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3                    8Adding and Subtracting      Fractions
Adding Fractions with common        denominators         3 4       7          +    =         8 8       8
Adding Fractions with different             denominatorsProblem:You can’t add fractions with different denominatorswithout...
Finding the Lowest Common Denominator• The lowest common multiple of two numbers is  the lowest number in BOTH lists of mu...
Finding the Lowest Common Denominator• The lowest common multiple of two numbers is  the lowest number they will BOTH divi...
1 1                   +                        You can’t add fractions with                                              d...
1  2                      +                    2  5Lowest common denominator is 10 so make all fractions tenths 5 4 9  + =...
1  1                         +                       3  4 Turn both fractions into twelfths 4 3   7  + =12 12 12
3 3 2 7  ?   ?  9 14 23    2 × + × =   +   = +  =   =13 7 3 7  21 21 21 21 21 21                            Finally the fr...
Adding Mixed Numbers• Separate the fraction and the whole number sections,  add them separately and recombine at the end  ...
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Adding and subtracting fractions

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Adding and subtracting fractions

  1. 1. 3 8Adding and Subtracting Fractions
  2. 2. Adding Fractions with common denominators 3 4 7 + = 8 8 8
  3. 3. Adding Fractions with different denominatorsProblem:You can’t add fractions with different denominatorswithout getting them ready first. They will be ready toadd when they have common denominatorsSolution:Turn fractions into equivalent fractions with acommon denominator that is find the LowestCommon Multiple (LCM) of the two denominators
  4. 4. Finding the Lowest Common Denominator• The lowest common multiple of two numbers is the lowest number in BOTH lists of multiples1 1 Multiples of 2 are 2, 4, 6, 8, 10…… + Multiples of 3 are 3, 6, 9, 12, ………2 3 What is the lowest common multiple?
  5. 5. Finding the Lowest Common Denominator• The lowest common multiple of two numbers is the lowest number they will BOTH divide into1 1 2 divides into 2, 4, 6, 8….. + 3 divides into 3, 6, 9….2 3 What is the lowest number 2 and 3 both divide into?
  6. 6. 1 1 + You can’t add fractions with different denominators 2 3 +The Lowest Common Multiple of 2 and 3 is 6 so turn all fractions into sixths1 3 1 2 3 2 5 × + × = + =2 3 3 2 6 6 6 Special form of 1
  7. 7. 1 2 + 2 5Lowest common denominator is 10 so make all fractions tenths 5 4 9 + =10 10 10
  8. 8. 1 1 + 3 4 Turn both fractions into twelfths 4 3 7 + =12 12 12
  9. 9. 3 3 2 7 ? ? 9 14 23 2 × + × = + = + = =13 7 3 7 21 21 21 21 21 21 Finally the fractions are READY to It is 3/3 add. I just have to add the It is 7/7 So I multiply What is special form 9+14=23 numerators So I multiply What the lowest number What special form 3/7 by 3/3 2/3 by 7/7 ofBOTH change 7 3 into? will 3 and 7 divide 1 of 1 will change to 21. 21. Hmmmm? to Hmmmm? It is 21. So that is my Hmmmmm?????? common denominator Now 3x3=9 and 2x7=14 Now I know the new numerators
  10. 10. Adding Mixed Numbers• Separate the fraction and the whole number sections, add them separately and recombine at the end 1 2 +5 1 2 +5 1 1 3 = + + + 2 2 3 5 = 7+ 6 5 = 7 6

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