Explanation Method used: To add two fractions when the denominators are different: a). Find the least common multiple of the denominators. That number is the least common denominator, LCD. b). Multiply by 1, using an appropriate notation, n n , to express each number in terms of the LCD. c). Add the numerators, keeping the same denominator. d). Simplify, if possible. Calculation: To find the LCM of 15 and 20, list the multiples of 15 and 20. The multiples of 15 are 15, 30, 45, 60 , ..... . The multiples of 20 are 20, 40, 60, .... . The least number which is common to both the sets is 60. Thus, the least common denominator is 60. By the above mentioned method, simplify the expression as follows. 4 15 − 3 20 = 4 15 ⋅ 1 − 3 20 ⋅ 1 = 4

Basic College Mathematics (12th Edition)

12th Edition

ISBN: 9780321931900

Author: Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

Publisher: PEARSON

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Chapter 5, Problem 6CUR

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To simplify: The expression 415−320.

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Chapter 5, Problem 5CUR

Chapter 5, Problem 7CUR

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Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. f(x) = (x + 4x4) 5, a = -1 lim f(x) X--1 = lim x+4x X--1 lim X-1 4 x+4x 5 ))" 5 )) by the power law by the sum law lim (x) + lim X--1 4 4x X-1 -(0,00+( Find f(-1). f(-1)=243 lim (x) + -1 +4 35 4 ([ ) lim (x4) 5 x-1 Thus, by the definition of continuity, f is continuous at a = -1. by the multiple constant law by the direct substitution property

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Chapter 5 Solutions

Basic College Mathematics (12th Edition)

Ch. 5.1 - Prob. 1SR Ch. 5.1 - Prob. 2SR Ch. 5.1 - Prob. 1DE Ch. 5.1 - Find the ratio of 57.3 to 86.1.Ch. 5.1 - Prob. 3DE Ch. 5.1 - Record Snowfall. The greatest snowfall recorded in...Ch. 5.1 - Prob. 5DE Ch. 5.1 - Prob. 6DE Ch. 5.1 - Prob. 7DE Ch. 5.1 - Prob. 8DE

