1. 1.1 Whole Number Operations
See handout
Operation
Words
Algebra
Addition
the sum of
a + b
Subtraction
the difference of
a - b
Multiplication
the product of
a x b, a ∙ b
Division
the quotient of
a ÷ b, a/b

2. Addition/Subtraction – On Your Own
Find the value of the expression. Use estimation to check your answer.

3. Multiplication – On Your Own
Find the value of the expression. Use estimation to check your answer.

4. Division – On Your Own
Find the value of the expression. Use estimation to check your answer.

5. Division – On Your Own
Find the value of the expression. Use estimation to check your answer.

6. Division – On Your Own
Find groups means divide!

7. 1.2 Powers and Exponents

8. Power – On Your Own Power: a product of repeated factors
Write the product as a power:

9. Base and Exponent – On Your Own
Base of a power: the repeated factor
Exponent of a power: the number of times the base is used as a factor
Find the value of the power:

10. Perfect Square – On Your Own
Perfect square: the square of a whole number
9 = 32, so 9 is a perfect square.
Determine whether the number is a perfect square:

11. 1.3 Order of Operations
Numerical expression: an expression that contains only numbers and operations
Evaluate: to find the value
Order of Operations:
Parentheses
Exponents
Multiplication and Division left to right
Addition and Subtraction left to right
1.3 Notes

12. Using Order of Operations to Evaluate a Numerical Expression
1.1

13. 1.4 Prime Factorization
Factor tree: a diagram that splits whole numbers into factor pairs until all factors are prime
Factor tree for 60
Draw a factor tree for 24

14. Factor Pairs - On Your Own
Factor pair: a pair of numbers that are factors of a product
Factor pairs for 12:
1, 12 (1 x 12 = 12)
2, 6 (2 x 6 = 12)
3, 4 (3 x 4 = 12)
List the factor pairs of the number:

15. Prime Factorization - On Your Own
Prime factorization: a composite number written as a product of its prime factors
The prime factorization of 60:
Write the prime factorization of the number:

16. Prime Factorization - On Your Own
What is the greatest perfect square that is a factor of 1575?

17. 1.5 Greatest Common Factor
Common factors: factors that are shared by two or more numbers
Greatest common factor: the greatest of the common factors
Find the GCF of 24 and 40 using common factors:

18. Finding GCF Using Prime Factorization
Find the GCF of 12 and 56 using prime factorization: The GCF is 4.

19. Using GCF to Find the Greatest Number of Equal-sized Groups
You have 24 roses and 36 tulips. What is the greatest number of identical flower arrangements you can make?
24 = 2 ∙ 2 ∙ 2 ∙ 3
36 = 2 ∙ 2 ∙ 3 ∙ 3
The common factors are 2, 2, and 3.
The greatest number of identical arrangements is
2 ∙ 2 ∙ 3 = 12

20. Notes 1.6: Least Common Multiple
Common multiples: multiples that are shared by two or more numbers
List the common multiples of 4 and 6:
Least common multiple: the least of the common multiples

21. Finding LCM Using Prime Factorization
Find the LCM of 16 and 20 Write what they have in common: 2 ∙ 2 Write the remaining prime factors: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 Multiply: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 = is the LCM of 16 and 20.

22. Finding the LCM of Three Numbers
Find the LCM of 4, 15, and 18:
Write what two or three of the trees have in common: 2 ∙ 3
Write the remaining prime factors: 2 ∙ 3 ∙ 2 ∙ 3 ∙ 5
Multiply. 2 ∙ 3 ∙ 2 ∙ 3 ∙ 5 = 180
180 is the LCM of 4, 15, and 18.

23. Using LCM to Find When Two Things Happen at Same Time

24. On Your Own
A traffic light changes every 30 seconds. Another changes every 45 seconds. Both lights change. After how many seconds will both change at the same time?
Find LCM of 30 and 45 by listing multiples:
30, 60, 90, …
45, 90, …
The lights will change at the same time in 90 seconds (or one and a half minutes).

25. Finding GCF and LCM using Inverted Division

26. Notes 1.6 Extension: Adding and Subtracting Fractions
Least common denominator: the LCM of the denominators
To add and subtract fractions with unlike denominators:
Use a common denominator, simplify at end
Use the least common denominator