1 UNIT 1 NUMBER SYSTEMS

Transcription

1 UNIT NUMBER SYSTEMS

2 Comparing and Ordering Integers What are different types of numbers? Natural Numbers (Counting)- Whole Numbers- Integers- Inverse Place ONLY the integers on the number line. [a] [b] [c] [d] - [e] 0 [f] - [g] Determine the integer value of each of the following.. $.00 off the original price. degrees above zero. an 8 yard gain. a. yard loss 6. a $ deposit 7. a $.00 withdrawal Comparing Numbers To show a number is greater than another number we use. To show a number is less than another number we use. To show a number is equal to another number we use. Example: Compare

3 Comparing and Ordering Integers Compare each of the following to make the inequality true. 8. [a] 6 [b] 0 8 [c] 6 6 [d] 7 6 [e] [f] Determine the additive inverse for each of the following. [a] [b] [c] 899 [d] 900 [e] 9 0. Order the following integers from least to greatest: {-, -00,,, 0, -7, 00}. The temperature in Alaska at noon is -. Use the number line to answer the following questions [a] How many degrees warmer is 9? -7 [b] How many degrees colder is? [c] At midnight, the temperature had dropped, what is the temperature now? [d] How many degrees would the temperature at noon have to increase to get to 0? Which of the following is the largest integer? a) 00 b) c) 0 d) 0. Find the sum of each. [a] [b] - + [c] +

4 Comparing and Ordering Integers Write an integer for each situation.. an 8-yard gain. a loss of pounds. above zero. 0 ft. below sea level. Compare each of the following to make the inequalities true. a. c. b. 7 0 d Order the integers in this set from least to greatest: {-,, -7, -, 0} 7. Name the additive inverse of each integer. a. -7 b. c Find the sum of each. a. + b c A stock opened at $7 per share on Monday. a. The stock s value increased $ on Monday, what is the value now? b. On Tuesday, the value of the stock decreased by $. What is the stock s value now? c. By the end of the week, the value of the stock decreased by $9 from its original value. What is the value at closing on Friday? Use a number line to justify your answer.

5 Order of Operations Order of Operations- How can I remember this? Examples: Practice: Simplify the following: ( )

6 Order of Operations 6 Simplify the following: ( ). ( ) 7 8. ( ). (8 ) 9. ( ). + ( ) 0. 6 (7 ) +

7 Absolute Value 7 What is an absolute value? - Absolute Value is the distance from zero on a number line - Distance is ALWAYS positive - The symbol for absolute value is. Example: What is the distance from - to 0?. What is the distance from to 0?. What is the absolute value of -?. What is the absolute value of? Try the following on your own:

8 Absolute Value 8 Practice: Compare the following to complete the inequalities Order the integers in each set from least to greatest.. {,,,, 0} 6. {,,, 0, } 7. Decide if each of the following is always true, sometimes true, or never true for all integer values of x. [a] x = x [b] x = x [c] x = x [d] x = x 8. Jack rides his bike north miles from his home. Alex rides his bike 0 miles south from the same house. a. How far is Jack from his home? b. How far is Alex from the house? c. How far away is Jack from Alex? 9. A friend does not know how to order integers. Explain on the lines below how you would order the following set of integers: {-,,,, -0}

9 Absolute Value 9. The absolute value of two numbers that are additive inverses will be the same. a) always b) sometimes c) never. Which number added to negative three gives the sum of zero? a) 0 b) c) d) 0. Which two numbers have an absolute value of? Compare the following inequalities In a golf tournament, the lowest score is the leader. The chart to the right shows the scores of five different golfers after a tournament. a. How many strokes is Woods ahead of Mickelson? b. Which two golfers have scores that are additive inverses? Player Score T. Woods -0 V. Singh + E. Els +0 P. Mickelson - R. Goosen - c. How many strokes is Goosen ahead of Singh? d. Put the golfers in order from best score to worst score (least to greatest): Determine if the equation is True or False. If false, explain why = = = 00 +

10 Adding Integers 0 What is the result of an addition problem? Addition with a number line: Examples: ) + ) + ( ) Steps:. Start at - on the number line Steps:. Start at - on the number line Alternate Method (song):. Move spaces in the positive direction. Move spaces in the negative direction Same Signs Add and Keep Different Signs Subtract- Keep the sign of the larger number then you ll be exact!!! Let s try these together! (- ) + () ( ) 7. + ( ) (7) 8. + ( ) + 9. The temperature in Vermont is recorded at -. At the same time, the temperature in New York is warmer. What is the temperature in New York?

