Fractions, Decimals and Percents To convert a fraction to a percent, convert the fraction to a decimal number by dividing the numerator by the denominator. Then, multiply the decimal by 100 and add a percent symbol. 4 9 = 0.444 44 = 0.444 44 100% = 44.4% 1. Write each fraction as a decimal and a percent. a) 4 b) 1 6 2. Complete the following table. Fraction Decimal Percent a) 4 5 b) 0.66666. c) 4 11 d).% Probability The probability of an event is a measure of the likelihood that it will occur. The probability of an impossible event is 0 or 0%. The probability of a certain event is 1 or 100%. A coin is flipped. What is the probability that it lands heads up, P(H)? Write your answer as a fraction, a decimal, and a percent. favourable outcomes P(H) = possible outcomes = 1 2 The probability of heads is 1, 0.5, or 50%. 2
. BLM 11 2. (continued). The spinner is spun once. Find the following probabilities. Write each answer as a fraction, a decimal, and a percent. a) What is the probability of spinning 2, P(2)? b) What is P(< )? c) What is P(> )? Justify your response. Using Tables and Tree Diagrams Tables and tree diagrams are common ways to organize outcomes. A coin is flipped and a spinner is spun. a) What is the sample space or list of all possible outcomes? b) How many outcomes are there? c) What is P(T, )? a) Table Tree Diagram Spinner Coin 1 2 Heads (H) H, 1 H, 2 H, Tails (T) T, 1 T, 2 T, b) There are 6 favourable outcomes: (H, 1), (H, 2), (H, ), (T, 1), (T, 2), (T, ). c) P(T, ) = 1 6 P(T, ) is 1, 0.16, or 16.6%. 6 4. a) Create a table to show the sample space for the spinner and the fair six sided die. b) List the sample space. c) What is P(A, < 5)?
5. The following sample space represents all of the outcomes from flipping a coin and spinning a numbered spinner: (H, 1), (T, 1), (H, 2), (T, 2), (H, ), (T, ), (H, 4), (T, 4). a) Draw the spinner.. BLM 11 2. (continued) b) Display the sample space in a tree diagram. c) What is P(H or T, < 5)? Explain your thinking. Multiplying Fractions You can use paper folding to multiply proper fractions. To multiply fractions without a diagram, multiply the numerators and multiply the denominators. 1 1 1 1 = 2 2 1 = 6 6. What multiplication statement does each diagram represent? a) 7. Multiply. Show your answer in lowest terms. 1 a) 4 5 b) 5 5 6 c) 4 2 5 b)
Name: Date: Section 11.1 Extra Practice. BLM 11 5. Write the answers for #1 to #4 in your notebook. 1. At Antonio s Pizzeria, the pizzas come in three sizes: large, massive, and gargantuan. There are four varieties to choose from: Veggie Garden, Carnivore s Delight, Cheesy Wheezy, and Hawaiian Paradise. Use either a tree diagram or a table to display all of the possible choices. 2. Two dice are rolled. One die has the first six prime numbers on it. The other die has the first six letters of the alphabet on it. a) What are the possible rolls for each die? b) Draw a table to show the sample space. c) What is the total number of outcomes? d) What is the probability of P(E, 11)? Give your answer as a fraction, a decimal, and a percent. e) What is the probability of getting a vowel and an even prime number? Give your answer as a fraction, a decimal, and a percent.. A quarter is tossed into the air and lands. Then, a nickel is tossed into the air. a) List all the possible outcomes. b) What is the probability of landing one head and one tail? c) What is the probability of a head followed by a tail? d) Explain the difference between P(H, T) and P(H then T). 4. From a deck of cards, use only the hearts to answer the following questions. Shuffle the hearts and draw from them face down. a) What is the probability of drawing the six of hearts? Give your answer as a fraction, a decimal, and a percent. b) What is the probability of drawing a face card? Give your answer as a fraction, a decimal, and a percent. c) What is the probability of drawing the ace of hearts? d) Suppose you drew a card that was not the ace, kept it out of the pile, and drew another card. What would be the probability of getting an ace in the second draw? Give your answer as a percent.
Name: Date: Section 11.1 Math Link. BLM 11 6. This worksheet will help you with the Math Link on page 418. 1. Complete the following tree diagram to determine all the possible outcomes for a toss of four sticks. 2. a) How many possible outcomes are there? How many outcomes have b) only one decorated side up? c) two decorated sides up? d) three decorated sides up? e) four decorated sides up? f) no decorated sides up?. What is the probability of exactly three sticks landing decorated side up? Give your answer as a fraction, a decimal, and a percent.
Name: Date: Section 11.2 Extra Practice. BLM 11 7. 1. You flip a nickel, a dime, and a quarter. a) Use a tree diagram to show the number of possible outcomes. b) Use multiplying to show the number of possible outcomes. 2. Carlos was in charge of purchasing baseball hats for the team. He can get them in three colours: blue, green, and black. The green and blue hats come in fitted and one-size-fits-all, and in both washable and non-washable versions. Black hats come in only fitted and non-washable styles. How many hat choices does Carlos have? Show your thinking.. At a restaurant, if you order one appetizer, one main course, and one dessert, you have 72 different meal combinations to choose from. There are three choices of desserts and four choices of main courses. How many choices of appetizers are there? Show your thinking. 4. Make up a situation that would give the following number of combinations: 7 2 = 42 combinations. 5. Hana won the grand prize trip, but she has some choices to make. She can go to Paris, London, or Rome. She can go for a week in winter, in spring, or in summer. Hana may take her sister or her friend with her, or take nobody and receive an extra $4500 to spend instead. How many trip options does Hana have? Show your thinking.
