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# Introduction to Algebra MATH 100

UNM

GPA 3.78

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This 6 page Class Notes was uploaded by Julianne Welch on Wednesday September 23, 2015. The Class Notes belongs to MATH 100 at University of New Mexico taught by Emily Miller in Fall. Since its upload, it has received 17 views. For similar materials see /class/212176/math-100-university-of-new-mexico in Mathematics (M) at University of New Mexico.

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Date Created: 09/23/15

Fractions Review This is a summary of how you convert fractions add fractions subtract fractions multiply fractions and divide fractions These are the acceptable methods and procedures for Math 100 To reduce fractions 12 24 1 We first factor the numerator and the denominator 223 2223 2 We then rewrite this as four fractions with as many like numerators and denominators as we can 3 3 NIH 2 2 MIN 3 Note the numerator had three factors and the denominator had four We added a factor of one to the numerator so we could have four fractions Why were we able to do this 4 We can now do some dividing 2 3 1 E 1 and E 1 so we can rewrite what we have In step 2 as 1 1 1 3 5 Now we simplify by doing the multiplications leaving us with 1 To multiply two fractions OOIUJ w1 1 First we rewrite it 37 83 2 Then we multiply the numerator and the denominator 21 3 Then we see if the fraction can be reduced This one cannot so we move on To multiply more than two fractions U39IIC 4 3 lt3on 1 We proceed as we did with two fractions 346 835 2 And then we multiply 72 m 3 Now we reduce first we factor the numerator and denominator 22233 22235 4 Then we rewrite 3 3 me 2 2 2 2 MIN 5 Then we divide 1 1 1 1 3 5 6 Last we simplify to give us 3 5 To divide fractions 4 3 1 We first rewrite the problem what lets us rewrite them this way 3 d 339 4 A 3 8 And then we want to get rid of the fraction in the bottom to do this we multiply the top and the bottom by the same number why do we do this what made us pick 83 45 83 38 83 Now we can rewrite this as two multiplications 8 45 3 38 83 And we can rewrite this again 4 8 5 3 38 53 This looks really complicated but we can reduce the fraction in the denominator 48 53 1 So we can rewrite again to give us 48 53 And we know what to do with this 32 15 How could you do this more quickly To add fractions J OIN me We see that we cannot add these fractions at the moment because they have different denominators What do the denominators stand for 8 U1 339 So we need to find a way to make the denominators the same To do this we need to get a common denominator To get a common denominator we first have to multiply each fraction by another fraction that equals one why is this mIm 92 9 9 me We do our multiplication by first rewriting 3925 59 95 We continue multiplying do we get the same denominator 27 E 10 E Now we can add the numerators and we leave the denominator alone why do we leave the denominator alone 27 10 45 And we add to get 37 45 Our last step is to ask ourselves if this can be reduced In this case it cannot be reduced To subtract fractions N 3 mo who We rewrite this as the addition of a negative sign and see how things go 5 lt 9 We see that we cannot add these fractions at the moment because they have different denominators What do the denominators stand for So we need to find a way to make the denominators the same To do this we need to get a common denominator Tee 5 7 339 8 To get a common denominator we first have to multiply each fraction by another fraction that equals one why is this We do our multiplication by first rewriting 3 9 lt 2 5 5 9 9 5 We continue multiplying do we get the same denominator 27 lt 10 45 45 Now we can add like we did before The only thing we need to do is put the negative somewhere Since we want the denominators to be the same we attach the negative sign to the numerator of the second fraction and we leave the denominator alone why do we leave the denominator alone 27 10 45 And we can rewrite this to get 27 10 45 We subtract to get 17 45 10 Our last step is to ask ourselves if this can be reduced In this case it cannot be reduced onvert between mixed numbers and improper fractions J 4 7 9 We first realize that we have four wholes and sevenninths of a whole Each whole has nine pieces so we can rewrite the four as 36 9 4 9 4 9 1 9 9 9 9 999 9 no Toc 2 Now we add this to the sevenninths that we had 36 7 9 9 3 Our last step is to add 36 7 43 9 9 onvert between improper fractions and mixed numbers 43 9 1 We first remember that the fraction bar is a shorthand way of writing division So we can rewrite the problem 43 9 2 We then do long division and get 43 9 4 with a remainder of 7 3 We take the answer of four and we know it is four wholes so that is the integer we put out in front We see that we have seven left over and our whole is nine 50 we can write the mixed number as 47 9 4 This is our answer

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