Any rational number has a reduced form For example 12/70, 18/105, 600/3500 all represent the same reduced rational number, 6/35. Write down a characteristic of the numerator and denominator of a reduced fraction (hint: look at the prime factors).

Q: 4063 Find (with proof) the residue of 3200s when dividing it by 93.

A: Euler's phi function is very significant in calculating the residue. As Fermat's little theorem is…

Q: every rational number is a decimal true or false?

A: We know that rational numbers are of the form of terminating and repeating decimals whereas…

Q: 6. Find the rational number represented by the repeated decimal using the formula: 3.325

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Q: Show that every rational number has exactly two finite simple continued fraction expansions.

A: To Show : Show that every rational number has exactly two finite simple continued fraction…

Q: . Assuming every number born on a finite day is a dyadic rational: lowest terms and r 2 0. Given two…

A: Two dyadic rationals, a / 2r < b / 2s where r is greater than or equal to zero. Now, we have to…

Q: Find a Rational number between 1/4 and 1/3

A: We will use basic knowledge of rational numbers to answer this question.

Q: Find a rational number between √2 and √3

A: Topic = Algebra

Q: Justify whether it is true to say that the given is the nth term of an AP  1+n+n2

A: We have to say that whether the given nth term is in A.P. where, 1+n+n2 We have given nth term of…

Q: show that the following number is rational by writing it as a ratio of two integers. 2 9  +  2 3

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Q: In a group, there were 115 people whose proofs of identity we passport, some had voter id and some…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Show that the following number is rational by writing it as a ratio of two integers. 8/9 +2/5

A: A rational number is a real number that is the ratio of two integers. There are certain criteria for…

Q: ALilrary Expand the following rational function using Pantial fractions x-1 (Y-1) (x+1) B. 1.…

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Q: Are the rational numbers closed under addition? Choose the correct answer below. Yes O No

A: Given question :-  Are the rational numbers closed under addition ?

Q: Are the rational numbers closed under addition? ... Choose the correct answer below. Yes O No

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Q: Is this statement true or false? Prove each true statement directly from the definitions and give a…

A: Given: Given statement is The quotient of any two rational number is rational number.

Q: Name the rational numbers from the list below.   −4​, 0​, 33​, 9.81​, 11​, 49​, 214​,−15​,…

A: Rational Numbers:A rational number is a number that can be written in the form  pq , where  p  and…

Q: The process of decomposing a rational expression into two or more simpler fractions is called…

A: Given:The process of decomposing a rational expression into two or more simpler fractions is called…

Q: Identify the rational number {5, v7, /16, 3, 3.1458....} O {V7, 3.1458...} O (5, V16, 2} O{V7, V16,…

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Q: What is the horizontal asymptote if the degree of the leading term of the numerator is greater than…

A: To find the horizontal asymptote if the degree of the leading term of the numerator is greater than…

Q: Given the infinite continued fraction [n, 1,1,2,2,3,3,4,4,5,5,6,6 ... ] for an integer n > 1, find…

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Q: 8. The following rational expressions are proper fractions except: x²+2x³-3x²+x-5 3x² - 4 C.…

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Q: Prove that the extreme value theorem doesn’t work over rational numbers.

A: Answer is mentioned below

Q: Determine whether the statement Every decimal with a repeating pattern of digits is a rational…

A: Consider the given statement, Every decimal with a repeating pattern of digits is a rational number…

Q: The number 473.1987987987 is rational. Write it as a ratio of two integers.

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Q: Find the proportion of primes p in the interval from 10^12 and 10^12 + 1000 such that p-1 is B= 105…

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Q: For any two rationals a//b and c//d where a, b, c, d not equal to 0 ∈ Z, the product is given by…

A: The given statement is " For any two rational a//b and c//d where a, b, c, d not equal to 0 ∈ Z, the…

Q: nth term of an AP  1+n+n2

A:

Q: Find a rational fraction equivalent to following infinitely repeating decimal: a.)3.123123 b)…

A: a.let x=3.123123............(i)multiply by 10001000x=3123.123123...........(ii)substract…

Q: D. We extend from Q20 to Q by another application of the method of ordered pairs, exactly as we did…

A: To explain: Rational numbers in terms of pair of coordinates using addition operation.

Q: the periodic decimal 0.110110110110110...(continuing on in this pattern forever) as a ratio of two…

A: Given, the periodic decimal                                0.110110110110110...

Q: Find the rational number represented by the repeated decimal using the 6. formula: 3.325

A: Assume that x=3.325

Q: 1. 5.3535353, when expressed as a rational number, is:

A: we know the sum of infinite geometric  series  whose first term is  a and  whose common ratio is  r…

Q: Why do these rational numbers have terminating decimal? 1/30, 1/32, 1/40, and 3/60.

A: The number is said to be terminating if its denominator is in form of 2x5y. Simplify each number and…

Q: In Exercises 17-28, find the least common denominator of the rational expressions. 17. 11 14 and…

A: 17). To find the least common denominator of the rational expression. Rational expression are 1125x2…

Q: Is 0.101001000100001000001… a repeating decimal? Is it rational or irrational? Explain (hint if the…

A: Explained below

Q: perform the indicated operations involving rational numbers. Express final answers in reduced form.…

A: Given: 47÷16-21

Q: Find a rational number that is bigger than 3.14159 but smaller than 3.14159001

A: To find a rational number between to given number.

Q: Prove: If the sum or the difference of two irreducible fractions is an integer, the denominators of…

A: Proof: Let two irreducible fractions are ab and cd Since the fractions are irreducible, (a,b)=1 and…

Q: Use the quotient remainder theorem and division into cases to show for all integers n, the integer…

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Q: Consider the set of rational numbers under the operation of addition. What is the inverse of 9?

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Q: Take the Set Q of the rationals and the family of intervals {(a, b)} such that a, b E Q with a <b.…

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Q: 4. Write the difference between the rational numbers and the irrational numbers, giving an example…

A: Write the difference between the rational numbers and the irrational numbers, giving an example for…

Q: Show that n22-1 is division by 8, if n is an odd positive integer

A: If n is a odd positive integer n can be written as   n = 2k+1 by substituting in n2-1 n2-1 =…

Q: 1) Express with a rational denominator in simplest form. C Eynrocc the following with rotional…

A: Given:1.582.c2a2b

Q: 1/1, 21, 12, 1/3, 22, З/1, 4/1, 32, 23, 14, 1/5, 2/4, 33, 42, 5/1 1 1 1 1 skip 1 1 1 t t 1 1, 2, 3,…

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Q: 1/1, 2/1, 1/2, 1/3, 2/2, 3/1, 4/1, 3/2, 2/3, 1/4, 1/5, 2/4, 3/3, 4/2, 5/1 I t skip i skip 1, 2, 3,…

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Q: Let S be the set of all rational numbers that can be expressed as a repeating decimal in the form…

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Q: Show that the following number is rational by writing it as a ratio of two integers 0.79797979.

A: We have to write number 0.79797979... In the ratio of two integers . Lets=0.79797979...we can writ…

Q: Show

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Q: find the rational number represented by the repeating decimal. 0.451141414

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