UNIT 5. Integers and Rational Numbers on the Number Line CCM6 and CCM6+ Name: Math Teacher: Estimated Test Date:

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1 UNIT 5 Integers and Rational Numbers on the Number Line CCM6 and CCM6+ Name: Math Teacher: Estimated Test Date: Main Concepts Page(s) Unit 5 Vocabulary 2 Converting Fractions, Decimals, and Percents 3-12 Compare and Order Positive Fractions and Decimals Integer Vocabulary Basics Opposite, Absolute Value, Positive/Negative, Compare/Order Compare and Order Rational Numbers on the Number Line Study Guide Unit

2 Page 2 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) Unit 5 Vocabulary bank balance the amount of money in a bank account at any certain time bank deposit money put into the bank; money added to a bank account bank withdrawal money taken out of a bank account depth (in ocean) distance below sea level moving in a negative direction described with words such as down, lower, loss, drop, dive, depth moving in a positive direction described with words such as up, higher, gain, rise, spike, height negative number a number less than zero positive number a number greater than zero integer A number expressible in the form a or -a for some whole number a. opposites In math, numbers that are an equal distance from zero on the number line. For example, 8 and -8 are opposites. origin The starting point. On a number line, it is 0 inequality rational number absolute value A mathematical sentence that shows the relationship between quantities that are not equal, using the symbols < "less than, >; "greater than," "less than or equal to," and "greater than or equal to." A number that can be written as a simple fraction The magnitude of a quantity, irrespective of sign; the distance of a quantity from zero. The absolute value of a number is symbolized by two vertical lines, as 3 or 3 is equal to 3. Page 2

3 Page 3 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) The Real Number System Map of all Numbers Page 3

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6 Page 6 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) Name: Date: Class: Converting Fractions and Decimals Notes Any rational number can be represented by a decimal or a fraction One method for converting fractions to decimals is Divide the numerator by the denominator; ¾ = 3 4 = 0.75 Why does this method work? Can you think of any other methods? One method for converting decimals to fractions is Say the number and write it out, then reduce; 0.35 = thirty-five hundredths; = 35 = Why does this method work? Can you think of any other methods? Practice 1. Write each as a decimal a. 5 b c d Write each as a fraction Page 6 a. 2.2 b c. 1.6 d

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10 Page 10 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) Percents & Decimals What does percent mean? If we write the percent as a fraction without reducing, what will the denominator be? In order to write the percent as a decimal, where will the decimal point be in comparison to where it was in the percent? If you have to pay 7% tax on an item you buy, how much will be paid on a $1? Express each percent as a decimal: I. 25% II. 82% III. 7.3% IV. 0.55% If you get 85 questions right out of 100, write your score as a fraction in simplest form and a decimal. Now write your score as a percent. Express each decimal as a percent: V VI. 0.4 VII. 5.1 VIII Page 10

11 Page 11 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) Math Masterpiece Color Number Fraction Decimal Percent Page 11

12 Page 12 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) Fraction, Decimal, Percent Equivalency Fill in the missing percent, decimal, fraction, and/or dollar amount for each of the following: Number of squares out of 100 Fraction Decimal Percent Equivalent dollar amount 1 75 ¾ % $ / /25 48% % / / % Page 12

13 Page 13 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) Comparing and Ordering Fractions and Decimals In #1-4, order the rational numbers from least to greatest. Hint: Change them to the same kind! 1) 0.66, 32 50, 0.8, ) 0.44, 3 8, 0.5, 2 5 3) 0.2, 4 15, 0.21, 1 4 4) 0.66, 2 3, 0.7, 7 9 In #5-9, order the numbers from greatest to least. Hint: Change them to the same kind! 5) 0.56, 5 9, 0.5, ) 0.750, 3 4, 0.75, 6 8 7) 0.38, 2 5, 0.45, ) 0.2, 2 15, 0.15, 1 7 Page 13

14 Page 14 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) 5K Race Problem Jeannie, David, Tom and Sarah all ran in a 5K race last weekend. Jeannie s time was 1538 sec., David s time was 27 min. 15 sec., Tom s time was 1629 sec., and Sarah s time was 0.42 hours. Who came in 3rd place? Trees Problem Gen planted some trees in her yard last year. She measured their growth this spring. She found the Oak tree grew 2.03 inches; the Pine grew 3 1 inches less than the Maple. The Maple grew inches. The Pear tree grew 4 3 more than the Pine. The Birch grew 2.30 inches. Which tree grew the most? 60-Yard Dash Problem Susan, Bill, Corrina, and Chad ran in the 60- yard dash. They ran three heats to find their best time. Heat 1 Heat 2 Heat 3 Susan Bill Corrina Chad Bike to the Beach Problem Five friends biked to the beach. Each took a different route and arrived at 10-minute intervals. LaDonne arrived 20 minutes after Kathy. Frank and Paul were playing volleyball when Cindy arrived. Cindy arrived 10 minutes after LaDonne. Kathy went swimming before Paul arrived with the towels. In what order did they arrive? What was each person s best time? Did each person get faster or slower from one heat to the next? Explain. Page 14

