Chapter 5: Rational Numbers as Fractions
... 5.1.1.3. denominator – for , the integer in the bottom: b b a 5.1.1.4. proper fraction – a fraction , where 0 ≤ | a | ≤ | b | b a 5.1.1.5. improper fraction – in general a fraction , where | a | ≥ | b | > 0 b 5.1.1.6. equivalent fractions – when one fraction is a multiple of another fraction 5.1.1.7 ...
... 5.1.1.3. denominator – for , the integer in the bottom: b b a 5.1.1.4. proper fraction – a fraction , where 0 ≤ | a | ≤ | b | b a 5.1.1.5. improper fraction – in general a fraction , where | a | ≥ | b | > 0 b 5.1.1.6. equivalent fractions – when one fraction is a multiple of another fraction 5.1.1.7 ...
Multiplication and Division of Rational Numbers
... a. In one year, Melinda’s parents spend $2,640.90 on cable and internet service. If they spend the same amount each month, what is the resulting monthly change in the family’s income? ...
... a. In one year, Melinda’s parents spend $2,640.90 on cable and internet service. If they spend the same amount each month, what is the resulting monthly change in the family’s income? ...
solutions - Math-UMN
... 10.) Prove that the irrationals Qc are dense in R; i.e., any x ∈ R can be represented by a Cauchy sequence of√irrationals. Note that if√y ∈ Qc and z ∈ Q, then yz ∈ Qc (since y = [z(yz)−1 ]−1 ). Since 2 ∈ Qc , it follows that 2/N ∈ Qc for every N ∈ N. Namely, we get arbitrarily small irrational numbe ...
... 10.) Prove that the irrationals Qc are dense in R; i.e., any x ∈ R can be represented by a Cauchy sequence of√irrationals. Note that if√y ∈ Qc and z ∈ Q, then yz ∈ Qc (since y = [z(yz)−1 ]−1 ). Since 2 ∈ Qc , it follows that 2/N ∈ Qc for every N ∈ N. Namely, we get arbitrarily small irrational numbe ...
File
... 3. If 4 daps are equivalent to 3 dops, and 2 dops are equivalent to 7 dips, how many daps are equivalent to 42 dips? 4. A student added up the first 100 positive integers. However, instead of getting 5050 like he was supposed to, he accidentally switched the two digits of one of the integers and got ...
... 3. If 4 daps are equivalent to 3 dops, and 2 dops are equivalent to 7 dips, how many daps are equivalent to 42 dips? 4. A student added up the first 100 positive integers. However, instead of getting 5050 like he was supposed to, he accidentally switched the two digits of one of the integers and got ...
DMIST Chapter 1slides
... the ability to recognize that numbers or objects can be changed and returned to their original condition. ...
... the ability to recognize that numbers or objects can be changed and returned to their original condition. ...
Ch5 Formulas - Wah Yan College, Kowloon
... In the previous section, we learnt how to find the values of the terms in a sequence from the general term by substituting different values of n in the general term. ...
... In the previous section, we learnt how to find the values of the terms in a sequence from the general term by substituting different values of n in the general term. ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.