11 Adding Integers Adding Larger Integers: Keep in mind: If you are adding a positive, the number should get bigger (move in positive direction) If you are adding a negative, the number should get smaller (move in negative direction) Practice: (-) ( 0) ( ) ( ). 8 + ( ) + 6. A submarine is 0 feet below sea level, over the course of the next three hours, the submarine rose 0 feet. What is the submarine s distance below sea level? 7. An elevator starts on the ground floor. If it goes up floors, then down floors, and finally up 6 floors, what floor is it on? 8. The temperature in city A is -. If the temperature in city B is the additive inverse of -, how much warmer is city B? 9. The sum of -7 and what number is?

12 Adding Integers Find the sum of the following expressions (-) (-8) (-) REVIEW (MULTIPLE CHOICE): 7. Which of the following integers represents the greatest negative integer? a) - b) - c) 00 d) The absolute value of a number is: a) always positive b) always negative c) sometimes negative d) never positive 8. Which of the following integers is the smallest? a) -7 b) - c) 800 d) -00. The absolute value of a number is: a) always positive b) always negative c) sometimes negative d) never positive 9. Which of the following integers represents the distance from - to? a) b) c) 8 d) -8. Which of the following must be equal to x? a) x b) x c) x d) x

13 Subtracting Integers The result of a subtraction problem is called: Subtraction with a number line: To subtract an integer, add its opposite (inverse) a b = a + ( b) or a ( b) = a + (b) Examples: ) ) ( ) Steps: Steps:. Re-write the problem using addition Try these!. Start at - on the number line. Start at - on the number line. Move spaces to the. Move spaces to the ( ) 6. ( ). ( ) 7. ( ) + 6. (7) 8. ( ) 9. The temperature in Chicago is 8. It is 0 colder in North Dakota. What is the temperature in North Dakota? 0. The temperature in Maine is -. At the same time, the temperature in Texas is 79. What is the difference in the two temperatures?

14 Subtracting Integers Keep in mind: When you subtract a negative you are really adding. Ex. ( 0) = +0 Practice: ( 0) ( ). 7 ( ) ( ) + 9. The temperature in San Jose is recorded at 8. At the same time, the temperature in Seattle is 9 colder. What is the temperature in Seattle? (Draw a picture of a thermometer to help.) 0. The temperature in Michigan is -6. At the same time, the temperature in New Mexico is 9. What is the difference in the two temperatures? (Draw a picture of a thermometer to help.). Michael is 8 years old. His sister Anna is 7 years older than him, and his brother Rocco is years younger than his sister. How old is his brother?

15 Subtracting Integers (-6). - (-) Write 8 as many ways as you can. ) ) ) Think of anymore? 8. Ryan has $7 in his bank account. He withdraws $8, and then deposits $. What is Ryan s new balance? 9. Your friend is having trouble simplifying 0 ( 8). Write an explanation to help your friend solve the problem. 0. Revie! Complete the following. a. + b. + c. +

16 Commutative/Word Problems 6 Commutative Property- Example: Use the commutative property to simplify: Practice ( 7) ( 90) ( 8 ) + ( 7) + ( 8 ) Word Problems Positive Number Negative Number

17 Commutative/Word Problems 7 Practice:. Joey owes his friend $0. He pays back $, and then borrows another $7. How much money does Joey owe his friend?. A submarine is 800 feet below sea level. Over the course of the next few hours, the submarine ascends 00 feet, descends 00 feet, ascends 00 feet and descends 900 feet. How far below sea level is the submarine?. The temperature at midnight is recorded at -. Over the next ten hours, the temperature increased. What is the temperature after this ten hour period?. An elevator started on the 9 th floor goes up floors, then down floors, then up floors, then down 6 floors. On what floor is the elevator now?. The temperature in Anchorage, Alaska is recorded at -7. At the same time, the temperature in Los Angeles, California is 97 warmer than in Anchorage. What is the temperature in Los Angeles? 6. In Buffalo, New York, the temperature was - o F in the morning. If the temperature dropped 7 o F at :00pm, what is the temperature now? 7. A submarine was situated 70 feet below sea level. If it descends (goes down) 00 feet, what is its new position?