Ch. 5.1 - Prob. 9DE Ch. 5.1 - Prob. 10DE Ch. 5.1 - Prob. 11DE Ch. 5.1 - Prob. 1RC Ch. 5.1 - Prob. 2RC Ch. 5.1 - Prob. 3RC Ch. 5.1 - Prob. 4RC Ch. 5.1 - a. Find fraction notation for each ratio. You need...Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - a. Find fraction notation for each ratio. You need...Ch. 5.1 - Prob. 8E Ch. 5.1 - a. Find fraction notation for each ratio. You need...Ch. 5.1 - a. Find fraction notation for each ratio. You need...Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - b. Find the ratio of the first number to the...Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - For this right triangle, find the ratios of...Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Find the ratio of 334 to 578 and simplify.Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.2 - Prob. 1SR Ch. 5.2 - Divide using decimal notation. [4.4a] Divide. 2....Ch. 5.2 - Prob. 1DE Ch. 5.2 - Prob. 2DE Ch. 5.2 - Prob. 3DE Ch. 5.2 - Prob. 4DE Ch. 5.2 - Prob. 5DE Ch. 5.2 - Unit Price of Pasta Sauce. Gregory bought a 26-oz...Ch. 5.2 - Prob. 7DE Ch. 5.2 - Prob. 1RC Ch. 5.2 - Prob. 2RC Ch. 5.2 - Prob. 3RC Ch. 5.2 - Complete each sentence with the correct quantity...Ch. 5.2 - Prob. 1E Ch. 5.2 - Prob. 2E Ch. 5.2 - Prob. 3E Ch. 5.2 - Prob. 4E Ch. 5.2 - Prob. 5E Ch. 5.2 - Prob. 6E Ch. 5.2 - Prob. 7E Ch. 5.2 - Prob. 8E Ch. 5.2 - Prob. 9E Ch. 5.2 - Prob. 10E Ch. 5.2 - Prob. 11E Ch. 5.2 - Prob. 12E Ch. 5.2 - Broadway Musicals. In the 17 years from 1987...Ch. 5.2 - Prob. 14E Ch. 5.2 - Prob. 15E Ch. 5.2 - Prob. 16E Ch. 5.2 - Prob. 17E Ch. 5.2 - Prob. 18E Ch. 5.2 - Prob. 19E Ch. 5.2 - Prob. 20E Ch. 5.2 - Prob. 21E Ch. 5.2 - Prob. 22E Ch. 5.2 - Prob. 23E Ch. 5.2 - Prob. 24E Ch. 5.2 - Prob. 25E Ch. 5.2 - Prob. 26E Ch. 5.2 - Prob. 27E Ch. 5.2 - Prob. 28E Ch. 5.2 - Prob. 29E Ch. 5.2 - Prob. 30E Ch. 5.2 - Prob. 31E Ch. 5.2 - Prob. 32E Ch. 5.2 - Prob. 33E Ch. 5.2 - Prob. 34E Ch. 5.2 - Prob. 35E Ch. 5.2 - Prob. 36E Ch. 5.2 - Prob. 37E Ch. 5.2 - Prob. 38E Ch. 5.2 - Prob. 39E Ch. 5.2 - Prob. 40E Ch. 5.2 - Prob. 41E Ch. 5.2 - Divide. Simplify, if possible. 42. 95 10 [4.4a]Ch. 5.2 - Prob. 43E Ch. 5.2 - Prob. 44E Ch. 5.2 - Prob. 45E Ch. 5.2 - Prob. 46E Ch. 5.2 - Prob. 47E Ch. 5.3 - Prob. 1SR Ch. 5.3 - Prob. 2SR Ch. 5.3 - Prob. 1DE Ch. 5.3 - Prob. 2DE Ch. 5.3 - Prob. 3DE Ch. 5.3 - Prob. 4DE Ch. 5.3 - Prob. 5DE Ch. 5.3 - Prob. 6DE Ch. 5.3 - Prob. 7DE Ch. 5.3 - Prob. 8DE Ch. 5.3 - Prob. 9DE Ch. 5.3 - Prob. 10DE Ch. 5.3 - Prob. 11DE Ch. 5.3 - Prob. 12DE Ch. 5.3 - Prob. 1RC Ch. 5.3 - Prob. 2RC Ch. 5.3 - Prob. 3RC Ch. 5.3 - Prob. 4RC Ch. 5.3 - Prob. 1E