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nature of mathematics
Questions and Answers of
Nature Of Mathematics
Which of the numbers in Problems 7–10 are prime?a. 63b. 73c. 79d. 1,999
Which of the numbers in Problems 7–10 are prime?a. 43b. 97c. 171d. 2,007
Which of the numbers in Problems 7–10 are prime?a. 91b. 87c. 111d. 2,008
Are the statements in Problems 11–14 true or false?a. 6 | 48 b. 7 | 48 c. 8 | 48 d. 9 | 48
Are the statements in Problems 11–14 true or false?a. 6 | 39b. 5 | 30c. 16 | 576d. 3 | 7,823
Are the statements in Problems 11–14 true or false?a. 15 | 5b. 5 | 83,410c. 2 | 628,174d. 10 | 148,729,320
Are the statements in Problems 11–14 true or false?a. 15 | 4,814b. 17 | 255c. 9 | 7,823,572d. 10 | 148,729,320
Find all prime numbers less than or equal to 300.
Determine the largest prime you need to consider to be sure that you have excluded, in the sieve of Eratosthenes, all primes less than or equal to:a. 200b. 500c. 1,000d. 1,000,000
Write the prime factorization for each of the numbers in Problems 17–20. If the number is prime, so state.a. 24b. 30c. 300d. 144
Write the prime factorization for each of the numbers in Problems 17–20. If the number is prime, so state.a. 108b. 740c. 699d. 123
Write the prime factorization for each of the numbers in Problems 17–20. If the number is prime, so state.a. 120b. 90c. 75d. 975
Write the prime factorization for each of the numbers in Problems 17–20. If the number is prime, so state.a. 490b. 4,752c. 143d. 51
Each pair of numbers in Problems 21–28 lists one prime and one composite number. Identify the prime and give the canonical representation for the other.75 and 83
Each pair of numbers in Problems 21–28 lists one prime and one composite number. Identify the prime and give the canonical representation for the other.97 and 187
Each pair of numbers in Problems 21–28 lists one prime and one composite number. Identify the prime and give the canonical representation for the other.113 and 377
Each pair of numbers in Problems 21–28 lists one prime and one composite number. Identify the prime and give the canonical representation for the other.105 and 127
Each pair of numbers in Problems 21–28 lists one prime and one composite number. Identify the prime and give the canonical representation for the other.67 and 111
Each pair of numbers in Problems 21–28 lists one prime and one composite number. Identify the prime and give the canonical representation for the other.221 and 229
Each pair of numbers in Problems 21–28 lists one prime and one composite number. Identify the prime and give the canonical representation for the other.315 and 317
Each pair of numbers in Problems 21–28 lists one prime and one composite number. Identify the prime and give the canonical representation for the other.151 and 793
Find the g.c.f. and l.c.m. of the sets of numbers in Problems 29–34.{12, 54, 171}
Find the g.c.f. and l.c.m. of the sets of numbers in Problems 29–34.{11, 13, 23}
Find the g.c.f. and l.c.m. of the sets of numbers in Problems 29–34.{9, 12, 14}
Find the g.c.f. and l.c.m. of the sets of numbers in Problems 29–34.{3, 6, 15, 54}
Find the g.c.f. and l.c.m. of the sets of numbers in Problems 29–34.{75, 90, 120}
Find the g.c.f. and l.c.m. of the sets of numbers in Problems 29–34.{85, 100, 240}
In Problems 35–38,a. Find the g.c.f.b. Find the l.c.m.c. Divide the product of the two numbers by the g.c.f.d. Formulate a conclusion based on parts a–c.{60, 72}
In Problems 35–38,a. Find the g.c.f.b. Find the l.c.m.c. Divide the product of the two numbers by the g.c.f.d. Formulate a conclusion based on parts a–c.{24, 108}
In Problems 35–38,a. Find the g.c.f.b. Find the l.c.m.c. Divide the product of the two numbers by the g.c.f.d. Formulate a conclusion based on parts a–c.{75, 90}
In Problems 35–38,a. Find the g.c.f.b. Find the l.c.m.c. Divide the product of the two numbers by the g.c.f.d. Formulate a conclusion based on parts a–c.{144, 300}
Bill and Sue both work at night. Bill has every sixth night off and Sue has every eighth night off. If they are both off tonight, how many nights will it be before they are both off again at the same
Two movie theaters, UAI and UAII, start their movies at 7:00 p.m. The movie at UAI takes 75 minutes and the movie at UAII takes 90 minutes. If the shows run continuously, when will they again start
Find the absolute value of each number:a. | 5 |b. | -5 |c. | -(-3) |
Add the integers:a. 41 + 13b. -41 + (-13)c. 41 + (-13)d. -41 + 13
Indicate the sequence of keys to enter (-8) + (-5) into a calculator.
