Explanation Given information: The provided fraction is, 5 12 − 2 9 . Formula used: Use the following steps for subtracting the unlike fractions. Step1: Find the Least Common Denominator (LCD) of unlike fraction. Step2: Now raise all fractions to the terms of the LCD and make them the like fractions. Step3: Then subtract all the numerators and place them over the original denominator. Step4: If the result is a proper fraction then reduce it to lowest term or if improper then convert it to a whole or mixed number. Now use the following steps for determining the least common denominator of two or more fractions with the use of prime numbers, Step1: Write all the denominators in a row. Step2: Now find a prime number that divides evenly into any of the denominators and then write that prime number to the left of the row and divide while placing all quotients and undivided numbers in the next row down. Step3: Repeat the above process until new row contains all ones. Step4: Multiply all the prime numbers on the left to get the LCD of the fractions. Calculation: Consider the following fraction, 5 12 − 2 9 As these are unlike fractions and they must be converted to obtain the same denominator so find the LCD

Contemporary Mathematics for Business & Consumers

8th Edition

ISBN: 9781305886803

Author: Brechner

Publisher: Cengage

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Chapter 2.II, Problem 12TIE

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To calculate: The subtraction of the fractions, 512−29 and also reduce it to lowest terms.

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Chapter 2.II, Problem 11TIE

Chapter 2.II, Problem 13TIE

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Problem 11 (a) A tank is discharging water through an orifice at a depth of T meter below the surface of the water whose area is A m². The following are the values of a for the corresponding values of A: A 1.257 1.390 x 1.50 1.65 1.520 1.650 1.809 1.962 2.123 2.295 2.462|2.650 1.80 1.95 2.10 2.25 2.40 2.55 2.70 2.85 Using the formula -3.0 (0.018)T = dx. calculate T, the time in seconds for the level of the water to drop from 3.0 m to 1.5 m above the orifice. (b) The velocity of a train which starts from rest is given by the fol- lowing table, the time being reckoned in minutes from the start and the speed in km/hour: | † (minutes) |2|4 6 8 10 12 14 16 18 20 v (km/hr) 16 28.8 40 46.4 51.2 32.0 17.6 8 3.2 0 Estimate approximately the total distance ran in 20 minutes.

- Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2 multiple of n, i.e. n mod p, 2n mod p, ..., p-1 2 -n mod p. Let T be the subset of S consisting of those residues which exceed p/2. Find the set T, and hence compute the Legendre symbol (7|23). 23 32 how come? The first 11 multiples of 7 reduced mod 23 are 7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8. The set T is the subset of these residues exceeding So T = {12, 14, 17, 19, 21}. By Gauss' lemma (Apostol Theorem 9.6), (7|23) = (−1)|T| = (−1)5 = −1.

Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2 multiple of n, i.e. n mod p, 2n mod p, ..., 2 p-1 -n mod p. Let T be the subset of S consisting of those residues which exceed p/2. Find the set T, and hence compute the Legendre symbol (7|23). The first 11 multiples of 7 reduced mod 23 are 7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8. 23 The set T is the subset of these residues exceeding 2° So T = {12, 14, 17, 19, 21}. By Gauss' lemma (Apostol Theorem 9.6), (7|23) = (−1)|T| = (−1)5 = −1. how come?

Chapter 2 Solutions

Contemporary Mathematics for Business & Consumers

Ch. 2.I - For each of the following, identify the type of...Ch. 2.I - Prob. 2TIE Ch. 2.I - Convert the following mixed numbers to improper...Ch. 2.I - Prob. 4TIE Ch. 2.I - Prob. 5TIE Ch. 2.I - Prob. 6TIE Ch. 2.I - Prob. 1RE Ch. 2.I - Prob. 2RE Ch. 2.I - Prob. 3RE Ch. 2.I - Prob. 4RE

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The subtraction of the fractions, 5 12 − 2 9 and also reduce it to lowest terms.

Solution Summary: The author explains how to calculate the Least Common Denominator (LCD) of unlike tions.

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To calculate: The subtraction of the fractions, 512−29 and also reduce it to lowest terms.

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Chapter 2 Solutions