Ch. 5.3 - Prob. 2E Ch. 5.3 - Prob. 3E Ch. 5.3 - Prob. 4E Ch. 5.3 - a Determine whether the two pairs of numbers are...Ch. 5.3 - Prob. 6E Ch. 5.3 - Prob. 7E Ch. 5.3 - Prob. 8E Ch. 5.3 - Prob. 9E Ch. 5.3 - Prob. 10E Ch. 5.3 - Prob. 11E Ch. 5.3 - Prob. 12E Ch. 5.3 - Prob. 13E Ch. 5.3 - Prob. 14E Ch. 5.3 - Prob. 15E Ch. 5.3 - Prob. 16E Ch. 5.3 - Prob. 17E Ch. 5.3 - Prob. 18E Ch. 5.3 - Prob. 19E Ch. 5.3 - Prob. 20E Ch. 5.3 - Prob. 21E Ch. 5.3 - b Solve. 22. 89=32n Ch. 5.3 - Prob. 23E Ch. 5.3 - Prob. 24E Ch. 5.3 - Prob. 25E Ch. 5.3 - Prob. 26E Ch. 5.3 - Prob. 27E Ch. 5.3 - Prob. 28E Ch. 5.3 - Prob. 29E Ch. 5.3 - Prob. 30E Ch. 5.3 - Prob. 31E Ch. 5.3 - Prob. 32E Ch. 5.3 - Prob. 33E Ch. 5.3 - Prob. 34E Ch. 5.3 - Prob. 35E Ch. 5.3 - Prob. 36E Ch. 5.3 - Prob. 37E Ch. 5.3 - Prob. 38E Ch. 5.3 - b Solve. 39. 82.4=6y Ch. 5.3 - Prob. 40E Ch. 5.3 - Prob. 41E Ch. 5.3 - Prob. 42E Ch. 5.3 - Prob. 43E Ch. 5.3 - Prob. 44E Ch. 5.3 - Prob. 45E Ch. 5.3 - Prob. 46E Ch. 5.3 - Prob. 47E Ch. 5.3 - Prob. 48E Ch. 5.3 - Prob. 49E Ch. 5.3 - Prob. 50E Ch. 5.3 - Prob. 51E Ch. 5.3 - Prob. 52E Ch. 5.3 - Prob. 53E Ch. 5.3 - Prob. 54E Ch. 5.3 - Prob. 55E Ch. 5.3 - Prob. 56E Ch. 5.3 - Prob. 57E Ch. 5.3 - Prob. 58E Ch. 5.3 - Prob. 59E Ch. 5.3 - Prob. 60E Ch. 5.3 - Prob. 61E Ch. 5.3 - Prob. 62E Ch. 5.3 - Prob. 63E Ch. 5.3 - Prob. 64E Ch. 5.3 - Prob. 65E Ch. 5.3 - Prob. 66E Ch. 5.3 - Prob. 67E Ch. 5.3 - Prob. 68E Ch. 5.3 - Prob. 69E Ch. 5.4 - Prob. 1SR Ch. 5.4 - Solve equations of the type a x = b, where a and...Ch. 5.4 - Prob. 1DE Ch. 5.4 - Prob. 2DE Ch. 5.4 - Prob. 3DE Ch. 5.4 - Prob. 4DE Ch. 5.4 - Prob. 5DE Ch. 5.4 - Prob. 6DE Ch. 5.4 - Prob. 1RC Ch. 5.4 - Prob. 2RC Ch. 5.4 - Prob. 3RC Ch. 5.4 - Prob. 4RC Ch. 5.4 - Prob. 1E Ch. 5.4 - Prob. 2E Ch. 5.4 - Prob. 3E Ch. 5.4 - Prob. 4E Ch. 5.4 - Prob. 5E Ch. 5.4 - Prob. 6E Ch. 5.4 - Prob. 7E Ch. 5.4 - Prob. 8E Ch. 5.4 - Prob. 9E Ch. 5.4 - Prob. 10E Ch. 5.4 - Prob. 11E Ch. 5.4 - Prob. 12E Ch. 5.4 - Painting. Fred uses 3 gal of paint to cover 1275...Ch. 5.4 - Prob. 14E Ch. 5.4 - Prob. 15E Ch. 5.4 - Prob. 16E Ch. 5.4 - Prob. 17E Ch. 5.4 - Prob. 18E Ch. 5.4 - Prob. 19E Ch. 5.4 - Prob. 20E Ch. 5.4 - Prob. 21E Ch. 5.4 - Prob. 22E Ch. 5.4 - Prob. 23E Ch. 5.4 - Prob. 24E Ch. 5.4 - Prob. 25E Ch. 5.4 - Prob. 26E Ch. 5.4 - Prob. 27E Ch. 5.4 - Prob. 28E Ch. 5.4 - Estimating a Whak Population. To determine the...Ch. 5.4 - Prob. 30E Ch. 5.4 - Prob. 31E Ch. 5.4 - Prob. 32E Ch. 5.4 - Prob. 33E Ch. 5.4 - Prob. 34E Ch. 5.4 - Prob. 35E Ch. 5.4 - Prob. 36E Ch. 5.4 - Prob. 37E Ch. 5.4 - Prob. 38E Ch. 5.4 - Prob. 39E Ch. 5.4 - Prob. 40E Ch. 5.4 - Prob. 41E Ch. 5.4 - 42. 