# Integers

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Both versions accept a string variable as the first argument. One of the versions accepts a string to be output to cout for the user to read before prompting the user for input. The input will be assigned to the string variable provided by the first argument. Paren returns a string of the contents of the innermost parentheses of the provided string (first argument). The integer variable provided in the second argument will be assigned the position of the opening parenthesis of the parentheses…

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Little Theorem’, which states that if p is a prime number, then for every integer a, the number (ap – a) is an integer multiple of p. Fermat’s Little Theorem is the basis for many other results in Number Theory and is used by computers today to check whether a number is prime. Since there are an infinite number of prime numbers, Mathematicians and other people who study numbers as a hobby continue to search for large primes. Many of the largest primes known to us belong to a class known as…

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upcoming lessons and considering the timeline, we agreed that I would teach the students about coordinate planes, including the parts of the plane, how to plot points, find the distance between points, and reflect points across axes. The timing of this topic is fitting since the students just completed a unit on number lines, integers, and rational numbers. State, District, and National Standards Met The two AZ College and Career Readiness Standards, found on the Arizona Department of Education…

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subtraction operation. When given the question: 2-5= ?, students may give the answer: 2-5= 3, instead of the correct answer of: 2-5=-3. The student believes that the equation 2-5 cannot be done, so rearranges the equation to 5-2 to solve the equation and hence gives an incorrect answer. By rearranging the equation to bring the largest digit to the beginning of the equation, it is in turn asking a different question, and therefore gets the incorrect answer. How and Why the Misconception Occurs…

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The misconception or mistake lies in forgetting or not being aware that in subtraction, the amount you want to subtract is different from the quantity you have to subtract from. Furthermore, in subtraction, the original quantity that you have or want to subtract from is usually the larger digit (unless the equation involves positive and negative integers). A mistake like this can result in an incorrectly answered basic fact. Specific ways to help students avoid and/or overcome…

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4.3 ANURUPYENA (Ekadhikina Purvena) COROLLARY: Anurupyena (means Proportion) Meaning: By one more than the previous one Anurupyena Sutra is a specific method of division in Vedic Mathematics which shows how to divide numbers when Nikhilam and Paravartya are not applicable. Specific Condition Required: _ As we know the meaning of Anurupyena (as proportion/ratio), we multiply/divide by factor to make divisor closer to larger number (To apply Nikhilam) OR to make closer to smaller number (To apply…

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The SWOT (Strength, Weakness, Opportunity, and Threat) analysis is structured in a point-based system in order to visualize the recommendation result in a more quantitative view. Internal factors, strength and weakness, are rated in terms of technology, product quality, cost, demand and supply. External factors, opportunity and threat, are rated in terms of R&D, policy, demand and supply. The factors and their relative importance are explained in the next paragraphs. Technology in Strength and…

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Spencer Group topic: Where Do I Pull From? PO attended group on time and moderately engaged in the group discussion on “Spirituality and its role in recovery”. PO was able to identify the difference between spirituality and religion, stated “anything can be a higher power. I have always used my higher power for faith, and ask for help with logical things”. PO attentively listened while other group members shared their insights and thoughts on the topic discussion, and provided positive…

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