18 Commutative/Word Problems 8 Review! Write an integer to represent each situation:. Five dollars off the original price. two degrees above zero Compare the following Inequalities ( 9) 7 Evaluate each of the following (-9) 7. 8 Order these integers from least to greatest. 8. {,,, 0, } 9. Maggie deposits $ in the bank. She then withdraws $0 on Monday, deposits $ on Tuesday, and then withdraws $ on Wednesday. How much does Maggie have left in the bank? 0. A stock opens at $0 per share on Monday. The chart displays the change over the course of the next few days. What is the value of the stock per share at closing on Friday? Day Change Monday +$ Tuesday -$ Wednesday -$8 Thursday +$ Friday -$6

19 Word Problems 9 Complete the following word problems!. In the Sahara Desert one day it was 6 o F. In the Gobi Desert a temperature of -0 o F was recorded. What is the difference between these two temperatures?. Mt. Everest, the highest elevation in Asia, is 0,0 feet above sea level. The Dead Sea, the lowest elevation, is 8 below sea level. What is the difference between these two elevations?. A runner jogs miles in one direction. He then turns around and jogs 8 miles in the opposite direction. a. How far is the runner from his starting position? b. How far did the runner jog in total?. A scuba diver is 80 feet below sea level. She ascends feet, and then descends 8 feet. What is her current depth?. An explorer jumps out of a plane and parachutes into a cave. He jumped out of the plane at 00 feet above sea level, and lands at the bottom of the cave, which is 900 feet below sea level. a. How far was the explorer s jump? b. Once in the cave, the explorer continues deeper into the cave. If he climbs to the lowest point in the cave, and records the depth at feet below sea level, how far down did he climb from where he landed? 6. A roller coaster at Six Flags has a largest drop of -76 feet. A roller coaster at Dorney Park has a largest drop of -9 feet. How much bigger is the drop at the roller coaster at Six Flags?

20 Multiplying and Dividing Integers What is the result for a multiplication problem called? 0 What is the result for a division problem called? Rules: ) Count the negative signs Odd number of negative signs - Answer Negative Even number of negative signs - Answer Positive Any number multiplied by zero is Any number divided by zero is ) Multiply or Divide OR use this chart! Examples: Practice:. (7)(0). ( )

21 Multiplying and Dividing Integers 7. ( )(0) ( ). ( ) ( ) Extended Response: 7. One night in January, the temperature in Alaska is 6. The next day, the temperature is half of what it was the night before. What is the temperature? 8. The volunteer club raked leaves at several senior citizens homes in the neighborhood. If each group of three students could remove 8 cubic meters of leaves in one hour, find an integer to represent the number of cubic meters of leaves students could remove in hours? 9. During the fourth quarter, the Patriots were penalized times for the same amount for a total of yards. Write a division sentence to represent this equation. Then find the number of yards for each penalty.

22 Multiplying and Dividing Integers Compute the following expressions.. ( 9)( 8) ( )( ) 8. ( )( )( ) (6)( ) ( 8) 0 6. ( )( ). ( ) 8

23 Evaluating Expressions Algebraic expression Evaluate Variable - Substitution Property STEPS: ) Write the original problem. ) Rewrite the expression with the values of each variable substituted in (use parentheses to substitute). ) Simplify by using order of operations. SHOW ALL WORK! Examples: Evaluate each expression if n =, p =, and t = 6 ) n + p ) t p ) p n + Practice: Evaluate each expression if n =, p = and t = ) n + p ) -.t ) (p n) + ) p (t ) ) p n t 6) n p t 7) ( p ) (t ) 8) p n t USE THE GIVEN FORMULA TO EVALUATE: 9) Drew drove to Chicago at an average rate of 0 mph. The trip took him 7 hours. How far did Drew drive? Distance = Rate x Time

24 Evaluating Expressions Evaluate each expression if x =, y = and z =. x + z. xy. z x 6. x. x y + 7. x y. xy z 6x 8. z 9. John is deciding whether he wants to install a rectangular pool or a cylindrical pool in his back yard. The pool company shows him two models, one a rectangular prism and one a cylinder, that are the same price. He wants t determine which pool would hold a larger volume of water. a. The rectangular prism pool has a width of 0 feet, a length of 0 feet, and a height of feet. Using the formula for volume of a rectangular prism, determine the volume of this model. V = lwh b. The cylindrical pool has a radius of 0 feet, and a height of feet. Using the formula for volume of a cylinder, estimate the volume of this model. (use as an estimate for π at the very end of the problem) V = πr h c. Which pool has a greater volume? By how much?

