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Chapter 1 Review Notes 1.1 Placing fractions, decimals and whole numbers on a number line. Interpreting and writing statements of inequalities using ( <, > ) Tips: Number lines always have the lowest number to the left on a horizontal line 1 1.5 2 2½ 3 On a Vertical Number line the lowest number always starts on the bottom. 4 3 2 1 . Always use a on the number line to indicate what should be Represented. Lower# < Higher # or Higher # > Lower # 1.2 Express a whole number as a product of its prime factors ( prime factorization) Two methods: Factor Trees Ladder 2 X 2 x 7 = 42 2 x 2 x 2 x 3 x 7 = 168 1.3 Finding common factors and greatest common factor (GCF) of two whole numbers. Finding common multiples and least common multiple (LCM) of two whole numbers. Common Factors : list the factors of the whole numbers and find the common numbers 16: 1, 2, 4, 8, 16 24: 1, 2, 3, 4, 6, 8, 12, 24 Finding GCF use one of three methods: Listing factors and finding the largest 16: 1, 2, 4, 8, 16 24: 1, 2, 3, 4, 6, 8, 12, 24 GCF = 8 Using the prime factorization 16 =2 x 2 x 2 x 2 24 =2 x 2 x 2 x 3 2x2x2=8 GCF = 8 Using the Ladder: 2 16 24 2 6 12 2 4 6 2 3 2x2x2=8 GCF = 8 Finding Common Multiples: List the multiples of each number until you find the ones they have in common 5: 5, 10, 15, 20, 30, 35, 40, 45 15: 15, 30, 45 Hint once you find the 1st common multiple you can count by that number to find additional common multiples Finding LCM: List: 5: 5, 10, 15, 20, 30, 35, 40, 45 15: 15, 30, 45 Prime Factorization: 16= 2 x 2 x 2 x 2 24 =2 x 2 x 2 x 3 2 x 2 x 2 x 2 x 3 = 48 Ladder: 2 2 2 16 8 4 2 24 12 6 3 LCM = 48 2 x 2 x 2 x 2 x 3 = 48 LCM = 48 LCM = 30 1.4 Finding the square of a number Finding a square root of a perfect square 82 Exponent means 8 x 8 = 64 Base 32 --- 3 x 3 = 9 Square Root 100 2 x 2 x 5 x 5 = 100 10 10 make two matching sets ( for the 2 exponent) 2 5 2 5 (2x5) (2 x 5 ) 10 10 The square root of 100 = 10 1.5 Finding the cube of a number Finding the cube root of a number Order of Operations 23 means 2 x 2 x 2 = 8 Cube Root 8 4 2 8 2 2 2 4 2 2 2x2x2x2x2x2 Make 3 matching sets (3 exponent) ( 2x2) ( 2x2) (2x2) 4 4 4 Order of Operations Step 1 – Evaluate Exponents Step 2 – Evaluate inside Parentheses Step 3 – Multiply and divide from left to right Step 4 – Add and Subtract from left to right 4 + 6 x 3 – (23- 2) 4 + 6 x 3 – (8 – 2) 4+6x3–6 4 + 18 – 6 22 – 6 16