Algebra Demystified 2nd Ed

6 alGebra De mystif ieD PRACTICE Perform the division. 1.^7 6 1. 4 ÷= 2.^8 15 6 5 ÷= 3.^5 3 9 10 ÷= 4.^40 9 2 3 ÷= 5.^3 7 30 4 ÷ ...

Chapter 1 FraCtions 7 Simplifying Fractions When working with fractions, we are usually asked to “reduce the fraction to lowest ...

8 alGebra De mystif ieD PRACTICE Simplify the fraction. 1. 14 42 = 2.^5 35 = 3.^48 30 = 4.^22 121 = 5.^39 123 = 6.^18 4 = 7.^7 2 ...

Chapter 1 FraCtions 9 6.^184 =^2322 ⋅⋅⋅^3 =⋅^22332 ⋅ = 29 7.^7 210 7 2357 71 7235 7 7 1 235 1 30 = ⋅⋅⋅ ⋅ = or ⋅⋅⋅ =⋅ ⋅⋅ = 8.^240 ...

10 alGebra De mystif ieD PRACTICE Identify the GCD for the numerator and denominator and write the fraction in lowest terms. 1.^ ...

Chapter 1 FraCtions 11 6.^48 56 86 87 8 8 6 7 6 7 = ⋅ ⋅ =⋅= 7.^28 18 214 29 2 2 14 9 14 9 = ⋅ ⋅ =⋅ = 8.^24 32 83 84 8 8 3 4 3 4 ...

12 alGebra De mystif ieD SOLUTIONS 1.^600 1280 10 60 10 128 60 128 415 432 15 32 = ⋅ ⋅ ==⋅ ⋅ = 2.^68 578 234 2289 34 289 172 17 ...

Chapter 1 FraCtions 13 3.^1 6 1 6 += 4.^5 12 1 12 −= 112 += 119 SOLUTIONS 1.^4 7 1 7 41 7 3 7 −=− = 2.^1 5 3 5 13 5 4 5 +=+ = ...

14 alGebra De mystif ieD To compute a b c d + or a b c d − , we can “reverse” the simplification process to rewrite the fraction ...

Chapter 1 FraCtions 15 PRACTICE Find the sum or difference. 1.^5 6 1 5 −= 2.^1 3 7 8 += 3.^5 7 1 9 −= 143 += 21 5.^3 4 11 18 + ...

16 alGebra De mystif ieD being large or by having variables in them, it usually easier to use the LCD to add or subtract fractio ...

Chapter 1 FraCtions 17 Because 84 is the first number on each list, 84 is the LCD for 121 and 149. This method works fine as lon ...

18 alGebra De mystif ieD EXAMPLE Find the sum or difference after computing the LCD. 17 24 5 36 + SOLUTION 24 = 2 ⋅ 2 ⋅ 2 ⋅ 3 an ...

Chapter 1 FraCtions 19 SOLUTIONS 1.^11 12 5 18 11 12 3 3 5 18 2 2 33 36 10 36 −= ⋅^2     −⋅    =−=^33 36 2.^7 15 9 2 ...

20 alGebra De mystif ieD We can now work with^1912 + 101. The LCD for these fractions is 60. 19 12 1 10 19 12 5 5 1 10 6 6 95 60 ...

Chapter 1 FraCtions 21 PRACTICE Find the sum. 1.^5 36 4 9 7 12 ++ = 2.^11 24 3 10 1 8 ++= 3.^1 4 5 6 9 20 ++ = 4.^3 35 9 14 7 10 ...

22 alGebra De mystif ieD whole number by the fraction’s denominator and add this product to the fraction’s numerator. The sum is ...

Chapter 1 FraCtions 23 To subtract a fraction from a whole number, we multiply the whole number by the fraction’s denominator an ...

24 alGebra De mystif ieD from the fraction’s numerator. This difference will be the new numerator. The rule is: a b W aWb b −=− ...

Chapter 1 FraCtions 25 fraction division. We use one of three rules, depending on whether there is a fraction in the numerator, ...