25 Introduction to Fractions and Decimals Vocabulary: ) Decimal: ) Fraction: ) Difference: ) Product: ) Quotient: 6) Rounding: Replacing a number with another number that is approximately equal but shorter. Decimals: Place Value Word Bank Ten-thousands Tenths Thousands Tens Millions And Hundreds Thousandths Ones Hundredths Hundred-thousands Fill in the chart with the appropriate place value 8, 0, Rules for rounding: Step - Find the place value you are rounding to and underline it. Step - Look at the number to the right and think five or more add one more four or less let it rest Step - Write the appropriate number and drop all numbers to the right. Example: Round to the nearest hundredth. Five or more? Yes Add one more is the answer! Guided Practice: Round the following: to the nearest tenth.. to the nearest hundredth..9 to the nearest whole number..99 to the nearest tenth

26 6 Introduction to Fractions and Decimals ROUNDING Round the following decimals to the nearest tenth: Round the following decimals to the nearest hundredth: Round the following decimals to the nearest thousandth: Comparing Decimals Write <, >, or = Fractions: Converting Decimals to Fractions. METHOD : METHOD : WHAT ARE EQUIVALENT FRACTIONS? GIVE AN EXAMPLE. Given the decimal convert to a fraction

27 Introduction to Fractions and Decimals 7 Round the following:. 8.6 to the nearest tenth. 9.7 to the nearest hundredth. 0.8 to the nearest whole number. Which is greater 0. or ? Explain your reasoning. Compare the following decimals. Write <, >, or = ) State and explain if the following fractions are equivalent. 8. and and and

28 Converting Rational Numbers to Decimals 8 Vocabulary: ) Convert: ) Rational Numbers: Previous Knowledge: Write each as a decimal: = = = = PROPER FRACTIONS TYPES OF FRACTIONS TERMINATING DECIMALS TYPES OF DECIMALS IMPROPER FRACTIONS NON-TERMINATING DECIMALS MIXED NUMBERS REPEATING DECIMALS FRACTIONS TO REMEMBER: =. = =. =.7 =. =. =.6 =.8 =. = =. 8 =.7 8 =.6 8 =.87 9 =. 9 =. 9 =. 9 =. 7 9 = = =. 0 =. 0 =.7 0 =.9 Make connections! What would be: a) 8 b) c) D) E) 7 *F).. F) 6.8

29 Converting Rational Numbers to Decimals 9 Any rational number can convert to a decimal using long division; know that the decimal form of a rational number terminates in zeroes or eventually repeats. Guided Practice: Convert the fraction into a decimal using long division and determine if the decimal is repeating or terminating. ) = ) = ) 8 6 = decimal decimal decimal ) 9 = ) 8 = decimal decimal Try These: Remember to show all work Write each fraction as a decimal using long division and determine if the decimal is repeating or terminating. ) 8 = ) = ) = ) 9 decimal decimal decimal decimal ) = 6) = 7) = 8) = decimal decimal decimal decimal 9) Write a fraction that is equivalent to a terminating decimal between 0. and 0.7. Think: 0) Fractions in simplest form that have denominators of,,, 8, and 0 produce terminating decimals. Fractions with denominators of, 6, 9 and produce repeating decimals. What causes the difference? Explain.

30 Converting Rational Numbers to Decimals 0 Convert the following fractions to a decimal using long division. State whether it terminates or repeats. ) 9 = ) 6 = ) = ) 8 ) 6) 6 Word Problems: 7) Use the table that shows decimal and fraction equivalents. Which fraction represents 0.8? A) B) C) 6 D) 9 8 Decimal Fraction ) Zoe went to lunch with a friend. After tax, her bill was $.0. Which mixed number represents this amount in simplest form? A) B) C) 0 D) 0 00 Convert the following mentally. 9) 0) ).7 )..

