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Math 088 Fall, 2016 Worksheet 3.2: Prime Factorization and Fractions 1. Warm-up: Solve the following inequalities. Give your answer in interval notation, and use a test value to check your answer. 3x + 5 < -4 Check: 6 − 2x ≥ 2 Check: 2. Divisibility rules Any even number is divisible by 2 Example: 146 = 73 · 2 Any number ending in 0 or 5 is divisible by 5 365 = 73 · 5 Any number ending in 0 is divisible by 10 5670 = 567 · 10 If the sum of the digits is divisible by 3, then the number is divisible by 3 132 = 44 · 3, because 1 + 3 + 2 = 6 If the sum of the digits is divisible by 9, then the number is divisible by 9 504 = 56 · 9, because 5 + 0 + 4 = 9 Prime Factorization refers to factoring a number completely into prime numbers. Use the Divisibility Rules above to find the prime factorization of each of the following: 112 = 99 = 280 = 108 = 130 = 125 = 105 = 220 = 204 = 3. Multiplying Fractions When multiplying fractions, it’s always best to simplify first. Factor the numerators and denominators, cancel what you can, and then multiply the remaining terms. 25 9 100 9 12 · 10 = 99 · 10 = 21 75 · 45 14 = 39 20 · 4 9 6 7 · = 2 25 · 9 10 22 21 · 9 121 · 125 6 = 70 9 = · 4. Adding and Subtracting Fractions Use factoring to find the Least Common Denominator, then add or subtract as indicated. 3 20 + 5 12 7 44 + 3 8 = 8 15 + 4 9 − 7 9 = − 11 125 1 6 = 4 21 − 4 - 21 + = 7 100 5 8 − = 5 12 =