0.078 = 0.3·t [4.4b] Ch. 5.4 - Prob. 43E Ch. 5.4 - Prob. 44E Ch. 5.4 - Carney College is expanding from 850 to 1050...Ch. 5.4 - Prob. 46E Ch. 5.4 - Prob. 47E Ch. 5.4 - Prob. 48E Ch. 5.4 - Prob. 49E Ch. 5.5 - Prob. 1SR Ch. 5.5 - Prob. 2SR Ch. 5.5 - Prob. 1DE Ch. 5.5 - Prob. 2DE Ch. 5.5 - Prob. 3DE Ch. 5.5 - Prob. 4DE Ch. 5.5 - Prob. 5DE Ch. 5.5 - Prob. 6DE Ch. 5.5 - Prob. 1RC Ch. 5.5 - Prob. 2RC Ch. 5.5 - Prob. 3RC Ch. 5.5 - Prob. 4RC Ch. 5.5 - Prob. 1E Ch. 5.5 - Prob. 2E Ch. 5.5 - Prob. 3E Ch. 5.5 - Prob. 4E Ch. 5.5 - Prob. 5E Ch. 5.5 - Prob. 6E Ch. 5.5 - Prob. 7E Ch. 5.5 - Prob. 8E Ch. 5.5 - Prob. 9E Ch. 5.5 - Prob. 10E Ch. 5.5 - How high is a tree that casts a 27-ft shadow at...Ch. 5.5 - Prob. 12E Ch. 5.5 - Prob. 13E Ch. 5.5 - Prob. 14E Ch. 5.5 - Prob. 15E Ch. 5.5 - Prob. 16E Ch. 5.5 - Prob. 17E Ch. 5.5 - Prob. 18E Ch. 5.5 - Prob. 19E Ch. 5.5 - Prob. 20E Ch. 5.5 - Prob. 21E Ch. 5.5 - Prob. 22E Ch. 5.5 - Prob. 23E Ch. 5.5 - bIn each of Exercises 17-26. the sides in each...Ch. 5.5 - Prob. 25E Ch. 5.5 - Prob. 26E Ch. 5.5 - Prob. 27E Ch. 5.5 - Prob. 28E Ch. 5.5 - Prob. 29E Ch. 5.5 - Prob. 30E Ch. 5.5 - Prob. 31E Ch. 5.5 - Prob. 32E Ch. 5.5 - Prob. 33E Ch. 5.5 - Prob. 34E Ch. 5.5 - Prob. 35E Ch. 5.5 - Prob. 36E Ch. 5.5 - Prob. 37E Ch. 5.5 - Prob. 38E Ch. 5.5 - Prob. 39E Ch. 5.5 - Prob. 40E Ch. 5.5 - Prob. 41E Ch. 5.5 - Prob. 42E Ch. 5.5 - Prob. 43E Ch. 5.5 - Prob. 44E Ch. 5.5 - Prob. 45E Ch. 5.5 - Prob. 46E Ch. 5.5 - Prob. 47E Ch. 5 - Determine whether each statement is true or false....Ch. 5 - Prob. 2MC Ch. 5 - Prob. 3MC Ch. 5 - Prob. 4MC Ch. 5 - Prob. 5MC Ch. 5 - Prob. 6MC Ch. 5 - Prob. 7MC Ch. 5 - Prob. 8MC Ch. 5 - Prob. 9MC Ch. 5 - Prob. 10MC Ch. 5 - Prob. 11MC Ch. 5 - Prob. 12MC Ch. 5 - Prob. 13MC Ch. 5 - Prob. 14MC Ch. 5 - Prob. 15MC Ch. 5 - Prob. 16MC Ch. 5 - Prob. 17MC Ch. 5 - Prob. 18MC Ch. 5 - Prob. 19MC Ch. 5 - Prob. 20MC Ch. 5 - Prob. 21MC Ch. 5 - Prob. 22MC Ch. 5 - Prob. 23MC Ch. 5 - Prob. 24MC Ch. 5 - Prob. 25MC Ch. 5 - Prob. 26MC Ch. 5 - Prob. 27MC Ch. 5 - Prob. 28MC Ch. 5 - Prob. 29MC Ch. 5 - Prob. 30MC Ch. 5 - Prob. 31MC Ch. 5 - Prob. 32MC Ch. 5 - Prob. 33MC Ch. 5 - Prob. 34MC Ch. 5 - Prob. 35MC Ch. 5 - Prob. 36MC Ch. 5 - Prob. 37MC Ch. 5 - Prob. 38MC Ch. 5 - Prob. 1VR Ch. 5 - Prob. 2VR Ch. 5 - Prob. 3VR Ch. 5 - Prob. 4VR Ch. 5 - Prob. 5VR Ch. 5 - Prob. 6VR Ch. 5 - Prob. 1CR Ch. 5 - Prob. 2CR Ch. 5 - Prob. 3CR Ch. 5 - Prob. 4CR Ch. 5 - Prob. 1PE Ch. 5 - Prob. 2PE Ch. 5 - Prob. 3PE Ch. 5 - Prob. 4PE Ch. 5 - Prob. 5PE Ch. 5 - Prob. 6PE Ch. 5 - Prob. 7PE Ch. 5 - Prob. 8PE Ch. 5 - Prob. 1RE Ch. 5 - Write fraction notation for each ratio. Do not...Ch. 5 - Prob. 3RE Ch. 5 - Prob. 4RE Ch. 5 - Prob. 5RE Ch. 5 - Find the ratio of the first number to the second...Ch. 5 - Prob. 7RE Ch. 5 - Prob. 8RE Ch. 5 - Prob. 9RE Ch. 5 - Prob. 10RE Ch. 5 - Prob. 11RE Ch. 5 - Prob. 12RE Ch. 5 - Prob. 13RE Ch. 5 - Prob. 14RE Ch. 5 - Prob. 15RE Ch. 5 - Prob. 16RE Ch. 5 - Solve. [5.3b] 17. 