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5th ~ Answer Key ~ Grade Unit 12 Checking Progress 1. Steve rolls a 6-sided die and then flips a coin. How many different ways can the die roll and coin toss turn out? a. Use the Multiplication Counting Principle to answer. ____12______ different ways. b. Draw a tree diagram to show all the possible ways. Suggestion: Use the letters H and T to represent HEADS and TAILS. 1 H 2 T H 3 T H 4 T H 5 T H 6 T H T c. Which method do you think is easier for finding the number of possible results? _____Answers Vary__________________ 12a. Use tree diagrams to find all possible ways a sequence of choices can be made. 1 2 3 1 2 3 2. In Problem 1, what is the probability that Steve a. rolls a 5 and the coin lands on HEADS? 1/12 b. rolls a prime number? 6/12 or 3/6 or 1/2 c. tosses the coin so that it lands on HEADS? 6/12 or 1/2 12b. Compute the probability of outcomes when choices are equally likely. 1 1 2 2 3 3 A school cafeteria offers these choices for lunch: Main course: pizza, hot dog or taco Drink: milk or juice Dessert: cookies, ice cream or cake 3. How many different ways can a student choose one main course, one drink and one dessert? Use the Multiplication Counting Principle. ____3____ * ____2____ * ____3____ 4. Number of different ways to select foods for lunch: __18___ 5. What would be the number of different ways to select foods for lunch if you add one more drink choice. ________27_________ 12c. Use the Multiplication Counting Principle to find the total number of possible outcomes of a sequence of choices. 1 2 3 1 2 3 For each number below, draw a factor tree and write the prime factorization. 6. 60 60 = 2 * 2 * 3 * 5 7. 54 = 54 8. 2 * 3 * 3 * 3 12h. Find the prime factorizations of numbers. 33 33 = 3 * 11 1 2 3 1 2 3 9. What prime factors do 60 and 54 have in common? __2, 3_____ 10. What is the greatest common factor of 60 and 54? _____6____ Explain how you found it. _______SA_____________________ __________________________________________________ __________________________________________________ 12d. Find the greatest common factor of two numbers. 1 2 3 1 2 3 11. What is the least common multiple of 12 and 30? ___60______ 12. What is the least common multiple of 6 and 18? _____18_______ Explain how you found it. ____SA________________________ __________________________________________________ __________________________________________________ 12e. Find the least common multiple of two numbers. 1 2 3 1 2 3 Rewrite each fraction pair with a common denominator. 13. 3 5 and 8 12 9 10 and 24 24 14. Sally bought a large pizza. She wants to cut the pizza so that it can be shared equally by 2 people, 3 people, 4 people, 6 people, or 8 people. Into how many slices should Sally cut the pizza? ___24 slices________ (unit) 15. There are 30 students in Vicki’s class. Two-thirds of her class rides to school on the school bus. The other students walk to school. How many students walk to school? ___10 students______ (unit) 12g. Find and identify factors of numbers. 0-2 3-4 5-6 1 2 3 16. Holly was playing Name That Number. Of the 5 cards she turned over, 60% were black. How many black cards were there? __3 black cards______ (unit) 17. Three out of 7 cars parked on one street were red. If there were 28 cars, how many cars were red? __12 red cars_______ (unit) 18. Joy’s heart beats 11 times in 10 seconds. At this rate, about how many times would it beat in 1 minute? ____66 times_______ (unit) 12f. Solve ratio and ratio number stories. 0-2 3-4 5-6 1 2 3