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 You can remember this: 1. Evaluate expressions inside grouping symbols. G – grouping symbols (like parentheses) 2. Evaluate powers. E – exponents (Ex: 24 = 2 x 2 x 2 x 2) 3. Multiply & divide from left to right. M – multiply or divide from left to right 4. Add & subtract from left to right. S – subtract or add from left to right
Example A: 16 + 4 ÷ 2 – 6 First divide Example B: 4 + 23 First evaluate the power 16 + 2 – 6 Then add 4 + 8 Then add 18 – 6 Then subtract 12 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: 36 create branches with 2 factors that make 36
6 6 If the factors are prime then circle them, if not, then create branches and find 2 factors
2 3 2 3 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.
Least Common Multiple (LCM) – the smallest multiple of 2 or more numbers To find the LCM of 2 or more numbers: 1. Follow the same procedure used to find the GCF. 2. Multiply the GCF by all remaining numbers that have not been circled.
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.
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