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Divisibility and GCF Primes, Composites and Rational # Simplifying Fractions and Problems Exponents Scientific Notation $100 $100 $100 $100 $100 $200 $200 $200 $200 $200 $300 $300 $300 $300 $300 $400 $400 $400 $400 $400 $500 $500 $500 $500 $500 Divisibility and GCF for $100 Is 68,301 divisible by 9? Answer Yes, because 6+8+3+0+1 = 18 and 18 is divisible by 9 Back Divisibility and GCF for $200 List the factors of 70 Answer 1, 2, 5, 7, 10, 14, 35, 70 Back Divisibility and GCF for $300 Write a 5 digit number that is divisible by 3 Answer Answers vary, but the sum of the digits must be divisible by 3. i.e. 31,260 = 3+1+2+6+0 = 12. Since 12 is divisible by 3, 31,260 is also divisible by 3. Back Divisibility and GCF for $400 Find the GCF of 200 and 145 Answer Factor trees! 200 = 100*2 = 5*20*2 = 5*5*4*2 = 5*5*2*2*2 145 = 5 * 29 Thus the GCF is 5 (only factor in common) Back Divisibility and GCF for $500 Find the GCF of 56x2y3 and 16x4y Answer 56x2y3 = 2*2*2*7 *x*x*y*y*y 16x4y = 2*2*2*2*x*x*x*x*y Top and bottom have 2, 2, 2, x, x, y in common, so the GCF is 8x2y Back Primes, Composites, and Rational Numbers for $100 Is 57 prime, composite or neither? Answer Composite – 57 has 1, 3, 19, and 57 as factors. Back Primes, Composites, and Rational Numbers for $200 Write two numbers that are neither prime, nor composite Answer 1 and 0 1 only has 1 factor 0 cannot be made by multiplying 2 non-zero numbers together. Back Primes, Composites, and Rational Numbers for $300 Graph the number (5/7) on a number line Answer (5/7) Back Primes, Composites, and Rational Numbers for $400 Evaluate for a = -3 and b = 5: -2 a * 2 (4b – 10) Answer a-2 * (4b2 – 10) = (-3)-2 * (4*52 – 10) = (1/9) * (100-10) = (1/9) * 90 = 10 Back Primes, Composites, and Rational Numbers for $500 Explain how to find all of the prime numbers less than a certain number. Answer Write out all the numbers 1 to the number. Then, find all the prime numbers less than the square root of the number. Then cross off all the multiples of the primes less than the square root. The numbers left are prime numbers. Back Simplifying Fractions and Problems for $100 Simplify: 21/33 Answer 21/33 = (7*3)/(11*3) = 7/11 Back Simplifying Fractions and Problems for $200 Simplify: xy/y Answer xy/y = x Back Simplifying Fractions and Problems for $300 Simplify: 2 45yz 2 36xy Answer 2 45yz = 3*3*5*y*z*z 2 36xy = 2*2*3*3*x*y*y 3, 3, and y cancel out: 2 5z 4xy Back Simplifying Fractions and Problems for $400 Crystal wants to put a fence around her vegetable garden. Her garden is 5 ft wide and 4 ft long. She plans to put a post at each corner and at every foot. How many fence posts will Crystal need? Answer There will be 6 posts on each width and 5 posts on each length = 6+6+5+5 = 22. However, this means the four corners are repeated, so 22-4 = 18 posts. Back Simplifying Fractions and Problems for $500 Jane has 5 marbles in her pocket. She has one blue, one orange, one yellow, one green and one red. If she chooses two without looking, how many possibilities are there? Answer Possibilities are B,O,Y,G,R, So BO, BY, BG, GR, OY, OG, OR, YG, YR, GR. = 10 possibilities Or, n(n-1)/2 Back Exponents for $100 Simplify: 450 *423 Answer 50 4 * 23 4 = 50 + 23 4 = 73 4 Back Exponents for $200 Simplify: (2y4)3 Answer 4 3 (2y ) = 3 2 * 4*3 y = 12 8y Back Exponents for $300 Simplify: (8x2)/(16x5) Answer (8x2)/(16x5) = (8/16)(x2/x5) = (1/2)(x2-5) = (1/2)(x-3) = (x-3)/2 or 1/(2x3) Back Exponents for $400 Simplify: (x4 * x3 * x5)3 Answer 4 (x * 3 x * 5 3 x) = (x4+3+5)3 = (x12)3 = x12*3 = x36 Back Exponents for $500 Simplify and write the answer without using a division symbol: 5 2 35x y 7 7x y Answer 35x5y2 = (35/7)(x5/x7)(y2/y) = 5x-2y 7x7y Back Scientific Notation for $100 Write the following number using standard notation: 4.56 x 107 Answer 7 7 4.56 x 10 => the 10 causes the decimal to move to the right 7 places 45,600,000 Back Scientific Notation for $200 Write the following number using scientific notation: 2355000 Answer 2355000 => The decimal point goes between the 2 and 3 because it goes after the first non zero number. This moves it 6 places from the original spot, so. = 2.355 x 106 Back Scientific Notation for $300 Write 0.0000045 in scientific notation. Answer 0.0000045 = 4.5 x -6 10 Back Scientific Notation for $400 Write in scientific notation: 35.2 x 1010 Answer 35.2 x 1010 = 3.52 x 1011 Back Scientific Notation for $500 Simplify – Write your answer using scientific Notation: (3 x 104) x (5 x 10-8) Answer (3 x 104) x (5 x 10-8) = (3*5) * (104 x 10-8) = 15 x 10-4 = 1.5 x 10-3 Back