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35 Cards in this Set

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 A ________ number "n" is an integer > 1 that is only divisible by itself and 1. Prime All odd numbers are prime numbers [True or False] _______ False A ____________ number n is an integer > 1 that is not a prime number (divisible by more than just itself and 1). Composite Write the number 12 as a product of only prime numbers. 6 × 2 12 × 1 4 × 3 3 × 2 × 2 3 × 2 × 2 Write the number 136 as a product of only prime numbers. 34 × 2 × 2 34 × 4 17 × 2 × 2 × 2 17 × 4 × 2 17 × 2 × 2 × 2 A number has the prime factors of 2, 5 and 7. What is the smallest possible number which could have these three as prime factors? 70 42 35 21 70 Which of the following has ONLY prime numbers as its factors? 1 × 2 × 3 × 5 × 7 2 × 3 × 5 × 9 × 11 3 × 6 × 13 × 7 2 × 3 × 5 × 11 2 × 3 × 5 × 11 Each of 6 people has exactly 4 feet, 4 inches of cloth. What is the total length of cloth? 26 feet, 6 inches 25 feet, 6 inches 27 feet 26 feet 26 feet 4 feet, 4 inches = (4*12) + 4 = 52 inches. 52 × 6 = 312 inches total 312 / 12 = 26 Ted has three different sizes of stone. What is the total combined weight of all three stones? Stone 1 = 12 pounds 4 ounces Stone 2 = 10 pounds 6 ounces Stone 3 = 14 pounds 10 ounces 36 pounds, 4 oz. 37 pounds, 4 oz. 35 pounds, 6 ounces 36 pounds 37 pounds, 4 oz. One bowl can hold 420 marbles. A smaller bowl can hold 318 marbles. How many more marbles can the larger bowl hold? 120 102 200 100 102 The perimeter of a square can be represented by the formula 4x. If x = 8, what is the total perimeter of the square? 40 36 32 30 32 The perimeter of a shape is the total length of the sides. In this square, the perimeter can be found by the formula 4x, which means multiplying whatever number x represents by 4. If x = 8, then 4 × 8 = 32. The circumference of a circle can be found using the formula 2Pr (P = 3.14). If the diameter of a circle is 20, what is the circumference of the circle? 75.2 72.6 62.8 68.4 62.8 The distance around a circle is not called the perimeter--it's referred to as the circumference. The standard formula for circumference is 2 x pi x radius. Pi is always equal to 3.14. The radius is half of the diameter, so: D = 20, so r =(20 / 2) = 10 2(3.14)×10 = 6.28×10 = 62.8 There are 3 feet in 1 yard. How many poles measuring 2 feet 6 inches long can be laid down, end to end, on a 100-yard football field? 110 125 115 120 120 100 yards = 300 feet =3,600 inches 2 feet 6 inches = 30 inches 3,600 / 30 = 120 Two trees each have a height of 36 feet 8 inches. Two other trees each have a height of 28 feet 10 inches. What is the average height of each tree? 32.5 33.75 33 32.75 32.75 total feet + total inches = (36 +36 +28 +28) + (8+8+10+10) = 128 feet + 36 inches = 131 feet 4x = 131 x = 32.75 Solve the equation: -2 + 2 –(-5) + 4 -5 -1 9 1 9 Working this problem from left to right: -2 + 2 = 0 0-(-5) +4 = 5 + 4 = 9 Notice that two negatives makes a positive, so -(-5) results in +5 The ________ ____ ___________ refers to which computations are done first in a compound equation. Order of Operations List the order of operations in an equation? Acronym BEDMAS is used to remember the order of operations: Brackets Exponents Division Multiplication Addition Subtraction Solve the following equation: -5 + (7 - (-9)) + 2 23 19 13 18 13 Complete the following equation: 10(2 × 3) – 10 (20 – 16) 20 160 10 200 20 Complete the following equation: -10 – (-10) + 50 – (60 – 10) 10 -10 20 0 0 Solve the following equation: 1/2 - (-1/2 - 3/4) 1/2 -1/2 1 3/4 3/4 1 3/4 Find the missing number in the equation: 25 –(-25 + (-25 + 25)) + __ = 50 25 -50 -25 0 0 A _________ is a number that is multiplied to get a product. Factor When factoring a number you take the number apart to find its factors; either a composite or prime number. For example the factors of 16 are: 1, 2, 4, 8, 16 A number's factors are those numbers that will evenly divide into it. A _________ factor is a factor that is a prime number. Prime A prime factor is a factor that has no other factors than 1 and itself. A list of prime numbers up to 100: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 Writing any composite number as a product of prime factors is called prime _______________. Factorization To find the prime factors of a number, divide the number by the smallest possible prime number and work up the list of prime numbers until the result is itself a prime number. Example: prime factors of 160. Since 160 is even, start by dividing 2. 