TOPIC 2 STUDY GUIDE
NAME ____________________________________DATE______________PERIOD________
1. Write an expression equivalent to (23 + m) + 0 by the Associative Property of Addition?
2. Write an expression equivalent to 23 by the Identity Property of Addition.
3. Write an expression equivalent to 2 ∙ (n ∙ 4) by the Associative Property of Multiplication.
4. Write an expression equivalent to 7 by the Identity Property of Multiplication.
5. Write an expression equivalent to 0 by the Zero Property of Multiplication.
6. Use the distributive property to write and model an expression equivalent to 35 + 63. Find the GCF
using factor trees.
Commented [TJ1]:
Commented [TJ2R1]:
7. Use the distributive property to write and model an expression equivalent to 6(8 + 3).
8. Use the distributive property to find two expressions that are equivalent.
A) 3(4x – 2)
B) 3(2x)
C) 12x – 6
D) 12x – 2
9. Which expression is equivalent to 9a + 7a by the distributive property?
A) 16a
B) a (9 + 7)
C) 9(a + 7)
D) 63a
10. Use the distributive property to write an expression that is equivalent to 12(a + n).
11. Use the distributive property to write an expression that is equivalent to 12d + 7d.
12. Use the Commutative Property of Multiplication to write TWO equivalent expressions for 2 ∙ 3 ∙ 4.
13. Use the Commutative Property of Addition to TWO equivalent expressions for 9 + 8 + 7.
14. Evaluate.
(3 + 0) + (4 ∙ 1) + (9 ∙ 0)
15. Your Mom makes cookies and brownies. She sells them at bake sales through the holidays.
She sells a package of cookies for $2 and a package of brownies for $3. Write an expression for the
total amount of money she can make for selling c packages of cookies and b packages of brownies.
If she sells 4 packages of cookies and 2 packages of brownies, how much money can she make?
16. It costs $16 per person to buy food for a road trip to California. You and 3 friends are going on
the trip. Write two equivalent expressions that represents the amount of money spent on the trip for
food. How much money was spent on food?
17. Summer goes to the library every 5 days. Kyle goes to the library every 3 days. How often did
they see each other at the library?
Summer and Kyle saw each other at the library every ____days.
18. Melissa made 24 chocolate chip cookies and 60 sugar cookies. She wants to group them so that
each group has the same number of chocolate chip and sugar cookies.
What is the greatest number of groups possible? How many chocolate chip cookies and sugar
cookies are in each group?
19. Annie has two pieces of ribbon. The pink ribbon is 120 cm long and the purple ribbon is 90 cm
long. She wants to cut both ribbons into pieces that are the same length. What is the maximum length
that the ribbons could be? How many of each ribbon would you have?
20. Find the least common multiple of 9 and 12.
21. Kevin uses the properties of operations that he learned in class to write an equivalent expression
for 3(5 +4). He incorrectly writes that the expression is equivalent to 3 ∙ 5 + 4. What property could
you use to write an equivalent expression to 3(5+4)? Then using that property, write an equivalent
expression.
22. Use a factor tree to find the prime factorization of 64.
23. Najeeb says that 23 is a prime number, Karli says that it is a composite number. Which student is
correct and why? Justify your answer.
24. Find the Greatest Common Factor of 42 and 68 using two methods: listing factors and prime
factorization.
Listing factors:
GCF = _________
Prime Factorization:
GCF = _________
25. Mrs. Hernandez waters her rose plant every 3 days and her tulips every 5 days. If she waters
both of them today, how many days will it be before she waters both of them on the same day again?
26. Find the least common multiple of 4 and 9.
27. Find the prime factorization of 48.