Multiply the given integers.a. (41) (13)b. (-41) (-13)c. (41) (-13)d. (-41) (13)
Subtract the given integers.a. 41 - 13b. 41 - (-13)c. -41 - 13d. -41 - (-13)
Divide the given integers.a. 12 / 6b. -18 / 2c. 10 / (-2)d. -65 / (-13)
Explain how to add integers.
Explain how to subtract integers.
Explain how to multiply integers.
Explain how to divide integers.
Explain the difference between 0 / 5 and 5 / 0.
Why is division by 0 not defined?
Evaluate each absolute value expression in Problems 7–8.a. |30|b.|-30|c. -|30|d. |30|-|-30|
Evaluate each absolute value expression in Problems 7–8.a. |18|b. |-18|c. |-(-18)|d. |-18|+ |18|
Simplify the expressions in Problems 9–37. a. 5 + 3
Simplify the expressions in Problems 9–37. a. 4 + (-7)
Simplify the expressions in Problems 9–37. a. 7+3
Simplify the expressions in Problems 9–37. a. -10 + 4
Simplify the expressions in Problems 9–37. a. 15 + 8
Simplify the expressions in Problems 9–37. a. 18+ (-10)|
Simplify the expressions in Problems 9–37. a. 10 - 7
Simplify the expressions in Problems 9–37. a. 6 - (-4)
Simplify the expressions in Problems 9–37. a. 3(-6)
Simplify the expressions in Problems 9–37. a. TIT
Simplify the expressions in Problems 9–37. a. 14(-5)
Simplify the expressions in Problems 9–37. a. -5(8 - 12)
Simplify the expressions in Problems 9–37. a. -2
Simplify the expressions in Problems 9–37. a. 12 -4
Simplify the expressions in Problems 9–37. a. -528 -4
Simplify the expressions in Problems 9–37. a. (-1) b. 10)
Simplify the expressions in Problems 9–37. a. 7(-8) b. -5(15)
Simplify the expressions in Problems 9–37. a. -5(-6) -42 b. =32
Simplify the expressions in Problems 9–37. a. -2 b. (-2)
Simplify the expressions in Problems 9–37. a. (-3) b. -3
Simplify the expressions in Problems 9–37. a. -48 b. 31 + (-16)
Simplify the expressions in Problems 9–37. - a. -14 - 21 b. 9+16+ (-11)
Simplify the expressions in Problems 9–37. a. 162 + (-12) b. -12 + [(-4) + (-3)]
Simplify the expressions in Problems 9–37. a. -46 (-46) b. |7-(-3)|
Simplify the expressions in Problems 9–37. a. |-5-(-10)| b. 5 - (-5)|
Simplify the expressions in Problems 9–37. a. -7- (-18) b. 62 - (-112)
Simplify the expressions in Problems 9–37. a. -8+ (-8) b. -9 (45) -
Simplify the expressions in Problems 9–37. a. -(23 + 14) b. -7- (6-4)
Simplify the expressions in Problems 9–37. a. -6-(-6) b. 18 - 5
Simplify the expressions in Problems 38–50. a. -8 + 7 + 16 b. 14+ (-10) - 8 - 11
Simplify the expressions in Problems 38–50. a. 6+ (-8) - 5 b. -2(-3) + (-1)(6)
Simplify the expressions in Problems 38–50. a. -5(7) - (-9) b. -2(3)-(-8)
Reduce the given fractions: a. 24 30 b. 300 144
Multiply the given rational numbers. X a. SIN b. x C. -5X3 d. 3/2 2 / e. 1 3
Justify the rule for division of rational numbers.
Divide the given rational numbers. a. 4 7 b. 43
Simplify the given expressions. a. + 7 30 b. 19 300 +2+ 25 108 C. - 18 24 d.
What does it mean for a fraction to be reduced? Describe a process for reducing a fraction.
Describe the process for multiplying fractions.
Describe the process for dividing fractions.
Describe the process for adding fractions.
Completely reduce the fractions in Problems 7–18. 2.14 b.38
Completely reduce the fractions in Problems 7–18. 78 a. 455 b. 75 500
Completely reduce the fractions in Problems 7–18. a. 150 1,000 b. 2,500 10,000
Completely reduce the fractions in Problems 7–18. a. 18 30 b. 70 105
Completely reduce the fractions in Problems 7–18. a. 2,431 3,003 b. 47,957 54,808
Completely reduce the fractions in Problems 7–18. a. b.
Completely reduce the fractions in Problems 7–18. a. 240 672 b. 5,670 12,150
Completely reduce the fractions in Problems 7–18. mla a. 9 b. 6la
Completely reduce the fractions in Problems 7–18. a. 12 b. 12
Completely reduce the fractions in Problems 7–18. 92 a. 20 b. 72 15
Completely reduce the fractions in Problems 7–18. a. 50 400 b. 140 420
Use algebra to show where the formula for subtracting fractions comes from.
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