31 Converting Mixed Numbers and Improper Fractions Vocabulary: ) Improper Fraction: ) Mixed Number: Converting Mixed Number to Improper Fractions: Rules: ) Multiply the denominator and the integer ) Add the product to the numerator ) Take that sum and place it over the ORIGINAL denominator Model Problem: ) = Step ) = 0 Step ) 0 + = Step ) Examples: ) = ) = ) 6 = 0 + ) 8 = ) 6 = 0 6) 7 = 7 To convert an improper fraction to a mixed number: Rules: ) Divide the numerator by the denominator ) Write down the integer ) Write the remainder over the original denominator Model Problem: = remainder

32 Converting Mixed Numbers and Improper Fractions Examples: 7) 8) 68 9) ) 6 ) 66 0 ) 987 ) Sally is baking a birthday cake for her mom. The recipe calls for 9 cups of flour and cups of oil. However, her measuring cup is only labeled in mixed numbers. How much flour would 9 cups be as a mixed number? How much oil would cups be as a mixed number? ) Steven is putting away test tubes in science class. He has 0 test tubes and will fit on each rack. How many rack racks will Steven fill? Write the answer as a mixed number. ) Chrissy ordered pizzas cut into 8 slices each. 0 slices were eaten. Write the remaining number of pies as a mixed number. 6) Cole was 8 miles away from Betty. How many miles is that as a mixed number?

33 Converting Mixed Numbers and Improper Fractions Convert the following into an improper fraction:. 6 = =. 7 = Convert the following into a mixed number: Word Problems: 7. Marty drove his Lamborghini DeLorean miles to get to the clock tower. How far is that as an improper fraction? 8. Spot the dog ran away from home. A neighbor called and said that he was found in their backyard 6 miles away. How far is that as a mixed number? Convert mentally to a decimal

34 Comparing and Ordering Rational Numbers METHOD. CONVERT ALL NUMBERS TO DECIMALS (ALL TO THE SAME PLACE). COMPARE OR ORDER METHOD. CONVERT ALL NUMBERS TO FRACTIONS WITH A COMMON DENOMINATOR. COMPARE OR ORDER EX:, 0, 8, 0., 0.7 EX:, 0, 8, 0., 0.7 COMPARE: ORDER FROM LEAST TO GREATEST AND PLOT THE GIVEN SET OF NUMBERS ON THE NUMBER LINE: 9. 7, 0, 8, 0., ,,, 0.,.7.,,, 0., 0.. 6,,, 9, π FRACTIONS AND DECIMALS-COMPARE AND ORDER DAY HOMEWORK

35 Comparing and Ordering Rational Numbers COMPARE: ORDER THE GIVEN SET OF NUMBERS FROM LEAST TO GREATEST: 7. 9,, 8, 0., ,, 8,,.,,, 6. 7,, 6,

36 Comparing and Ordering Rational Numbers 6 PLOT THE GIVEN SET OF NUMBERS ON THE NUMBER LINE:. 0,,,.,.9.,,,,. ANGELA ATE 8 OF A BAG OF CHIPS. ALEX ATE OF THE BAG. [A] WHO ATE MORE? [B] WHAT FRACTION OF THE BAG REMAINS? COMPARE THE FOLLOWING: ORDER THE FOLLOWING RATIONAL NUMBERS FROM GREATEST TO LEAST: 7., 7 0, 8, 69,,.7

37 Adding, Subtracting, Multiplying, Dividing Decimals 7 Adding/ Subtracting Decimals: Rules: ) Line up the decimals ) Add or subtract Find the Sum or Difference: ) 9. + (-.6) ) ) ) 9.6. ) ) 9.00 (-.) ) ) ) -. Multiplying Decimals: Rules: ) Ignore the decimals in the numbers ) Multiple the given numbers as if they were whole numbers ) Count the places after the decimal in each number ) Count that number of places from the right side in your answer Examples: Find each product: ).0 ) - 8 ) -. x.6 x -. x. 6 ) (8.7)(0.) ) (.)(.) 6) (0.9)(.7) 7) An apple costs $.60. How much will it cost to purchase a dozen apples?

38 Adding, Subtracting, Multiplying, Dividing Decimals 8 Dividing Decimals: Rules: ) Rewrite each division problem as long division. ) Do not start dividing until you change the outside number to a whole number ) Move the inside decimal the same amount of places as you did the outside number ) Write the decimal up into the answer ) Divide the two numbers as whole numbers to find the quotient Examples: Find each quotient: ) ) 9.. ) ) 00 7 ) ) Look at the denominators of each of the above three problems. Notice that the decimal point moves one place to the left from one exercise to the next. Describe what happens to the quotients. Word Problems: 7) Peanuts costs $.7 per jar. How many jars can you buy with $? 8) You spend $.9 for fabric. Each yard costs $.. How many yards of fabric do you buy? 9) After digging up lilac bushes in a garden, a landscape architect uses sod to cover the ground. The sod costs $. per yard. He pays $.0. How much sod does he buy? 9) A car travels 60. miles. It uses. gallons of gas. How many miles per gallon of gas does the car get?

