number line 2) But now you have the y 5 You still put the dot but now also darken in an arrow going to the right showing all those numbers are also solutions 3) Finally, you find in another example that y > 5 You still have the arrow pointing right, but now you OPEN THE DOT on the 5 to show that 5 IS NOT A SOLUTION! TRANSLATING WORDS: Some key words to know: AT LEAST means greater than or equal NO LESS THAN also means greater than or equal AT MOST means less than or equal NO MORE THAN also means less than or equal I need at least $20 to go to the mall means I must have $20, but I'd like to have even more! I want at most 15 minutes of homework means that I can have 15 minutes, but I'm hoping for even less! Solving Inequalities with adding and subtracting Simply use the Additive Inverse Property as if you were balancing an equation! The only difference is that now you have more than one possible answer. Example: 5y + 4 > 29 You would -4 from each side, then divide by 5 on each side and get: y > 5 Your answer is infinite!

5 Any real number bigger than 5 will work! Always finish with the variable on the left. If you don t, you may misunderstand the answer and graph it in the opposite position. 5 > y is not the same as y > 5! 5 > y means that y < 5! Check with whatever solution is easiest in the solution set! Set builder notation: Get familiar with the following notation: {x I x 5} which is read: x SUCH THAT x is greater than or equal to Solving Inequalities by Multiplying or Dividing Again, you will use your equation skills, but this time with the Multiplicative Inverse Property. ONE MAJOR DIFFERENCE FROM EQUATIONS! When you multiply or divide by a NEGATIVE to BALANCE, you must SWITCH the inequality SYMBOL! (Does not apply to adding or subtracting negatives.) EXAMPLE: -3y > 9 You need to divide both sides by NEGATIVE 3 so the symbol will switch from > to < in the solution y < -3 is the answer If you want to understand why: 3 < 10 Now multiply both sides by -1 (mult prop of equality) You get -3 < -10, but THAT'S NOT TRUE!!! You have to SWITCH THE SYMBOL to make the answer true: -3 > -10 REMEMBER: when you MULTIPLY or DIVIDE by a NEGATIVE, the symbol SWITCHES DOING 2 STEPS WITH INEQUALITY SIGNS

6 Same as equations except make sure you switch the symbol if you multiply or divide by a negative! Always finish with the variable on the left. Check with whatever solution is easiest in the solution set! With two steps: Before you start, you may want to clear fractions or decimals, but if you don't mind using them, just get started with the checklist below. If you want to clear them, you should do that right after you distribute (between steps 1 and 2 below) 1. Do distributive property first (if necessary) 2 Combine like terms on each side of the wall (equal sign) 3. Jump the variables to one side of the wall (get all the variables on one side of the equation) by using the Additive Inverse Property (add or subtract using the opposite sign of the variable term) 4. Add or subtract 5. Multiply or divide (only flip the symbol if you multiply or divide by a NEGATIVE TO BALANCE) 6. Make sure the variable is on the LEFT side when finished.