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Unit 1: The Number System
Parents: You may find the following notes/examples/websites helpful as we work through Unit 1.
Order of Operations
Order of Operations Steps
1. Evaluate expressions inside grouping symbols.
2. Evaluate powers.
3. Multiply & divide from left to right.
4. Add & subtract from left to right.
You can remember this:
G – grouping symbols (like parentheses)
E – exponents (Ex: 24 = 2 x 2 x 2 x 2)
M – multiply or divide from left to right
S – subtract or add from left to right
Example A: 16 + 4 ÷ 2 – 6  First divide
16 + 2 – 6  Then add
18 – 6
 Then subtract
12
Example B: 4 + 23  First evaluate the power
4 + 8  Then add
12
Why? It is important to use the order of operations to solve problems so that everyone everywhere will get the same
answer to a math problem.
The Distributive Property – This property says that you can multiply the number outside the parentheses by each
number inside the parentheses. Then add or subtract those numbers. You can also use the distributive property to
help you do mental math with larger numbers by breaking the largest number apart and then multiplying each part
separately. For example: 4 (3 + 5) = 4 x 3 + 4 x 5
6 x 85  6 (80 + 5)
12 + 20
6 x 80 + 6 x 5
32
480 + 30
510
Why? Even though we typically do the parentheses first, students need to understand the distributive property because
we will be working with algebraic expressions that use a letter in place of a number. They will need to simplify problems
such as 3(x + 8) by using the distributive property.
Factors and Multiples
prime number = has only 2 factors, 1 & itself (Ex: 31)
composite number = has more than 2 factors (Ex: 20)
Website for practice: http://www.sheppardsoftware.com/mathgames/numbers/fruit_shoot_prime.htm
prime factorization – use a factor tree to write the number as product of prime numbers
ex:
 create branches with 2 factors that make 36
36
6
6
2 3 2 3
 If the factors are prime then circle them, if not, then create branches and find 2 factors
 When you are left with only prime numbers, write the answer as a product using exponents if possible
prime factorization = 2 x 2 x 3 x 3  final answer = 22 x 32
helpful website: http://www.mathplayground.com/howto_primefactorization.html
practice website: http://www.math-play.com/Spinner-Game-Prime-Factorization/Spinner-Game-Prime-Factorization.html
Unit 1: The Number System
Parents: You may find the following notes/examples/websites helpful as we work through Unit 1.
Greatest Common Factor (GCF) – the greatest factor of 2 or more numbers
To find the GCF of 2 or more numbers:
1. Use factor trees to find the prime factorization.
However, do NOT write the prime factorization with exponents.
2. Write the prime factorization products of each number
over each other.
3. Circle the factors that are common to all numbers.
4. Multiply the circled factors to find the GCF.
Ex: Find the GCF of 18 and 27
18
27
2
9
3
9
3 3
3 3
12: 2 x 3 x 3
27: 3 x 3 x 3
GCF = 3 x 3
=9
Least Common Multiple (LCM) – the smallest multiple of 2 or more numbers
To find the LCM of 2 or more numbers:
Ex: Find the LCM of 18 and 27
1. Follow the same procedure used to find the GCF.
18
27
2
9
3
9
2. Multiply the GCF by all remaining numbers that have
3 3
3 3
not been circled.
circled #s leftovers
12: 2 x 3 x 3 LCM = 3 x 3 x 2 x 3
27: 3 x 3 x 3
= 54
Why? GCF and LCM have real-world applications, such as dividing items into groups or purchasing multiple items.
practice websites:
GCF: http://www.sheppardsoftware.com/mathgames/fractions/GreatestCommonFactor.htm
GCF & LCM: http://www.quia.com/rr/800522.html?AP_rand=1883212074
Dividing Fractions
Turn any mixed numbers into improper fractions before starting.
Remember:
KEEP the first fraction
CHANGE the ÷ to x
FLIP the 2nd fraction (use its reciprocal)
Then just multiply the numerators then the denominators.
Example:
7/8 ÷ 3/4  7/8 x 4/3
7 x 4 = 28
8 x 3 = 24
Simplify:
28/24 = 1 4/24 = 1 1/6
Simplify your answer if possible.
Why? Dividing fractions has real-world applications, such as splitting a check or sharing leftover pizza.
practice websites:
http://www.math-play.com/math-basketball-dividing-fractions-game/math-basketball-dividing-fractions-game.html
http://www.jamit.com.au/htmlFolder/Frac1009.html