Adding Fractions with Unlike Denominators

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Adding Fractions with Unlike Denominators

  1. 1. Adding Fractions With Unlike Denominators Fourth Grade Math Mr. Mitchell
  2. 2. Adding Fractions with Unlike Denominators• When adding fractions with unlike denominators it is a little different than fractions with like denominators.• Unlike denominators means that the denominators of the fractions are different. 2 1 1 2 3 1 3 5 6 9 12 6 The fractions above have different denominators, called unlike denominators.
  3. 3. Adding Fractions with Unlike Denominators• The goal of adding fractions with unlike denominators is to get the denominators to be the same.• When the denominators are the same the fraction is easier to add.• As you have learned before, adding fractions with like denominators are easier, because you will just add the numerators.• Our focus for this lesson is: To make our denominators the same.
  4. 4. Adding Fractions with Unlike Denominators• The following are the steps to adding fractions with unlike denominators.• Example: 2 1 5 3 As you can see, our fractions have unlike denominators. To make them the same we need to find the Least Common Denominator or LCD.
  5. 5. Adding Fractions with Unlike Denominators• To find our LCD we need to first find the multiples of both of our denominators, and then identify the Least Common Multiple, or LCM.• The LCM will become our LCD.• A multiple is the answer to a multiplication problem.  Example: multiples of 4 are: 4,8,12,16,20 and so on.  Multiples of 7 are: 7,14,21,28,35 and so on
  6. 6. Adding Fractions with Unlike Denominators 2 1 5 3 •Step 1 •Find the multiples of the denominators, 5 and 3. •Start with the lowest valued number, because at times your larger number may be a multiple of your smaller number. •Multiples of 3: •3,6,9,12,15,18,21,24 •Multiples of 5: •5,10,15 •Stop finding multiples when you have found one they both have in common.
  7. 7. Adding Fractions with Unlike Denominators 2 1 5 3 •Step 2 •Identify the LCM •The multiples are: 3: 3,6,9,12,15,18,24 5: 5,10,15 The Least Common Multiple is 15
  8. 8. Adding Fractions with Unlike Denominators 2 1 5 3 •Step 3 •Create equivalent fractions to your current fractions, using your LCM as your new denominator 2 ? 1 ? 5 15 3 15
  9. 9. Adding Fractions with Unlike Denominators 2 1 5 3 •To find an equivalent fraction, you will need to find out what you multiplied each of the original denominators by to get the new denominator. •First look at your multiples: •3,6,9,12,15 •5,10,15 •You can count the number of multiples of 3 by counting how many multiples it takes to get to 15 •Do the same for your multiples of 15
  10. 10. Adding Fractions with Unlike Denominators 2 1 5 3 •Step 3 continued: •Remember, to find equivalent fractions, whatever you do to the denominator you must do the same to the numerator. • For the fraction 2/5, you multiplied the denominator by 3 so you need to multiply the numerator by 3 as well. •The equivalent fraction will become: 2 6 5 15
  11. 11. Adding Fractions with Unlike Denominators 2 1 5 3 •Step 3 continued: •Remember, to find equivalent fractions, whatever you do to the denominator you must do the same to the numerator. • For the fraction 1/3, you multiplied the denominator by 5 so you need to multiply the numerator by 5 as well. •The equivalent fraction will become: 1 5 3 15
  12. 12. Adding Fractions with Unlike Denominators 2 1 5 3 •The fractions in the addition problem then become: 6 5 15 15
  13. 13. Adding Fractions with Unlike Denominators 2 1 5 3 •Our goal was to convert our fractions into fractions with the same denominators. Following the steps you have ended up with the following fractions. 6 5 15 15
  14. 14. Adding Fractions with Unlike Denominators 2 1 5 3 Step 4 •Add the numerators of the fraction together. •6+5=11 •Eleven will be the numerator of your answer. 6 5 11 15 15 ?
  15. 15. Adding Fractions with Unlike Denominators 2 1 5 3 Step 5 •The denominators are not added together. The denominator tells us the equal number of pieces all together so this number does not change. •Remember the following: •If the denominators are the same, keep them the same. If they are not the same, make them the same. 6 5 11 15 15 15
  16. 16. Adding Fractions with Unlike Denominators 2 1 5 3 6 5 11 15 15 15 The final step is to reduce the fraction if needed. This fraction is already in the simplest form, so reducing is not needed.
  17. 17. Adding Fractions with Unlike Denominators• For further practice of adding fractions with unlike denominators you can visit the following websites:  http://www.mathplayground.com/fractions_add.ht ml  http://www.aaamath.com/fra66kx2.htm  http://www.math.com/school/subject1/practice/S 1U4L3/S1U4L3Pract.html  Template for presentation provided by Microsoft PowerPoint 07

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