6x=4856 Ch. 5 - Prob. 18RE Ch. 5 - Solve. [5.3b] 19. 4.5120=0.9x Ch. 5 - Prob. 20RE Ch. 5 - Prob. 21RE Ch. 5 - Prob. 22RE Ch. 5 - Prob. 23RE Ch. 5 - Prob. 24RE Ch. 5 - Prob. 25RE Ch. 5 - Prob. 26RE Ch. 5 - Prob. 27RE Ch. 5 - Prob. 28RE Ch. 5 - How high is a billboard that casts a 25-ft shadow...Ch. 5 - Prob. 30RE Ch. 5 - Prob. 31RE Ch. 5 - Prob. 32RE Ch. 5 - Prob. 33RE Ch. 5 - Prob. 34RE Ch. 5 - Prob. 35RE Ch. 5 - Write fraction notation for each ratio. Do not...Ch. 5 - Write fraction notation for each ratio. Do not...Ch. 5 - Prob. 3T Ch. 5 - Prob. 4T Ch. 5 - Prob. 5T Ch. 5 - Prob. 6T Ch. 5 - Prob. 7T Ch. 5 - Prob. 8T Ch. 5 - Prob. 9T Ch. 5 - Prob. 10T Ch. 5 - Determine whether the two pairs of numbers are...Ch. 5 - Prob. 12T Ch. 5 - Prob. 13T Ch. 5 - Prob. 14T Ch. 5 - Prob. 15T Ch. 5 - Prob. 16T Ch. 5 - Prob. 17T Ch. 5 - Prob. 18T Ch. 5 - Prob. 19T Ch. 5 - Charity Work. Kayla is crocheting hats for a...Ch. 5 - Prob. 21T Ch. 5 - Prob. 22T Ch. 5 - Prob. 23T Ch. 5 - Prob. 24T Ch. 5 - Prob. 25T Ch. 5 - Prob. 1CUR Ch. 5 - Prob. 2CUR Ch. 5 - Prob. 3CUR Ch. 5 - Prob. 4CUR Ch. 5 - Prob. 5CUR Ch. 5 - Prob. 6CUR Ch. 5 - Prob. 7CUR Ch. 5 - Prob. 8CUR Ch. 5 - Prob. 9CUR Ch. 5 - Prob. 10CUR Ch. 5 - Prob. 11CUR Ch. 5 - Prob. 12CUR Ch. 5 - Prob. 13CUR Ch. 5 - Prob. 14CUR Ch. 5 - Prob. 15CUR Ch. 5 - Prob. 16CUR Ch. 5 - Prob. 17CUR Ch. 5 - Prob. 18CUR Ch. 5 - Prob. 19CUR Ch. 5 - Prob. 20CUR Ch. 5 - Prob. 21CUR Ch. 5 - Prob. 22CUR Ch. 5 - Prob. 23CUR Ch. 5 - Prob. 24CUR Ch. 5 - Prob. 25CUR Ch. 5 - Prob. 26CUR Ch. 5 - Prob. 27CUR Ch. 5 - Prob. 28CUR Ch. 5 - Prob. 29CUR Ch. 5 - Prob. 30CUR Ch. 5 - Prob. 31CUR Ch. 5 - Prob. 32CUR Ch. 5 - Prob. 33CUR Ch. 5 - Prob. 34CUR Ch. 5 - Prob. 35CUR Ch. 5 - Prob. 36CUR Ch. 5 - Prob. 37CUR Ch. 5 - Prob. 38CUR Ch. 5 - Prob. 39CUR Ch. 5 - Prob. 40CUR Ch. 5 - Prob. 41CUR

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The expression 4 15 − 3 20 .

Solution Summary: The author explains how to simplify the expression by adding two tions when the denominators are different.

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To simplify: The expression 415−320.

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Chapter 5 Solutions