Name: Section 11. Extra Practice Date:. BLM 11 10 Write your answers for #1 in your notebook. 1. Shea-Lee rolled a regular die and recorded the results in a tally chart. a) How many times in total did Shea-Lee roll the die? b) What is the experimental probability of rolling a? c) What is the theoretical probability of rolling a? d) Which number s experimental probability matches its theoretical probability? e) What could Shea-Lee do to get all of the numbers to match their theoretical probability better? 2. Mallory rolls a six-sided die and Rose flips a coin. a) Draw a tree diagram in your notebook. What is the probability of the girls getting tails and an odd number? b) Use multiplication to get your answer. c) What is this same probability written as a percent and as a decimal?. Bill and Ravi made two spinners, one with eight equal sectors each with a different colour, and one with 25 equal sectors each with a different number. Determine the probability of spinning black and 15 as quickly as possible. a) Determine P(black, 15). b) Write this probability as a fraction, a decimal, and a percent. c) Why is calculating the answer easier than drawing a table or a tree diagram? 4. Ivan created a spinner for a simulation. He knew the theoretical probability for an event was 2. This is the spinner he created. Is this a fair spinner for the simulation? Explain your thinking.
Chapter 11 BLM Answers BLM 11 2 Chapter 11 Get Ready 1. a) 4 = 0.75 = 75% b) 1 = 0.16 = 16.6% 6 2. a) 4 5 b) 2 Fraction Decimal Percent c) 4 11 d) 1 0.8 80% 0.66666. 0.66. 0.. 66.6% 6.6%.% BLM 11 5 Section 11.1 Extra Practice 1. Large Massive Gargantuan Veggie Garden Carnivore s Delight Cheesy Wheezy Hawaiian Paradise Veggie Garden Carnivore s Delight Cheesy Wheezy Hawaiian Paradise Veggie Garden Carnivore s Delight Cheesy Wheezy Hawaiian Paradise. a) 1, 0.,.% b) 2, 0.6, 66.6% c) 0, 0.00, 0%. There are no numbers greater than on the spinner so there is 0 probability. 4. a) 1 2 4 5 6 A A, 1 A, 2 A, A, 4 A, 5 A, 6 B B, 1 B, 2 B, B, 4 B, 5 B, 6 b) (A, 1), (A, 2), (A, ), (A, 4), (A, 5), (A, 6), (B, 1), (B, 2), (B, ), (B, 4), (B, 5), (B, 6) c) P(A, < 5) = 4 12 or 1 b) 5. a) Possible number of choices: 12 2. a) Die 1: 2,, 5, 7, 11, 1; Die 2: A, B, C, D, E, F b) 2 5 7 11 1 A A, 2 A, A, 5 A, 7 A, 11 A, 1 B B, 2 B, B, 5 B, 7 B, 11 B, 1 C C, 2 C, C, 5 C, 7 C, 11 C, 1 D D, 2 D, D, 5 D, 7 D, 11 D, 1 E E, 2 E, E, 5 E, 7 E, 11 E, 1 F F, 2 F, F, 5 F, 7 F, 11 F, 1 c) 6 possible outcomes d) P(E, 11) = = 0.02778 = 2.778% 1 6 c) P(H or T, < 5) = 100%. Every outcome in the sample space will consist of either a head or a tail and a spin of less than 5. 6. a) 2 1 2 = 1 b) 4 2 = 1 2 7. a) 20 b) 1 2 c) 8 15 e) P(vowel, even prime number) = 2 6 = 0.05 = 5.556%. a) quarter head, nickel head; quarter head, nickel tail; quarter tail, nickel head; quarter tail, nickel tail b) P(H, T) = 1 2 c) P(H followed by T) = 1 4 d) Answers will vary. Example: P(H, T) and P(H then T) are different because the second one is more specific than the first. P(H, T) means that
either the quarter or the nickel can be heads or tails, while P(H then T) means that the quarter must be heads and the nickel must then be tails. 4. a) 1 1, 0.077, 7.69% b) 1, 0.21, 2.1% c) 7.78% d) second draw 1 = 8.% 12 BLM 11 10 Section 11. Extra Practice 1. a) 60 b) = c) d) 4 12 1 1 60 5 6 e) Answers will vary. Example: Roll many more times. 2. a) BLM 11 6 Section 11.1 Math Link 1. 2. a) 16 b) 4 c) 6 d) 4 e) 1 f) 1. 4, 0.25, or 25% 16 12 b) 1 6 2 = 12 or 1 4 c) 25%, 0.25. a) 1 8 1 25 = 1 200 b) 1, 0.005, 0.5% 200 c) Answers will vary. Example: A table or tree diagram would take too long to draw and be very complicated. Calculation is much quicker. 4. Answers will vary. Example: This is a fair spinner because 10 of the 15 sections are shaded. The probability of spinning a shaded section is. 2 BLM 11 7 Section 11.2 Extra Practice 1. a) b) 2 2 2 = 8 2. four kinds of blue, four kinds of green, two kinds of black = ten choices. 4 = 72. There are six choices of appetizers. 4. Answers will vary. Example: 7 days a week meals a day 2 types of beverages = 42 beverage choices each week 5. 27