39 Adding, Subtracting, Multiplying, Dividing Decimals 9 Evaluate ) ) ) ) (.6)(.9) ) (-.8)(0.7) 6) (.)(.6) 7) ) ) Breakfast Menu Egg $.7 Toast $0.99 0) a) If Michael orders egg, toast, bacon, and milk, how much will it cost? Bacon $.0 Milk $. b) Michael gives a $0 bill to the cashier. How much change will he receive? ) Alicia paid $. for a bag of potato chips. The chips cost $0. per pound. How much does the bag of potato chips weigh? ) Nina and three friends ate lunch at a café. They decided to split the bill evenly. The total bill was $7.8. How much was each person s share?

40 Adding and Subtracting Factions and Mixed Numbers 0 ADD/SUBTRACT FRACTIONS RULES: ) FIND A COMMON DENOMINATOR ) ADD OR SUBTRACT NUMERATORS ) KEEP THE DENOMINATOR THE SAME ) SIMPLIFY FRACTION INTO LOWEST TERMS FIND THE SUM OR DIFFERENCE WITHOUT USING A CALCULATOR: (USE A SEPARATE PIECE OF PAPER) ) ) 6 6 ) 7 0 ( 0 ) ) ) 7 6 6) ) ) ) ) + 9 ) ) ) 6 + ) 6 8 ) 9 6) ) 8 8) + 0

41 Adding and Subtracting Factions and Mixed Numbers WORD PROBLEMS: 9) TO MAKE LEMONADE, YOU USE CUPS OF LEMON CONCENTRATE AND CUPS OF WATER. HOW MANY CUPS OF LEMONADE DO YOU MAKE? 0) YOU HAVE CUPS OF FLOUR AND YOU NEED TO USE CUPS OF FLOUR FOR A COOKIE RECIPE. HOW MUCH FLOUR WILL YOU HAVE LEFT? ) MARK DRIVES HIS CAR 7 MILES WEST ON THE LONG ISLAND EXPRESSWAY, HOWEVER HE DROVE PAST HIS EXIT. HE TURNS AROUND AND GOES EAST FOR MILES TO HIS EXIT. HAD HE NOT MISSED HIS EXIT, HOW FAR WOULD MARK HAVE HAD TO TRAVEL ON THE HIGHWAY? ) JESSICA S CAR HAS A GAS TANK THAT HOLDS 8 GALLONS OF GAS. JESSICA KNOWS THAT THE TANK ONLY HAS GALLONS OF GAS LEFT IN IT. HOW MUCH GAS WOULD IT TAKE TO FILL UP THE GAS TANK? ) MEGAN WENT TO A YANKEE GAME IN MAY. IT TOOK HER HOURS TO GET TO THE GAME. THE GAME HAD A HOUR RAIN DELAY BEFORE STARTING. AFTER THE DELAY, THE GAME TOOK HOURS. IT THEN TOOK MEGAN 6 HOURS TO GET HOME. HOW LONG WAS IT FROM THE TIME MEGAN LEFT HER HOME UNTIL THE TIME SHE GOT BACK HOME?

42 Adding and Subtracting Factions and Mixed Numbers FIND THE SUM OR DIFFERENCE WITHOUT A CALCULATOR: ) + ) 7 ) 9 ( 6 ) ) ) ) 6 7) + 8) WORD PROBLEMS: 9) ON SATURDAY, YOU HIKED MILES. 8 ON SUNDAY, YOU HIKED MILES. HOW FAR DID YOU HIKE DURING THE WEEKEND? 0) THE GAS TANK IN YOUR FAMILY S CAR WAS 7 FULL WHEN YOU LEFT YOUR HOUSE. WHEN YOU ARRIVED AT 8 YOUR DESTINATION, THE TANK WAS FULL. WHAT FRACTION OF A TANK OF GAS DID YOU USE DURING THE TRIP? ) SAWYER ROWED MILE. MAGGIE ROWED 8 MILE. WHO ROWED FURTHER? HOW MUCH FURTHER? 0

