Math 122 Review Exam 2
1) Show a number line model and a picture model for the addition problem 8 + 5 = 13.
2) Explain how to simplify this problem using the associatiive property.
36 + (64 + 89)
3) Use the lattice method to add 453 + 267.
4) Which method of estimating will work best if you are in the supermarket and you want to make sure you have
enough money for your purchases? Why?
5) What connection do you see between these two problems?
56 + 21 = 77
71 - 21 = 56
Make up a similar set of problems.
6) Show a number line model and a picture model for the subtraction problem 27 - 13 = 14.
7) What properties do addition and subtraction have? Make up problems to demonstrate each property.
8) Use a number line to illustrate 4 - 5 = -1
9) Explain why 13 × 25 is the same as (10 + 25) × (3 + 25).
10) What are the properties for multiplication and division? Make up problems to illustrate each property.
11) If you forgot what 8 × 6 is, how could you use repeated addition to figure it out?
12) Use the lattice method to obtain the product of 42 and 27.
13) Use the Russian peasant method to find the product of 25 and 84.
14) Describe an everyday situation that is commutative. Describe an everyday situation that is not commutative.
15) How would you use the distributive property to simplify this multiplication?
(24 × 53) + (6 × 53)
16) How would you use the distributive property to simplify this multiplication?
32 × 51
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17) You multiply 9 × 17 in the traditional way. Your friend Susie says that she has trouble remembering her
multiplication facts, so she gets her answer by doubling. She doubles 17, doubles again, and then adds 17. Does
her method work? Explain your answer.
18) Explain how multiplication and division are related to each other.
19) What connection do you see between these two problems?
79 × 23 = 1817
1817 ÷ 79 = 23
Make up a similar set of problems.
20) I am thinking of a number that has a remainder of 27 when divided by 45. What number works? Is there more
than one? How many are there?
21) If I start with a number, double it, add 15, divide the result by 5, and add 2, I get 27. What is my number?
22) Arrange the parentheses so that the answer to the following will be 30.
12 ÷ 4 - 2 × 5
23) Use the scaffolding method to divide 19890 ÷ 78
24) Use the divisibility rules for 2 and 3 to create a 5-digit number divisible by 6.
25) Use the divisibility rules for 8 and 5 to create a 6-digit number divisible by 40.
26) Write a divisibility rule for 15.
27) Draw a two-circle Venn diagram in which one circle represents the numbers that are divisible by 2 and the
other circle represents the numbers that are divisible by 3. Place all the natural numbers from 1 to 30 in the
appropriate region. What can be said about the numbers that appear in the intersection?
28) If a|b and a|c, will a|(b + c) ? Prove it.
29) Which of the following numbers are divisible by 9 ?
3436 621 2476 252
30) Which numbers between 120 and 130 are prime?
31) If you are checking for factors to determine whether a number is prime or composite, what is the largest factor
you need to check and why?
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32) If a number is divisible by 2, 3, 5, and 7, what other factors can you be sure it has?
33) Find the prime factorization of 3960.
34) Find the GCF and the LCM of each of the following pairs.
100, 150
54, 60
70, 90
35) The product of two numbers is 360 and the GCF is 6. What are the two number?
36) The LCM of two numbers is 280 and the GCF is 5. What are the two numbers?
37) James works as the manager of a small store. He has three employees who work different days because they are
students. Amy works every fourth day, Josh works every sixth day, and Jerry works every seventh day. If they
all three worked together on Monday, how many days will it be before James will again schedule them to work
together? What day will it be?
Use least common multiple or greatest common divisor to solve the problem.
38) Planets A, B, and C orbit a certain star once every 3, 7, and 18 months, respectively. If the three planets are now
in the same straight line, what is the smallest number of months that must pass before they line up again?
39) Bob's frog can travel 7 inches per jump, Kim's frog can travel 9 inches, and Jack's frog can travel 13 inches. If the
three frogs start off at point 0 inches, how many inches will it be to the next point that all three frogs touch?
40) Mark has 207 hot dogs and 171 hot dog buns. He wants to put the same number of hot dogs and hot dog buns
on each tray. What is the greatest number of trays Mark can use to accomplish this?
41) Find the LCM of 24, 4, and 28
42) Find the GCF of 52, 152, and 116.
Perform the indicated operation.
43) 56eight + 32eight
44) 14five + 44five
45) 32eight - 13eight
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