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(Revised 10/26/01) Name ________________________________________ 6th – Everyday Math Unit 3 Date ________________________ Page 1 Study Guide for Unit 3 Assessment 1) Numerator in a fraction is the top number or the number of equal parts you are talking about. 2) Denominator in a fraction is the bottom number or the number of equal parts in all. Example: 3) 5 8 5 is the numerator 8 is the denominator Improper or Top-heavy Fractions A fraction that names a number greater than or equal to 1 ; a fraction whose numerator is greater than or equal to its denominator. Examples are: 7/3, 5/4, 9/9, 16/4. To change an improper fraction or top heavy fraction into a mixed number divide the numerator by the denominator. Then place the remainder over the denominator. Example: To change 35/8 back to a mixed number, 35 divided by 8 equals 4 with 3 left over. Place the 3 over the denominator 8, so your answer is 35/8 = 4 3/8. 4) Practice by converting each improper (top heavy) fraction to a mixed number. a. 17/4 = __________ b. 12/5 = ___________ c. 35/6 = __________ d. 18/7 = ___________ e. 24/4 = __________ f. 139/10 = ___________ To change a mixed number to an improper (top heavy) fraction – You need to do three steps Change 2 1/2 to a fraction. 1/2 2 + 1) Multiply the whole number by the denominator, = 5/2 (2 * 2 = 4) 2) Add on the numerator to that answer. (1 + 4 = 5). 3) Then, place that number over the denominator. (5 over 2 = 5/2). * So, 2 1/2 = 5/2 5) Practice by converting each mixed (top-heavy) number into an improper fraction. a. 2 2/5 = _________ b. 1 3/10 = _________ c. 4 4/5 = _________ d. 6 5/12 = _________ e. 2 2/3 = _________ f. 1 2/9 = _________ Name ___________________________________ 6th – Everyday Math Date __________________ Unit 3 Page 2 The Greatest Common Factor of two numbers is the largest number that is a factor of both numbers. Ex. 1) 2) Find the greatest common factor of 12 and 8. List all of the factors of 12: 1 x 12, 2 x 6, 3 x 4 In order, 1, 2, 3, 4, 6 and 12 are factors. List all of the factors of 8: 1 x 8, 2 x 4 In order, 1, 2, 4, and 8 are factors. 1, 2, and 4 are on both lists. They are common factors. 4 is the largest. It is the greatest common factor. 6) Find the greatest common factors. a 4: 7: GCF: _______ b) 3: 21: GCF: _______ c) 6: 4: 2: GCF: ________ d) 9: 12: GCF: _______ e) 3: 15: GCF: _______ f) 5: 6: GCF: ________ The Least Common Multiple of two whole numbers is the smallest number that is a multiple of both numbers. Ex. 1) 2) Find the least common multiple of 12 and 8. List a few multiples of 12: 12, 24, 36, 48, 60, 72 List a few multiples of 8 8, 16, 24, 32, 40, 48, 56, 64, 72 24, 48, and 72 are on both lists. They are common multiples. 24 is the smallest. It is the least common multiple of 12 and 8. 7) Find the least common multiples. a) 4: 7: LCM: _______ b) 3: 21: LCM: _______ c) 6: 4: 2: LCM: ________ d) 9: 12: LCM: _______ e) 3: 15: LCM: _______ f) 5: 6: LCM: ________ Adding and Subtracting Negative Numbers When adding two numbers, think of the first addend as a starting point on a number line, the second addend as a move away from that starting point to the sum or difference. (Start at 1, Add –5) Example: -6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 1 + (-5) = -4 8) Solve: a) -3 + 5 = _____ b) 5 + (-3) = _____ c) -8 – (-3) = _____ d) (the two minuses make a plus) 9 – (-3) = _____ Name ___________________________________ 6th – Everyday Math 9) perimeter Date __________________ Page 3 Unit 3 The distance around a two-dimensional shape. A formula for a parallelogram is 2" P = 2 * (length + width). 3" Ex. This parallelogram is 2" by 3" . Either add all sides: 2 + 3 + 2 + 3 = 10" or 2 * ( 2" + 3") = 10" 2" 10) area The measure of a surface inside a boundary. The formula for measuring the area of a rectangle is 6" Area = Length * Width. Ex. Area = 6" X 2" = 12 square inches or 12 in.2. 11) Find the perimeter and area of each of the figures below. 