43 Multiplying and Dividing Factions and Mixed Numbers IMPORTANT VOCABULARY: COMPLEX FRACTIONS: RECIPROCAL: MULTIPLYING FRACTIONS BY HAND RULES:. CONVERT MIXED NUMBERS TO IMPROPER FRACTIONS (IF NECESSARY). SIMPLIFY EACH FRACTION. MULTIPLY STRAIGHT ACROSS FIND EACH PRODUCT: ) ) - ) DIVIDING FRACTIONS BY HAND (WITHOUT A CALCULATOR) RULES:. CONVERT MIXED NUMBERS TO IMPROPER FRACTIONS (IF NECESSARY). CHANGE TO MULTIPLICATION OF THE RECIPROCAL. FOLLOW MULTIPLICATION STEPS FIND EACH QUOTIENT: ) ( 8 ) ) 6) 6 FIND THE PRODUCT OR QUOTIENT: 7) 7 9 8) ) 8 9 0

44 Multiplying and Dividing Factions and Mixed Numbers WORD PROBLEMS **IN WORD PROBLEMS, WHEN DEALING WITH FRACTIONS THE WORD OF MEANS TO MULTIPLY** EXAMPLE : OF 8 EXAMPLE : OF 9 0 PROBLEM SOLVING 0) IF MET HATS? OF THE,000 PEOPLE AT THE MET GAME ARE WEARING METS HATS. HOW MANY PEOPLE ARE WEARING ) ANTHONY OF AN APPLE PIE. THE NEXT DAY, KYLE ATE EAT? OF THE REMAINING PIE. HOW MUCH DID KYLE ) ERIN MAKES CUPS OF PUDDING. HOW MANY CUP SERVINGS CAN SHE GET FROM THE PUDDING? ) DEVEN CAN RUN MILE IN MINUTES. HOW LONG SHOULD IT TAKE TO RUN MILES? 6

45 Multiplying and Dividing Factions and Mixed Numbers FIND THE PRODUCT OR QUOTIENT WITHOUT A CALCULATOR SHOW ALL WORK ) 0 ) ) 9 6 ) ) 6 6) 6 7) 8 8) **9) WORD PROBLEMS 0) JOANNE HAS YARDS OF MATERIAL TO MAKE COSTUMES. EACH COMPLETE COSTUME REQUIRES YARDS FOR THE TOP AND YARD FOR THE BOTTOM. HOW MANY COMPLETE COSTUMES CAN SHE MAKE? ) ON THE FIRST DAY THE APPLE iphone S WAS RELEASED, THE LOCAL STORE HAD 00 IN STOCK. BY 8:00 PM, THE STORE HAD SOLD OF THEIR STOCK. [A] HOW MANY iphones WERE LEFT IN THE STORE S STOCK? [B] IF EACH iphone SOLD FOR $00, HOW MUCH MONEY DID THE APPLE STORE MAKE IN iphone SALES?

46 Complex Fractions 6 Vocabulary Proper Fraction Improper Fraction Mixed Number Complex Fraction - a fraction where the numerator, denominator, or both contain a fraction. Change the following mixed numbers to an improper fraction. a) b) c) 8 0 Review Solve each of the following and reduce your answers to lowest terms... 6 ( ). ( ) ( ) Guided Practice. 9 0.

47 Complex Fractions 7 Try These Solve each of the following questions and be sure to show all work.. Luke walked his dog mile every day. It takes him hour to walk that distance. How fast does he walk in miles per hour?. The length of a kangaroo s leap can be up to far can it jump? 6 times its height. If a kangaroo is 7 feet tall, how. Susan threw the javelin 76 meters for her first throw and much longer was her first throw than her second throw? 7 meters for her second throw. How *. Mr. McCahill wants to make a shelf with boards that are many pieces can he cut from the big board? feet long. If he has an 8 foot board, how

48 Complex Fractions & Review Evaluate. Use separate paper if you need more room. ) 7 ( ) ) 6 8 ) ) 8 0 ) 6) 6 Thinking Question Take one step at a time! 7) 8) 9) Sandy is having trouble with his assignment. His shown work is as follows: x However, her answer did not match the answer that his teacher gives him. What is Sandy s mistake? Find the correct answer.