Unit 1 Review: GCF, LCM, GEMDAS and Prime Factoring

Distributive Property

100

USE DISTRIBUTIVE PROPERTY TO SOLVE

5(4+3)

20+15

= 35

200

USE DISTRIBUTIVE PROPERTY TO SOLVE

8(10 - 2)

(8*10) - (8*2)

80 - 16

64

300

USE DISTRIBUTIVE PROPERTY TO SOLVE

7(2+3)

(7*2) + (7*3)

14 + 21

35

400

Use the Distributive Property to solve:

10(5 + 11)

10*5 + 10*11

50 + 110

160

500

Use the Distributive Property to Solve:

22(4 - 2)

(22*4) - (22 * 2)

88 - 44

44

Prime Factorization

100

WHAT IS THE PRIME FACTORIZATION OF 72 using exponents if necessary? 

2x2x2x3x3

2³X3²

200

WHAT IS THE PRIME FACTORIZATION OF 80  using exponents if necessary?

2x2x2x2x5

2⁴ x 5

300

WHAT IS THE PRIME FACTORIZATION OF 99 using exponents if necessary?

3x3x11

3²x11

400

WHAT IS THE PRIME FACTORIZATION OF 170 using exponents if necessary?

2x5x17

500

WHAT IS THE PRIME FACTORIZATION OF 200 using exponents if necessary?

2x2x2x5x5

2³x5²

GEMDAS

100

(5²-4) ÷ 3

7

200

(67-17) ÷ 2x5

125

300

10²-(4x5)+13

93

400

12-8+(3x8-4)÷(6-2)

9

500

5²-(10+5-12) ÷ 3

24

Story Problems

100

Two bells ring at different intervals.

• Bell A rings every 6 minutes.
• Bell B rings every 8 minutes.

If both bells ring together at 9:00 a.m., how many minutes will pass before they ring together again?

24 minutes; they will ring together again at 9:24am

200

Three groups of students rotate through activities in gym class.

• Group A switches activities every 4 minutes.
• Group B switches every 6 minutes.
• Group C switches every 10 minutes.

If all three groups switch activities at the same time right now, how many minutes will pass before all three switch at the same time again?

In 60 minutes (1 hour)

300

A teacher has 24 granola bars and 36 fruit snacks. She wants to make identical snack bags using all of the snacks, with the same number of each type in every bag.

What is the greatest number of identical snack bags she can make?

12 snack bags

400

A community center offers three different activities on repeating schedules:

• Art class meets every 9 days.
• Science club meets every 12 days.
• Game night happens every 15 days.

Today, all three activities happen on the same day. How many days from now will all three happen on the same day again?

180 days

500

A teacher has 42 pencils, 56 erasers, and 70 stickers. She wants to divide all of the supplies into identical sets so that each set has the same number of pencils, erasers, and stickers.

How many pencils, erasers, and stickers will be in EACH SET?

GCF: 14, so 14 sets

42/14 = 3 pencils in each

56/14 = 4 erasers in each

70/14 = 5 stickers in each

LCM and GCF

100

Find the LCM of 5 and 10 using prime factorization.

10

200

Find the GCF of 18 and 27 using prime factorization.

9

300

Find the LCM of 12 and 10 using prime factorization.

60

400

Find the GCF of 120 and 48 using prime factorization.

24

500

Find the LCM and GCF of 25 and 90 using prime factorization.

LCM: 450

GCF: 5