6 ft. 4 in. 9m 4 ft. 8 in. 6m a) Perimeter ________ c) Perimeter ________ e) Perimeter ________ b) Area ____________ d) Area ____________ f) Area ____________ 12) A rectangle has a length of 8 in. and a width of 6 in. a) What is its area? ____________ b) What is its perimeter? ____________ Name ___________________________________ 6th – Everyday Math 13) Date __________________ Unit 3 Page 4 Complete the table for the given rule. Plot the points and connect them to make a line graph. Hint: (To find the coordinates or plot a point on a graph with an X and Y axis always begin with x.) Rule: x = (1/4 * y) + 5 x y y 0 20 4 18 ________________________________________________________ ________________________________________________________ 16 7 12 9 20 *Remember to plot the x axis first then plot the y axis. ________________________________________________________ 14 ________________________________________________________ 12 ________________________________________________________ 10 ________________________________________________________ 8 ________________________________________________________ 6 ________________________________________________________ 4 ________________________________________________________ 2 ________________________________________________________ 0 X 0 12 14) 2 14 4 16 6 8 18 10 20 A sixth grade teacher used the spreadsheet below to record the students' scores on 3 math tests. A B C D E 1 STUDENT Test 1 Test 2 Test 3 Mean 2 Joe 60% 80% 100% 80% 3 Mandy 70% 85% 100% 85% 4 Jonathan 90% 100% 86% 92% 5 Amanda 75% 85% 80% a. What score did Jonathan receive on Test 3? ________________________ b. Calculate Amanda's mean score and write it in Cell E5. c. What is shown in Cell B4? _______________________________ d. If Joe had received a 90% on Test 1 what would his mean average have been? ____________ Name ___________________________________ 6th – Everyday Math 15) Date __________________ Unit 3 Page 5 This formula can be used to find a length in centimeters when the length in inches is known. (or vice versa) i is the number of inches, and C is the number of centimeters. C = 2.54 * i a. How many centimeters are there in 2 inches? ____________________________ b. How many centimeters are there in 5 inches? ________________ c. Circle the best approximation for the number of cm in 1 yard. 100 cm 4 cm 40 cm 254 cm 16) Equations – Number sentences that contain the relation symbol “=” are called equations. Example: 7 * 5 = 35 17) Variables A variable is a letter or symbol that represents a number. Example 1: 7*5=x Example 2: 7 * b = 35 x = 35 b=5 Algebraic expression An expression that contains a variable; much like writing a formula. Ex. Maria is two inches taller than Joe, and if the variable M represents Maria's height, then the expression M – 2 represents Joe's height. Write an algebraic expression for this one. Joe is 3 years younger than Maria. _________________________ 18) 19) Look at this general pattern. (w * w * w) - z = w3 - z (5 * 5 * 5) – 2 125 - 2 123 Give two more special cases for the general pattern above. A special case for this problem would be: = 53- 2 = 125 - 2 = 123 a) ________________________________________________________ b) ________________________________________________________ 20) Refer to the drawing at the right. Write an algebraic Expression that describes each of the following. a) The depth of the submarine if it dives 80 meters lower __________ b) The depth of the submarine if it climbs 100 meters. __________ c) The depth of another submarine b meters below this sub __________ d meters Name ___________________________________ 6th – Everyday Math Date __________________ Page 6 Unit 3 21) Circle all of the statements below that describe the special cases at the right. 4+4+4=3*4 a) x + y + z = 3 * xyz 1.5 + 1.5 + 1.5 = 3 * 1.5 b) x+x+x=3*x c) 2 + 2 + 2 = 23 d) Adding a number to itself is the same as tripling it. 21) The sixth graders in Butler School District did a survey to see what months of the year: People play outdoor sports People play indoor sports People swim outdoors 7+7+7=3*7 They made graphs to show their results. Label the graphs below with the most appropriate titles. a) ________________________ Number b) _____________________ of People Jan. Apr. July Oct. Dec. Number of People Jan. c) _______________________ Number of People Jan. Apr. July Oct. Dec. Apr. July Oct. Dec.