Prove: If the sum or the difference of two irreducible fractions is an integer, the denominators of the fractions are equal.

Q: Determine the least common denominator of all the fractions appearing in both the numerator and…

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Q: 5 4 Simplify your answer and write it as a proper fraction, improper fraction, or whole number. cos…

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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: In a car lot, the ratio of the number of new cars to the number of preowned cars is 6 to 5. The…

A: There is total 66 cars in the lot.

Q: 9. Rewrite the fraction with all the variables 4g in the numerator. (work required)

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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: Consider the set of all fractions equal to12. If you take any10 of those fractions, add their…

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Q: Find the tangent of LI. 17 15 8. Simplify your answer and write it as a proper fraction, improper…

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Q: If there are (2n+1) term in AP.then prove that the ratio of the sum of odd terms and the sum of even…

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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: Evaluate cosh(In 3). Enter your answer as a reduced fraction.

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Q: A fraction is said to be “irreducible” if the numerator and denominator are relatively prime, i.e.…

A: Introduction -  Reducible -Reducible fraction is a fraction that has some common factor and can be…

Q: If the rational number r is also an algebraic integer, prove that r must be an ordinary integer.

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Q: 4 Compute the quantity, W, using w= -3 W W -5 W = (Type integers or simplified fractions.)

A: Given query is to find indicated vector operation.

Q: Show that if the simple continued fraction expression of the rational number α, α > 1, is [a0;…

A: Remark : In the question, the reciprocal has a missing element. I am providing the solution with…

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: 1. Convert the mixed number to an improper fraction. 2 6= = (Type an integer or a simplified…

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Q: If the student attends class on a certain Friday, then he is five times as likely to be absent the…

A: 1) The transition matrix for this Markov process is given as:  P=T11T12T21T22…

Q: 1. What are the possible remainders of prime numbers greater than 2 when it is divided by 7? а. 1,…

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Q: 1. Compute the simple continued fractions for the following rational numbers: 1. r = 2. s = 3. t=

A: We have to find the simple continued fraction of given rational numbers as shown below

Q: 3. When 4 is wrilten as an improper fraction in sim- plest form, what is the numerator of the…

A: To convert a mixed fraction into an improper fraction, multiply the denominator with whole and add…

Q: Write out the form of the parial fraction decomporition of the funchion inction 3. du 2. n Cu+1) 2.

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Q: Solve the following equation for x.

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Q: What is the fraction representation of 0.196 ? Use the number pad to enter your answer in the bo:

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Q: nth term of an AP  1+n+n2

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Q: What is the limo+ (√In(x))? For answers that are fractions infinity ti infinitu write... in decimal…

A: We are asked to find the limit of the function.

Q: of all rabbits in a country are in one state and - of the rabbits are in a different state, what…

A: We have that 5/32 of all rabbits in a country are in one state and 2/7 of the rabbits are in a…

Q: 1 The rational numbers such as 5 and are examples of fractions. 10

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Q: Express the following fraction in simplest form using only posia exponents.

A: We have to simplify the given fraction.

Q: 3. Let F be the set of fractions in simplest form between 0 and 1 that can be written with a…

A: See the attachment

Q: Find the smallest positive interger x such that 1001 x leaves a remainder of 70 when divided by 315

A: The given statement can be expressed as an expression, which ix given below  315y+70=1001x Now,…

Q: 1 Consider the following fractions: 6. 7 8. 48 Rewrite all 3 fractions with the lowest common…

A: Given fractions  -1/6, -5/8, -7/48 To rewrite with the lowest common denominator.

Q: What is the limo+x².In(x) For answers that are fractions infinity negative infinity write... in…

A: L' Hospital Rule  :   If limx→a f(x)g(x) = 00 and ±∞±∞ form , then               limx→a f(x)g(x) =…

Q: How do I prove that if a,b are rational numbers, then so is (a+b)/2

A: If a,b are two rational numbers, then we have to prove thata+b2 is also a rational number.

Q: 4.4 The rectangle of Xs shown below is of another original rectangle of Xs. Show what the original…

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Q: Find the difference between the maximum and minimum of the quantity p2q2/50, where p and q are two…

A: Given:    p + q = 10    Let f = p2q2 / 50

Q: Of addition of integers, subtraction of whole numbers and division of rationals, which operation and…

A: Note: The natural numbers along with zero form the collection of whole numbers. Remark: Let * is a…

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

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Q: is (1,87, 3) and (1,87, –3), where z is defined implicity by the equ plic notation and fractions…

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Q: what number must be added to both numerator and denominator of the fraction 3/7 so that the…

A: Answer and explanation is given below

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

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Q: is ​{x | x is a fraction between 71 and 72​} finite or infinite

A: We will solve the problem. There are infinite real numbers between any two natural numbers. These…

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: Prove that C(n + 4, r + 1) = C(n + 3, r + 1) + C(n + 3, r). Hint: expand each Combination and use…

A: Explanation of the answer is as follows

Q: If the student attends class on a certain Friday, then he is three times as likely to be absent the…

A: We are provided with the information that if a student attends class (present in class), then the…

Q: Represent 9/17 as a sum of distinct unit fractions without repetitions using the splitting method…

A: Step:- 1 Given that 917 Using Splitting Method:- Let  a=917;and  a=917×22=1834 Now, splitting 18…

Q: 4. What is an example of a situation in which it is appropriate to use a rational number but not an…

A: Rational number : Numbers which are written in the form of p/q, where q is not equal to 0.

Q: 3- if a belongs to the set of all even natural numbers, and b belongs to the set of natural numbers…

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Q: 1.What is the smallest number that can be exactly divided by 2, 3, 4, 5  and 8 ? 2.What are the…

A: To answer the given questions.