UNIT 4 PRACTICE PROBLEMS
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1 UNIT 4 PRACTICE PROBLEMS 1. Solve the following division problems by grouping the dividend in divisor size groups. Write your results as equations. a = Division Equation: Multiplication Equation: b = Division Equation: Multiplication Equation: 1
2 c = Division Equation: Multiplication Equation: d = Division Equation: Multiplication Equation: 2. Solve the following division problems using a calculator. Write your results as equations. a = Division Equation: Multiplication Equation: b = Division Equation: Multiplication Equation: 2
3 c = Division Equation: Multiplication Equation: 3. Solve the following application problems using division with remainders. Make sure to include units in your answers. a. Terri is sending care packages to troops overseas. She baked 112 cookies. She wants to share the cookies equally among the 6 different troops. How many cookies will each troop get? How many cookies will be leftover? b. Sean is biking at a rate of 14 miles per hour. He wants to bike a total of 71 miles. What is the maximum number of whole hours he will spend biking? How many miles will he have left to travel after riding the maximum number whole hours? 3
4 c. Judy's favorite t-shirts are on sale for $19. She has $195 and wants to buy as many t-shirts as possible. How many t-shirts can Judy buy? How much money will she have leftover? 4. Rewrite the factor questions as divisibility questions and the divisibility questions as factor questions. Determine the answer to the questions and justify your work. a) Is 6 a factor of 46? Equivalent divisibility question: b) Is 56 divisible by 4? Equivalent factor question: c) Is 13 a factor of 104? Equivalent divisibility question: 4
5 d) Is 112 divisible by 7? Equivalent factor question: e) Is 9 a factor of 558? Equivalent divisibility question: f) Is 23 divisible by 88? Equivalent factor question: g) Is 45 divisible by 15? Equivalent factor question: h) Is 5 divisible by 15? Equivalent factor question: 5
6 5. Complete the Table of Perfect Squares. 2 2 = 5 2 = 8 2 = 11 2 = 3 2 = 6 2 = 9 2 = 12 2 = 4 2 = 7 2 = 10 2 = 13 2 = 6. Find all factors of the given numbers by finding factor pairs. Use the table of perfect squares to see what the largest number you have to check is. Write your final answer as a list of factors separated by commas. a) 12 Largest number you have to check: List of Factors: b) 48 Largest number you have to check: List of Factors: c) 185 Largest number you have to check: List of Factors: 6
7 7. Fill in the blanks: a. A number is a whole number greater than 1 whose factor pairs are only the number itself and one. b. A number is a whole number greater than 1 which has at least one factor other than itself and one 8. Determine all of the prime numbers less than Verify that the following numbers are prime by checking to see if the number is divisible by any prime numbers whose square is less than the number given. a) 107 b) 83 c) 261 d) 39 7
8 10. Determine whether the numbers are prime or composite. If it is composite, show at least one factor pair of the number besides 1 and itself. If it is prime, show the numbers you tested and the results of your division. a. 107 b. 61 c. 261 d Fill in the blank: The of a number is the number written as a product of only prime factors. 8
9 12. Find the prime factorizations for the given numbers using factor trees. Write the final result in exponential form and factored form. a) 32 b) 175 c) 72 d) 280 9
10 13. Use two different factor trees to determine the prime factorizations of 90. Write the final result in exponential form and factored form. 14. Fill in the blanks: a. Common factors of two or more numbers are factors that both numbers. b. The of two or more numbers is the largest of the two numbers common factors. 15. Find the GCF of the given numbers. a. 8 and 20 b. 30 and 105 c. 16 and 18 d. 22 and 25 e. 12, 8, 24 10
11 16. Fill in the blanks: a. A of a number is a product of the number with any whole number. b. The is the smallest multiple of 2 or more numbers. 17. Find the LCM for the given numbers. a. 4 and 6 b. 10 and 8 c. 15 and 9 d. 2, 6, and 15 11
12 18. Find the prime factorizations using factor trees for the following pairs of numbers. Then find the LCM and GCF. a. 4 and 6 b. 10 and 8 c. 15 and 9 d. 12 and 26 12
13 19. Consider the numbers 30 and 105 a. Determine the Greatest Common Factor (GCF) of 30 and 105. b. Find the Least Common Multiple (LCM) of 30 and 105 by using the relationship below. Product of numbers GCF = LCM 20. Consider the numbers 60 and 48 a. Determine the Least Common Multiple (LCM) of 60 and 48. b. Find the Greatest Common Factor (GCF) of 60 and 48 by using the relationship below. Product of numbers LCM = GCF 13
14 21. Penny and Sheldon are assembling hair clips. Penny can assemble a hair clip in 6 minutes and Sheldon can assemble a hair clip in 9 minutes. a. If they start making the hair clips at the same time, what is the least amount of minutes it will take for them finish a hair clip at the same time? b. After this amount of minutes, how many hair clips will Penny have made? c. After this amount of minutes, how many hair clips will Sheldon have made? 22. Kathryn is packing bags of food at the local food pantry. She has 24 jars of tomato sauce and 30 cans of soup. a. If she wants each bag to have the same numbers of tomato sauce and soup, what is the greatest number of bags she can pack? b. How many jars of tomato sauce will each bag have? c. How many cans of soup will each bag have? 23. Paige is buying hot dogs and buns for a family reunion. Each package of hot dogs contains 8 hot dogs. Each package of buns contains 10 buns. a. What is the least total amount of hot dogs and buns she needs to buy in order for the amounts to be equal? b. How many packages of hot dogs will she buy? c. How many packages of buns will she buy? 14
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