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Name ___________________________________________ Date ___________ Period ______Final Exam Review: Negative Numbers and the Number Line Jane completes several example problems that ask her to find the opposite of the opposite of a number, and for each example, the result is positive. Jane concludes that when she takes the opposite of the opposite of any number, the result will always be positive. Is Jane correct? Explain, on the lines below, why or why not.(Before you answer this question, find the opposite of the opposite of a few numbers. See what happens and then determine if Jane is correct or not correct. Use your examples to help you explain your decision about Jane. Remember that “opposite of the opposite” sounds confusing but it just means to find the opposite of a number and then the opposite of that.)____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Order the following set of rational numbers from least to greatest. Then explain how you determined their order. 1371600444500____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________In a recent survey, a magazine reported that the recommended room temperature in the summer is 68°F. A wall thermostat, like the ones shown below, tells a room’s temperature in Fahrenheit. 12573001333500Which bedroom is warmer than the recommended room temperature? Which bedroom is cooler than the recommended room temperature? Sarah notices that her room’s temperature is 4°F above the recommended temperature and the downstairs bedroom’s temperature is 4°F below the recommended temperature. She graphs 72 and 64 on a vertical number line and determines they are opposites. Is Sarah correct? Explain. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________If zero lies between a and d, give one set of possible values for a, b, c and d. 11430010985500a = ______b = ______c = ______d = ______In math class, Christina and Brett are debating the relationship between two rational numbers. Read their claims below, and then write and explanation of who is correct. Use a number line to support your answer. Christina’s Claim: I know that 3 is greater than 212, so -3 must be greater than -212.Brett’s Claim: Yes, 3 is greater than 212, but when you look at their opposites, their order will be opposite. That means that -212 is greater than -3. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Interpret the number line diagram shown below and write an inequality statement about the temperature for Tuesday compared to Monday at 11:00pm. 68580014795400Inequality Statement: ____________________________________Kendra collected date for her Middle School Science Fair project. She surveyed people by asked them how many hours they sleep during a typical night. The chart below shows how each person’s response compares to 8 hours (which is the amount of hours doctors suggest people get)8001005588000125730036703000Plot and label each of the numbers in the right-most column of the table above on the number line below. List the numbers from the right-most column from least to greatest.Using your answer from part b, write one inequality statement that shows the relationship among all of the numbers. Complete the number line scale. Explain, on the lines below, how to find 2 and the opposite of 2 on a number line. 02730500________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Jessie and his family drove to a picnic area on a mountain in Berkshires. In the morning, they followed a train that led to the mountain summit, which was 2,000 feet above the picnic area. They then returned to the picnic area for lunch. After lunch, they hiked on a trail that led to the mountain overlook, which was 3,500 feet below the picnic area. 411480044132500Locate and label the elevation of the Mountain Summit and the Mountain Overlook on a vertical number line. The picnic area represents zero. Write a rational number to represent each location. Picnic area: 0Mountain Summit: _______Mountain Overlook: _______Use absolute value to represent the distance on the number line from each location from the picnic area. Distance from the picnic area to the Mountain Summit: ______Distance from the picnic area to the Mountain Overlook: _______What is the distance between the elevations of the Summit and Overlook? Use absolute value and your number line from part a to explain your answer. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Mason was ordering the following ration numbers in math class: -3.3, -15, -889Order the numbers from least to greatest.List the order of their absolute values.Explain why the orderings in parts a and b are different. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Loni and Daryl call each other from opposite sides of Watertown. Their locations are shown on the number line below using miles. Use absolute value to explain who is further distance (in miles) from Watertown. How much closer is one than the other? 11430015240000____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________30861004254500The picture below is a flood gauge that is used to measure how far (in feet) a river’s water level is above or below its normal level. Explain what the number 0 on the gage represents and explain what the numbers above and below 0 represent. __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Describe what the picture indicates about the river’s current water level.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________What number represents the opposite of the water level shown in the picture, and where is it located on the gauge? What would it mean if the river water were at that level? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________If heavy rain is forecast for the area for the next 24 hours, what reading might you expect to see on the gauge tomorrow? Explain your reasoning. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Cole, Joachim and Austin play on the same soccer team. So far this season, Cold has scored 3 times as many goals as Austin and Joachim combined. If Austin has scored 2 goals and Joachim has scored 4 goals, how many goals has Cole scored? Write and simplify an expression to determine the number of goals that Cole has scored. During a family reunion last summer, 7 adults and 17 children from the Nakai family went to a water park. Admission was $16 per adult and $9 per child. What was the total cost of the admission? Write and simplify an expression to determine the cost of admission to the water park. The table shows the grams of protein for several food items. Food (Single Serving Size)Protein (g)Low-fat Yogurt (8 ounces)4Low-fat Pudding (8 ounces)6Low-fat Cottage Cheese (8 ounces)4Hard Cheese (1.5 ounces)12Write and simplify an expression that gives the total grams of protein in 2 servings of hard cheese and 2 servings of yogurt.Place one pair of parentheses in the expression so that its value is 25. Then show the steps for simplifying the expression.40 ÷ 23 × 8-3 ................
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