160 divided by 2 is 80. Then divide 80 by 2 = 40 40 / 2 = 20 20 / 2 = 10 10 / 2 = 5 (prime number) 5 is a prime number, 160 is fully factored. The prime factors are the divisors. The prime factors then are 2 × 2 × 2 × 2 × 2 × 5 To check, multiplying the factors equals 160 The greatest _________ __________ (GCF) is the greatest factor that divides two numbers evenly. Common Factor. The Greatest Common Factor for two numbers is the largest factor that will divide evenly into both of the numbers. To find the GCF of two numbers: 1. List the prime factors of each number. 2. Multiply the factors that both numbers have in common. If there are no common prime factors, the GCF is 1. Example: find the GCF of 36 and 45 First, find the prime factors of each number, using prime factorization. 36: 36 / 2 = 18, 18 / 2 = 9, 9 / 3 = 3 Prime factors: 2 × 2 × 3 × 3 45: 45 / 3 = 15, 15 / 3 = 5 Prime factors: 3 × 3 × 5 Next, identify the prime factors that both numbers have in common, and multiply them. Both of them have 3 × 3, thus 9 is the GCF. Find the GCF of 14 and 49. 49 2 7 14 7 List the prime factors of each: 14: 2 × 7 49: 7 × 7 7 is the only common factor; therefore, 7 is the GCF. The least ________ __________ (LCM) of two numbers is the smallest number (not zero) that is a multiple of both. Common Multiple. The Least Common Multiple for two numbers is the smallest number which both act as a factor for. Example: Find the LCM of 30 and 45. First, find list the prime factors of each number. 30: 2 × 3 × 5 45: 3 × 3 × 5 Then, multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs. 2: once 3: twice 5: once 2×3×3×5 = 90 = LCM After you've calculated a least common multiple, always check to be sure your answer can be divided evenly by both numbers. Find the LCM of 3, 9, and 21 27 567 189 63 63 List the prime factors of each. 3: 3 9: 3×3 21: 3×7 Multiply each factor the greatest number of times it occurs. 3 occurs twice and 7 occurs once 3×3×7 = 63 63 can be divided evenly by 3, 9, and 21. To reduce a fraction to _________ terms you divide the numerator and denominator by their GCF. Lowest A fraction is reduced to lowest terms, or simplified, when its numerator and denominator have no common factors; no number, except 1 can be divided evenly into both the numerator and the denominator. Example: Simplify 27/18 First, find the prime Factors. 18: 2×3×3 27: 3×3×3 Next, find the factors common to both the numerator and denominator. 3×3 is common to both 18 and 27 Finally, divide the numerator and denominator by all common factors (called canceling). 18/9 = 2 27/9 = 3 18/27 is simplified to 2/3 Simplify 9/45. 3/5 1/3 1/5 3/15 1/5. 9 is the GCF, so divide both the numerator and denominator by 9: (9/9)/(45/9) = 1/5 Which is a common factor of 27/36 that reduces it to lowest terms? 3 9 36 27 9 3 is a common factor that reduces the equation to 9/12 but 9/12 is not in lowest form. Dividing top and bottom by 9 (GCF) reduces it to 3/4. Which of the following CANNOT be a factor of 275? 15 5 25 30 30 30 can only be a factor of a number ending in zero (e.g., 30, 60, 90, etc.) To solve a polynomial equation it must be written in ___________ form. Standard A polynomial equation is one in which you have multiple powers of the variable 'x'. A polynomial in standard form has all the terms (listed from highest to lowest power) on one side of the equation and 0 on the other. Example: To solve 2x³ + 6x² + 12x = –8 It must be put into standard form: 2x3 + 6x2 + 12x + 8 = 0 After that it can be simplified by factoring out the common factors: Factor out a 2: x3 + 3x2 + 6x + 4 = 0 Note: The point of this is simply to show you what standard form is. We will work further with polynomials in later sections. Simplify the equation 7 – 6x – 15x2 – 2x3 = 0. x3 + 15x2 + 3x – 7 =0 2x3 + 15x2 + 6x – 7=0 –x3 – 15x2 – 3x + 7=0 –2x3 – 15x2 – 6x + 7=0 2x3 + 15x2 + 6x – 7=0. Standard form: –2x3 – 15x2 – 6x + 7 = 0 Factor out a –1 so that the highest power has a positive coefficient. –(2x3 + 15x2 + 6x – 7)= 0 2x3 + 15x2 + 6x – 7 = 0