previous lessons‚ the students had learned about positive and negative integers. Using concrete and realistic situations‚ the students were able to understand the concept and were now ready to learn about adding and subtracting integers using algebra tiles. This would eventually allow the students to be able to solve simple equations‚ with and without the algebra tiles. However‚ the students were able to learn how to add integers conceptually while using the tiles first. This becomes even more important
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math.BigDecimal; import java.util.*; /** * * @author: Huma UmmulBanin Zaidi * @Project:Project1‚ Data Structure. * Running program looks like: This program finds sum or product of a LARGE numbers of integers. Enter as many integers > 0 as you would like. Enter the numbers: 1 3 5 7 7 5 3 1 Please select the number of one of these options: 1. Sum the numbers in the list 2. Multiply the numbers in the
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is the following; multiplication and division always produces larger and smaller values respectively. This is related to the order in which children are taught the concepts of multiplication‚ Division and extending the set of numbers from integers to non integers and fractions. Misconception | Demonstration of why this is incorrect | Multiplication always makes a number larger or it stays the same stays the samesolution larger than original number (5) | Multiplication can make numbers smaller
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from 1. Whole numbers are a collection of all natural numbers including 0. Rational numbers are the numbers that can be written in p form‚ where p and q are q integers and q 0 Closure property 1. Whole numbers are closed under addition and multiplication. However‚ they are not closed under subtraction and division. 2. Integers are also closed under addition and multiplication. However‚ they are not closed under subtraction and division. 3. Rational numbers: i. Rational numbers are closed under
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even. “0” and “1” are not prime numbers. A natural number greater than 1 that is not a prime number is a composite number. Factoring Polynomials Polynomials: Basic Operations An algebraic expression involving only nonnegative-integer powers of one or more variable and containing no variable in a
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_____________. (Points : 6) Sizes Numbers Integers Subscripts None of the above | 4. Which is the simplest search technique to use to find an item in an array? (Points : 7) Sequential Binary Bubble Select None of the above | 5. Which of the following arguments must be passed when passing an array as an argument? (Points : 6) The array itself An integer that specifies the number of elements in the array The
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Lemma: If n is a positive integer‚ [pic] proof: [pic] [pic] [pic] = an − bn. Theorem: If 2n + 1 is an odd prime‚ then n is a power of 2. proof: If n is a positive integer but not a power of 2‚ then n = rs where [pic]‚ [pic]and s is odd. By the preceding lemma‚ for positive integer m‚ [pic] where [pic]means "evenly divides". Substituting a = 2r‚ b = − 1‚ and m = s and using that s is odd‚ [pic] and thus [pic] Because 1
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include negative numbers; does not include fraction (such as 6/7 or 9/7); does not include decimals (such as 0.87 or 1.9) Whole numbers : The numbers {0‚ 1‚ 2‚ 3‚ ...} There is no fractional or decimal part; and no negatives: 5‚ 49 and 980. Integers : Include the negative numbers AND the whole numbers. Example: {...‚ -3‚ -2‚ -1‚ 0‚ 1‚ 2‚ 3‚ ...} Rational numbers: It can be written as a fraction. For example: If a is 3 and b is 2‚ then: a/b = 3/2 = 1.5 is a rational number 2. Give examples
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accessing that variable. Most programs have many many modules. This makes global variables very time consuming to debug. Algorithm Workbench Review Questions 1‚5‚6‚ and 7 from page 111 1. Design a module named timesTen. The module should accept an Integer argument. When this module is called‚ it should display the product of its argument multiplied by 10 1. Declare a variable called number and set the value of it 2. Call the module timesTen passing as an argument the variable number by reference
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circumference of the circle? A. 2.5π B. 3π C. 5π D. 4π E. 10π 5. Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set? A. 4 B. 7 C. 8 D. 12 E. it cannot be determined from the information given. 6. If f(x) = (x + 2) / (x-2) for all integers except x=2‚ which of the following has the greatest value? A. f(-1) B. f(0) C. f(1) D. f(3) E. f(4)
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