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25 Page 25 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) Practice I. What number is represented by each letter on the number line? A B C D A: B: C: D: 0 II. Graph the following integers on a number line. Draw your own number line. 3, 0, 5, -2, 2, -7 III. Use an integer to represent each of the following situations. A football player loses 5 yards on a carry. The temperature rises 15. You put $10 in your savings account. The scuba diver went down 25 feet below water. Page 25

26 Page 26 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) Opposite has a symbol, too! What is the opposite of 3? (3) = 3 A negative sign in front of ( ) or in front of means the opposite of that value. Try these: ( 4) = 4 = 4 = Page 26

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31 Page 31 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) Comparing and Ordering Rational Numbers 1. Turn all fractions into decimals 2. Compare the decimals by lining up the decimals points Convert the fractions into decimals by dividing Compare the following by using <, >, or = Order the following decimals in ascending order (least to greatest) Order the mixed numbers in descending order (greatest to least) Page 31

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34 Page 34 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) Name Date Compare and Order Arrange the following in DECENDING ORDER. Comparing and Ordering Rational Numbers Practice 1.) 0.65, 1.21, , ) 18, -0.82, , Arrange the following in ASCENDING ORDER. 3.) 11.1, -10, -12, ) -2.33, 19.25, -2.01, 19 Use the symbols (,, ) to answer the following questions. 5.) ) ) Word Problems-Show your work 8.) While exploring a cave, Ricky noticed that the temperature dropped 4 F for every 30 ft. he descended. What is Ricky s depth if the surface temperature is 12 lower than the temperature at the surface? 9.) Asheka s checking account had a balance of $50. She then deposited $65 into her account. That same day she wrote a check for $18.00, bought lunch that cost $7.50, and spent $41.50 at the mall. What is Asheka s new checking account balance? 10.) Tom, Kim, and Jordan went on a family vacation to Hawaii. Tom climbed to the top of a mountain which measured feet. Kim went scuba diving and dove 18.3 feet below sea Page 34 level. Jordan went shopping at a local straw market that was feet above sea level. Place their elevation in order from least to greatest.

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37 Page 37 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) UNIT 5 Study Guide CCM6 and CCM6+ I. What is an integer? 1. An integer is a number that is,, or. 2. Three examples of integers:,, 3. Three examples of numbers that are NOT integers:,, 4. A submarine dives down 80 feet below the surface, then dives down another 15 feet. Write the current depth of the submarine as an integer:. 5. You withdraw $50 from your savings account, then deposit $30. What is the net change written as an integer? 6. On an elevator, you ride down to basement level 8. Write that level as an integer:. 7. You are at basement level 8 and ride up 12 floors. Write your current floor as an integer:. II. Absolute Value and Opposite 8. The absolute value of a number is the from. 9. A number s absolute value will never be. 10. The opposite of a number is the same distance from except on the other side of. 11. Complete the following equations that include symbols for opposite and absolute value. a. ( 3)= b. (5) = c. 7 = d. 8 = e. 12 = f. 3 = 12. Why is absolute value often described as magnitude? What can t you find with absolute value? Page 37

38 Page 38 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) III. Convert and Compare Fractions, Decimals, and Percents Write each fraction or mixed number as a decimal Write each decimal as a fraction or a mixed number in simplest form Convert these fractions and decimals to percents = % = % = % = % 5 8 Convert these percents to fractions (all fractions must be simplified) % % % Convert these percents to decimals % % % 29. True or False? All integers are rational numbers. True or false? All rational numbers are integers. Page 38

39 Page 39 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) 30. Inside the box, write >, <, or =. a) b) c) d) Which point on the number line is the graph of 0.875? P Q R S Order the set of rational numbers from least to greatest , -1.1, , Which is the least: 3 4, 0.4, 4 11, 0.035, or 5 13? 34. Which is the greatest: 7 9, 0.778, 0. 78, 11 13, or 0.787? Page 39

40 Page 40 Unit 5: Rational Numbers CCM6 and CCM6+ ( ) IV. Ordering and Comparing Integers Continent Highest Point Elevation (ft) above sea level Lowest Point Elevation (ft) below sea level Africa Mount Kilimanjaro 19,340 Lake Assal -512 Bentley Subglacial Antarctica Vinson Massif 16,066 Trench -8,327 Asia Mount Everest 29,035 Dead Sea -1,349 Australia Mount Kosciusko 7,310 Lake Eyre -52 Europe Mount Elbrus 18,510 Caspian Sea -92 North America Mount McKinley 20,320 Death Valley -282 South America Mount Aconcagua 22,834 Valdes Peninsula What is the highest point on Earth? It s elevation is ft. 36. Which point on Earth is lower the Caspian Sea or Lake Eyre? 37. Write the continents in order from least to greatest according to their elevations BELOW sea level. 38. Write the continents in order by their highest points, from greatest to least feet ABOVE sea level. 39. Which set of integers is written from greatest to least? Circle your choice. a) 7, -4, -5, 2 b) 7, -5, 4, -2 c) 7, 5, -4, -2 d) 7, 5, -2, How can a number line help you to order or compare integers? Page 40

Comparing and Ordering Integers

Practice A Comparing and Ordering Integers Use the number line to compare each pair of integers. Write < or >. 1. 4 3 2. 1 3 3. 2 5 4. 2 2 5. 5 1 6. 0 4 Use the number lines to order the integers from